CN102460253B - Evanescent electromagnetic wave conversion apparatus and methods - Google Patents

Abstract

Apparatus, methods, and systems provide conversion of evanescent electromagnetic waves to non-evanescent electromagnetic waves and/or conversion of non-evanescent electromagnetic waves to evanescent electromagnetic waves. In some approaches the conversion includes propagation of electromagnetic waves within an indefinite electromagnetic medium, and the indefinite medium may include an artificially-structured material such as a layered structure or other metamaterial.

Description

Electromagnetic wave conversion apparatus and method suddenly die

The cross reference of related application

The application relate to and require in the following application (" related application ") of listing the earliest can with the rights and interests of effective submission date (for example, the application of the related applications such as any or whole parents, Zu Muti, great-grandfather's parent, for the application except temporary patent application, require can use the earliest the rights and interests on right of priority date, for temporary patent application, require the rights and interests according to United States code the 35th chapter the 119th (e) article).All themes of the applications such as any and whole parents of related application and related application, Zu Muti, great-grandfather's parent by reference to mode be incorporated to content herein, such theme is consistent with the theme of this paper.

Related application:

According to the extra legal requirements of USPTO, the application is formed in submission on April 17th, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION APPARATUS I " the 12/386th, the part subsequent application of No. 522 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on April 17th, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION APPARATUS II " the 12/386th, the part subsequent application of No. 523 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on April 17th, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION APPARATUS III " the 12/386th, the part subsequent application of No. 521 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on July 13rd, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION METHODS I " the 12/460th, the part subsequent application of No. 137 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on October 30th, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION LENSES I " the 12/589th, the part subsequent application of No. 913 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on July 13rd, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION METHODS II " the 12/460th, the part subsequent application of No. 136 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on October 30th, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION LENSES II " the 12/590th, the part subsequent application of No. 010 U.S. Patent application, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on July 13rd, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION METHODS III " the 12/460th, the part subsequent application of No. 122 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

According to the extra legal requirements of USPTO, the application is formed in submission on October 30th, 2009, Jeffrey A.Bowers, Roderick A.Hyde, Edward K.Y.Jung, John Brian Pendry, David Schurig, David R.Smith, Clarence T.Tegreene, Thomas Allan Weaver, Charles Whitmer, Lowell L.Wood, Jr. as inventor, title be " EVANESCENT ELECTROMAGNETIC WAVE CONVERSION LENSES III " the 12/589th, the part subsequent application of No. 925 U.S. Patent applications, it is current is co-pending, or be endowed the current co-pending application of the rights and interests of submission date.

United States Patent Office (USPO) (USPTO) has issued a bulletin, its to the effect that the computer program of USPTO require patent applicant reference sequences number and point out that this application is subsequent application or part subsequent application.The USPTO Official Journal http://www.uspto.gov/web/offices/com/sol/og/2003/weekl 1/patbene.htm in rights and interests on March 18th, 1 of the application of the first submit of Stephen G.Kunin.The application's entity (hereinafter referred to as " applicant ") provides the concrete reference of the application that is required right of priority above according to legal requiremnt.Applicant understands for the right of priority that requires U.S. Patent application, and law is clear and definite to the regulation of concrete reference language, and without sequence number or any characteristic description such as " follow-up " or " part is follow-up ".Although there is afore mentioned rules, the computer program that applicant understands USPTO has some data input requirements, and therefore the application is appointed as the part subsequent application of its parent application as mentioned above by applicant, be interpreted as never in any form about whether the application comprises the newly statement of any type of theme arbitrarily except the theme of its parent application and/or admits but explicitly point out such appointment.

Technical field

The application disclose relate to comprise electromagnetic near field lens and/or the electromagnetic wave that suddenly dies to non-electromagnetic conversion and/or the non-apparatus and method of electromagnetic wave to the electromagnetic response of the electromagnetic conversion of suddenly dying that suddenly die of suddenly dying.

Brief description of the drawings

Fig. 1 shows the transformational structure with the plane of being essentially and parallel in fact the first and second surf zones.

Fig. 2 shows the hierarchy as the exemplary realization of the transformational structure of Fig. 1.

Fig. 3 shows the hierarchy as the exemplary realization of the transformational structure of Fig. 1.

Fig. 4 shows the first surface region with the plane of being essentially and the transformational structure that is essentially nonplanar second surface region.

Fig. 5 shows the hierarchy as the exemplary realization of the transformational structure of Fig. 4.

Fig. 6 shows the hierarchy as the exemplary realization of the transformational structure of Fig. 4.

Fig. 7 shows the transformational structure with the second surface region that is essentially nonplanar first surface region and is essentially plane.

Fig. 8 shows the hierarchy as the exemplary realization of the transformational structure of Fig. 7.

Fig. 9 shows the hierarchy as the exemplary realization of the transformational structure of Fig. 7.

Figure 10 shows has the various transformational structures that are essentially nonplanar the first and second surf zones.

Figure 11 shows the hierarchy as the exemplary realization of the transformational structure of Figure 10.

Figure 12 shows the first technological process.

Figure 13 shows second technological process reciprocal with the first technological process.

Figure 14 shows the system that comprises the converting unit that suddenly dies.

Describe in detail

In following detailed description, with reference to forming its a part of accompanying drawing.In the accompanying drawings, unless otherwise provided, the identical identical parts of label ordinary representation.The illustrative embodiment of describing is in the detailed description, drawings and claims not intended to restriction.Not departing under the spirit or scope of the theme presenting herein, can adopt other embodiment, and can carry out other amendment.

Embodiment provides for the electromagnetic wave that will suddenly die and has been transformed into the non-electromagnetic wave and/or for the non-electromagnetic wave that suddenly dies is transformed into the electromagnetic apparatus and method that suddenly die of suddenly dying.Conventionally, the electromagnetic wave that suddenly dies is amplitude is exponential damping electromagnetic wave with distance, and for example, its wave vector is imaginary number at least partly.For example, electromagnetic electric field component can have the 2D Fourier expansion that (1) formula provides:

$E(r,t)=\underset{\mathrm{\σ},k_x,k_y}{\mathrm{\Σ}}{E}_{\mathrm{\σ}}(k_x,k_y)\exp ({\mathrm{ik}}_{z}z+{\mathrm{ik}}_{x}x+{\mathrm{ik}}_{y}y-\mathrm{i\ωt}).---\left(1\right)$

For illustrative purposes, suppose that ripple is present in the medium that refractive index is n, has fourier's pattern propagate and there is real wave component vector electromagnetic wave, and have fourier's pattern be to there is empty wave component vector the electromagnetic wave that suddenly dies.The electromagnetic wave that suddenly dies is exponential damping with distance z.For example, in traditional far-field optics application, wherein z can representation case as the distance of the objective plane of the far field optical systems to traditional, evanescent wave substantially can be in the near field corresponding to objective plane the scope that suddenly the dies μ～1/|k in (or the near field of wanting the target proximity of imaging) _z| outside continue, and propagation wave lasts till that outside near field far field for example, to comprise far field image (, on the plane of delineation of traditional far field optical systems).Therefore, traditional far field optical systems has the maximum transversal wave vector k corresponding to propagation wave _maxresolution limit Δ (being sometimes called as diffraction limit or Abbe Rayleigh limit):

$\mathrm{\Δ}~\frac{2\mathrm{\π}}{k_{\max }}=\frac{2\mathrm{\πc}}{\mathrm{n\ω}}=\frac{c}{\mathrm{nv}}=\frac{{\mathrm{\λ}}_0}{n}---\left(2\right)$

Wherein, λ ₀the free space wavelength corresponding with frequency v.On the other hand, embodiment disclosed herein, by indefinite electromagnetic medium (indefinite electromagnetic medium), evanescent wave being converted to propagation wave (vice versa), provides the apparatus and method that exceed this resolution limit.

Conventionally, indefinite electromagnetic medium is a kind of electromagnetic medium for example, with the electromagnetic parameter (specific inductive capacity and/or magnetic permeability) that comprises indefinite tensor parameter.In the whole disclosure that comprises follow-up claim, term " indefinite " has its algebra meaning; Therefore, indefinite tensor (indefinite tensor) is the tensor of the nonnegative definite again (having all negative eigenwerts) that (has all positive eigenwerts) neither positive definite, but has the tensor of at least one positive eigenwert and at least one negative eigenwert.Some exemplary indefinite media are shown in D.R.Smith and D.Schurig, " Indefinite materials ", Application No. 10/525,191; D.R.Smith and D.Schurig, " Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors; " Phys.Rev.Lett.90,077405 (2003); And D.R.Smith and D.Schurig, " Sub-diffraction imaging with compensating bilayers, " New.J.Phys.7,162 (2005); Each list of references is wherein incorporated herein by reference.

In some embodiments, indefinite medium is the electromagnetic medium with indefinite magnetic permeability.An example of indefinite magnetic permeability medium is the surface plate of z axle vertical with plate (x is parallel with plate with y axle), and electromagnetic parameter ε _y, μ _xand μ _zmeet inequality:

ε _yμ _x＞0，μ _x/μ _z＜0 (3)

(therefore, as long as μ _x< 0 < μ _zor μ _x> 0 > μ _z, magnetic permeability is indefinite).For electric field, along the axial TE polarization of y (being s polarization) electromagnetic wave, these electromagnetic parameters provide hyperbolic dispersion relation

$k_z^2={\mathrm{\&epsiv;}}_y{\mathrm{\&mu;}}_x\frac{{\mathrm{\&omega;}}^2}{c^2}-\frac{{\mathrm{\&mu;}}_x}{{\mathrm{\&mu;}}_z}{k}_x^2---\left(4\right)$

It allows to propagate has larger lateral wave vector k _xelectromagnetic wave (real k _z).Therefore,, if the even refracting medium that surface plate and refractive index are n is adjacent, the evanescent wave in adjacent media is (for example,, as equation (1), k _x> n ω/c) becomes propagation wave (or, reciprocity ground, the propagation wave in indefinite medium becomes evanescent wave in adjacent media) in indefinite medium.For enough large k _x(, in fact in the progressive region of hyperbolic dispersion relation (4)), propagation wave is characterized by the group rate vertical in fact with the asymptotic line of equation (4), and propagation wave is in fact along becoming θ with z axle in xz plane _x=tan ^-1(| μ _x/ μ _z|) angle the direction of propagation propagate (for example,, as the previously quoted the 10/525th, described in Figure 10 of No. 191 U.S. Patent applications); And, for enough little μ _x(, | μ _x| equal zero in fact and/or much smaller than | μ _z|), angle θ _xbecome in fact and equal zero, and multiple directions of propagation degeneracy is consistent with the z axle in fact single direction of propagation (in this case, indefinite medium should be called as the indefinite medium of degeneracy).Alternatively or additionally, surface plate has electromagnetic parameter ε _xand μ _y, meet optional or additional inequality

ε _xμ _y＞0，μ _y/μ _z＜0， (5)

For the TE polarized electromagnetic wave having along the axial electric field of x, provide another hyperbolic dispersion relation

$k_z^2={\mathrm{\&epsiv;}}_x{\mathrm{\&mu;}}_y\frac{{\mathrm{\&omega;}}^2}{c^2}-\frac{{\mathrm{\&mu;}}_y}{{\mathrm{\&mu;}}_z}{k}_y^2---\left(6\right)$

In this situation, for enough large k _y(, in fact in the progressive region of hyperbolic dispersion relation (4)), propagation wave is characterized by the group rate vertical in fact with the asymptotic line of equation (6), and propagation wave becomes θ along yz plane with z axle in fact _y=tan ^-1(| μ _y/ μ _z|) angle the direction of propagation propagate; And, for enough little μ _y(, | μ _y| equal zero in fact and/or much smaller than | μ _z|), angle θ _ybecome in fact and equal zero, and multiple directions of propagation degeneracy is consistent with the z axle in fact single direction of propagation (the indefinite medium of another degeneracy).When surface plate meet inequality (3) and (5) both time, the TE polarized wave that indefinite medium support is propagated along the direction of propagation that forms elliptic cone is in fact (for enough large lateral wave vector k _xand/or k _y), the circular cone axis of elliptic cone is consistent with z direction and have an as above half-angle θ about x and y axle _xand θ _y, at ε _x=ε _yand μ _x=μ _y, situation under, surface plate is the uniaxial medium that identical hyperbolic dispersion is provided for any TE polarized wave, and for larger lateral wave vector, the direction of propagation forms θ _x=θ _ycircular cone.

More generally, in some embodiments, indefinite magnetic permeability medium can define the axis direction corresponding to the first eigenvector of indefinite magnetic permeability matrix, and the first and second horizontal directions correspond respectively to second and the 3rd proper vector of indefinite magnetic permeability matrix.The parameter of indefinite magnetic permeability matrix can change along with the position in indefinite magnetic permeability medium, and correspondingly, the proper vector of indefinite magnetic permeability matrix also can change along with the position in indefinite magnetic permeability medium.The disclosure of above paragraph can comprise the more generally embodiment of indefinite magnetic permeability medium in the following manner: z axle should be understood to more generally to refer to the axis direction that can change in whole indefinite medium, x axle should be understood to more generally refer to first horizontal direction vertical with axis direction, and y axle should be understood to more generally refer to and axis direction and orthogonal the second horizontal direction of the first horizontal direction.Therefore, for example, the indefinite magnetic permeability medium of single shaft can have local axis parameter μ _a(corresponding to the axis direction that can change with the position in medium) and laterally parameter ε _t1=ε _t2=ε _t, μ _t1=μ _t2=μ _t, it meets inequality

ε _Tμ _T＞0，μ _T/μ _A＜0， (7)

Hyperbolic dispersion relation is provided

$k_A^2={\mathrm{\&epsiv;}}_T{\mathrm{\&mu;}}_T\frac{{\mathrm{\&omega;}}^2}{c^2}-\frac{{\mathrm{\&mu;}}_T}{{\mathrm{\&mu;}}_A}{k}_T^2,---\left(8\right)$

And the TE polarized wave that this dispersion relation support is propagated along the local direction of propagation that forms circular cone is in fact (for enough large lateral wave vector k _t), this circular cone has the circular cone axis consistent with local axis direction and half-angle of projection θ=tan ^-1(| μ _t/ μ _a|) (and, when | μ _t| < < | μ _a| time, medium is the indefinite medium of degeneracy, wherein the circular cone degeneracy of the direction of propagation is the single direction of propagation consistent in fact with local axis direction).

In some embodiments, indefinite medium is the electromagnetic medium with indefinite specific inductive capacity.An example of the medium of indefinite specific inductive capacity is the surface plate of z axle vertical with plate (x is parallel with plate with y axle), and electromagnetic parameter μ _y, ε _xand ε _zmeet inequality

μ _yε _x＞0，ε _x/ε _z＜0 (9)

(therefore, as long as ε _x< 0 < ε _zor ε _x> 0 > ε _z, specific inductive capacity is indefinite).For magnetic field, along for the axial TM of y polarization (being p polarization) electromagnetic wave, these electromagnetic parameters provide hyperbolic dispersion relation

$k_z^2={\mathrm{\&mu;}}_y{\mathrm{\&epsiv;}}_x\frac{{\mathrm{\&omega;}}^2}{c^2}-\frac{{\mathrm{\&epsiv;}}_x}{{\mathrm{\&epsiv;}}_z}{k}_x^2---\left(10\right)$

It allows to propagate electromagnetic wave (the real k with larger lateral wave vector _z).Therefore,, if the even refracting medium that surface plate and refractive index are n is adjacent, the evanescent wave in adjacent media is (for example,, as equation (1), k _x> n ω/c) becomes propagation wave (or, reciprocity ground, the propagation wave in indefinite medium becomes evanescent wave in adjacent media) in indefinite medium.For enough large k _x(, in fact in the progressive region of hyperbolic dispersion relation (10)), propagation wave is characterized by the group rate vertical in fact with the asymptotic line of equation (10), and propagation wave is in fact along becoming θ with z axle in xz plane _x=tan ^-1(| ε _x/ ε _z|) angle the direction of propagation propagate; And, for enough little ε _x(, | ε _x| equal zero in fact and/or much smaller than | ε _z|), angle θ _xbecome in fact and equal zero, and multiple directions of propagation degeneracy is consistent with the z axle in fact single direction of propagation (in this case, indefinite medium should be called as the indefinite medium of degeneracy).Alternatively or additionally, surface plate has electromagnetic parameter μ _xand ε _y, it meets optional or additional inequality

μ _xε _y＞0，ε _y/ε _z＜0， (11)

For having along the electromagnetic wave of the TM polarization in the axial magnetic field of x, provide another hyperbolic dispersion relation

$k_z^2={\mathrm{\&mu;}}_x{\mathrm{\&epsiv;}}_y\frac{{\mathrm{\&omega;}}^2}{c^2}-\frac{{\mathrm{\&epsiv;}}_y}{{\mathrm{\&epsiv;}}_z}{k}_y^2---\left(12\right)$

In this situation, for enough large k _y(, in fact in the progressive region of hyperbolic dispersion relation (12)), propagation wave in indefinite medium is characterized by the group rate vertical in fact with the asymptotic line of equation (12), and propagation wave is in fact along becoming θ with z axle in yz plane _y=tan ^-1(| ε _y/ ε _z|) angle the direction of propagation propagate; And, for enough little ε _y(, | ε _y| equal zero in fact and/or much smaller than | ε _z|), angle θ _ybecome in fact and equal zero, and multiple directions of propagation degeneracy is consistent with the z axle in fact single direction of propagation (the indefinite medium of another degeneracy).When surface plate meet inequality (9) and (11) both time, the TM polarized wave that indefinite medium support is propagated along the direction of propagation that forms elliptic cone is in fact (for enough large lateral wave vector k _xand/or k _y), the circular cone axis of elliptic cone is consistent with z direction and have an as above half-angle θ about x axle and y axle _xand θ _y, at ε _x=ε _yand μ _x=μ _y, situation under, surface plate is the uniaxial medium all for any TM polarized wave with identical hyperbolic dispersion, and for larger lateral wave vector, the direction of propagation forms θ _x=θ _ycircular cone.

More generally, in some embodiments, indefinite dielectric constant dielectric can define the axis direction corresponding to the first eigenvector of indefinite specific inductive capacity matrix, and the first and second horizontal directions correspond respectively to second and the 3rd proper vector of indefinite specific inductive capacity matrix.The parameter of indefinite specific inductive capacity matrix can change along with the position in indefinite dielectric constant dielectric, and correspondingly, the proper vector of indefinite specific inductive capacity matrix also can change along with the position in indefinite dielectric constant dielectric.The disclosure of above paragraph can comprise the more generally embodiment of indefinite dielectric constant dielectric in the following manner: z axle should be understood to more generally to refer to the axis direction that can change in whole indefinite medium, x axle should be understood to more generally refer to first horizontal direction vertical with axis direction, and y axle should be understood to more generally refer to and axis direction and orthogonal the second horizontal direction of the first horizontal direction.Therefore, for example, the indefinite dielectric constant dielectric of single shaft can have local axis parameter ε _a(corresponding to the axis direction that can change with the position in medium) and laterally parameter ε _t1=ε _t2=ε _t, μ _t1=μ _t2=μ _tmeet inequality

ε _Tμ _T＞0，ε _T/ε _A＜0， (13)

Hyperbolic dispersion relation is provided

$k_A^2={\mathrm{\&epsiv;}}_T{\mathrm{\&mu;}}_T\frac{{\mathrm{\&omega;}}^2}{c^2}-\frac{{\mathrm{\&epsiv;}}_T}{{\mathrm{\&epsiv;}}_A}{k}_T^2,---\left(14\right)$

And the TM polarized wave that this dispersion relation support is propagated along the local direction of propagation that forms circular cone is in fact (for enough large lateral wave vector k _t), this circular cone has the circular cone axis consistent with local axis direction and half-angle of projection θ=tan ^-1(| ε _t/ ε _a|) (and, when | ε _t| < < | ε _a| time, medium is the indefinite medium of degeneracy, wherein the circular cone degeneracy of the direction of propagation is the single direction of propagation consistent in fact with local axis direction).

In some embodiments, indefinite medium is the electromagnetic medium of a kind of " two indefinite ", has indefinite specific inductive capacity and indefinite magnetic permeability.An example of two indefinite media is the surface plates that limit z axle vertical with plate (x is parallel with plate with y axle), and described surface plate has and meets one of equation (3) and (5) (indefinite magnetic permeability is provided) or both and meet equation (9) and one of (11) (indefinite specific inductive capacity is provided) or both electromagnetic parameters.Two indefinite surface plates provide hyperbolic dispersion relation (as equation (4) and/or (5)) and also at least one TM polarized wave provides hyperbolic dispersion relation (as equation (10) and (12)), the equation that the ripple propagation characteristic of discussing in above paragraph comprises reference herein at least one TE polarized wave.

In some embodiments, two indefinite media can have in fact indefinite specific inductive capacity matrix and indefinite magnetic permeability matrix that can simultaneous diagonalization, and two indefinite media define the axis direction corresponding to the first common trait vector of indefinite matrix, the first and second horizontal directions correspond respectively to second and the 3rd common trait vector of indefinite matrix.With the same in above example, the parameter of indefinite matrix can change along with the position in two indefinite media, and correspondingly, the common trait vector of indefinite matrix also can change along with the position in two indefinite media.The disclosure of above paragraph can comprise the more generally embodiment of two indefinite media in the following manner: z axle should be understood to more generally to refer to the axis direction that can change in whole two indefinite media, x axle should be understood to more generally refer to first horizontal direction vertical with axis direction, and y axle should be understood to more generally refer to and axis direction and orthogonal the second horizontal direction of the first horizontal direction.Therefore, for example, the two indefinite media of single shaft can have localized axial parameter ε _a, μ _a(corresponding to the axis direction that can change with the position in medium) and meet the horizontal parameter ε of inequality (7) and (13) _t1=ε _t2=ε _t, μ _t1=μ _t2=μ _t, it provides hyperbolic dispersion relation (8) and (14), and these dispersion relations support respectively TE and TM polarized wave in two indefinite media, as discussed in above paragraph, and the equation that comprises reference herein.

Some embodiments provide the indefinite medium as conversion medium, and electromagnetic medium has the characteristic that can characterize according to transform optics.Transform optics is the emerging field of Electromagnetic Engineering, and transform optics device comprises the electromagnetic structure of impact, the bending (" conversion " in planimetric coordinates space) of electromagnetic wave in curvilinear coordinates space imitated in wherein said impact, for example, as A.J.Ward and J.B.Pendry, " Refraction and geometry in Maxwell ' s equations, " J.Mod.Optics 43, 773 (1996), J.B.Pendry and S.A.Ramakrishna, " Focusing light using negative refraction, " J.Phys.[Cond.Matt.] 15, 6345 (2003), the people such as D.Schurig, " Calculation of material properties and ray tracing in transformation media, " Optics Express 14, 9794 (2006) (" people (1) such as D.Schurig "), and U.Leonhardt and T.G.Philbin, " General relativity in electrical engineering, " New J.Phys.8, described in 247 (2006), wherein each list of references is incorporated herein by reference.The use of term " optics " does not imply any restriction about wavelength; Transform optics device is exercisable during growing to the scope of visible wavelength from radiowave and exceeding the wave band of this scope.

The first exemplary transform optics device is electromagnetism cape, and it is respectively people such as J.B.Pendry, " Controlling electromagnetic waves, " Science 312,1780 (2006); The people such as S.A.Cummer, " Full-wave simulations of electromagnetic cloaking structures, " Phys.Rev.E 74,036621 (2006); And the people such as D.Schurig, " Metamaterial electromagnetic cloak at microwave frequencies; " description in Science 314,977 (2006) people (2) such as (" ") D.Schurig, emulation and realization; Wherein each list of references is incorporated herein by reference.The 11/459th, No. 728 U.S. Patent application " Electromagnetic cloaking method " that is also shown in the people such as J.Pendry, it is incorporated herein by reference.For electromagnetism cape, curvilinear coordinates space is breakdown and stretch to generate the conversion of plane space in hole (cape region), and this conversion is corresponding to one group of formation parameter (electric specific inductive capacity and magnetic permeability) of conversion medium, in described conversion medium, electromagnetic wave is refracted to imitate curvilinear coordinates space around hole.

The second exemplary transform optics device is illustrated by the embodiment of electromagnetism pressure texture, visible J.B.Pendry, D.Schurig, the 11/982nd of D.R.Smith, No. 353 U.S. Patent applications " Electromagnetic compression apparatus; methods; and systems " and J.B.Pendry, D.Schurig, the 12/069th of D.R.Smith, No. 170 U.S. Patent applications " Electromagnetic compression apparatus, methods, and systems "; Each list of references is wherein incorporated herein by reference.In this article in described embodiment, electromagnetism pressure texture comprises the conversion medium having corresponding to the formation parameter of the coordinate transform of the area of space of the first and second locus in the middle of compression, applies effective space compression along the axis that connects the first and second locus.Thereby electromagnetism pressure texture provides the effective electromagnetism distance between the first and second locus of the physical distance being greater than between the first and second locus.

The 3rd exemplary transform optics device illustrates by the embodiment of electromagnetism cape and/or transformational structure, the 12/074th of visible J.T.Kare, No. 247 U.S. Patent applications " Electromagnetic cloaking apparatus; methods; and systems ", and J.T.Kare the 12/074th, No. 248 U.S. Patent applications " Electromagnetic cloaking apparatus; methods, and systems "; Each list of references is wherein incorporated herein by reference.In this article in described embodiment, electromagnetic conversion structure comprises the conversion medium of the apparent place of the electromagnetic transducer that provides different from the physical location of electromagnetic transducer, and wherein conversion medium has corresponding to the formation parameter of coordinate transform that physical location is mapped to apparent place.Alternatively or additionally, embodiment comprises near the electromagnetism cape structure of the electromagnetic radiation barrier (and barrier can be another transducer) that can operate to shift in transducer field.

The 4th exemplary transform optics device illustrates by the embodiment of various focusing and/or focus adjustment structure, the 12/156th of the people such as visible J.A.Bowers, No. 443 U.S. Patent applications " Focusing and sensing apparatus, methods, and systems "; The people's such as J.A.Bowers the 12/214th, No. 534 U.S. Patent application " Emitting and focusing apparatus, methods, and systems "; The people's such as J.A.Bowers the 12/220th, No. 705 U.S. Patent application " Negatively-refractive focusing and sensing apparatus, methods, and systems "; The people's such as J.A.Bowers the 12/220th, No. 703 U.S. Patent application " Emitting and negatively-refractive focusing apparatus, methods, and systems "; The people's such as J.A.Bowers the 12/228th, No. 140 U.S. Patent application " Negatively-refractive focusing and sensing apparatus, methods, and systems "; And, the people's such as J.A.Bowers the 12/228th, No. 153 U.S. Patent application " Emitting and negatively-refractive focusing apparatus, methods, and systems "; Each list of references is wherein incorporated herein by reference.In this article in described embodiment, focus on and/or focusing structure comprise the axis magnification that provides the extension degree of depth of focus/field to be greater than the nominal depth of focus/field or territory, internal focal point/place is provided much larger than or be less than 1 conversion medium.

The people such as the visible D.Schurig of transform optics device that other are exemplary, " Transformation-designed optical elements, " Opt.Exp.15,14772 (2007); The people such as M.Rahm, " Optical design of reflectionless complex media by finite embedded coordinate transformations, " Phys.Rev.Lett.100,063903 (2008); And A.Kildishev and V.Shalaev, " Engineering space for light via transformation optics, " Opt.Lett.33,43 (2008); Each list of references is wherein incorporated herein by reference.

Conventionally, for the coordinate transform of selecting, conversion medium can be identified, and wherein electromagnetic field forms in the curvilinear coordinates space of the coordinate transform corresponding to selecting.The formation parameter of conversion medium can be provided by equation (15) (16):

${\widetilde{\mathrm{\&epsiv;}}}^{i^{\&prime;}{j}^{\&prime;}}={\left[\det \left(\mathrm{\&Lambda;}\right)\right]}^{-1}{\mathrm{\&Lambda;}}_i^{i^{\&prime;}}{\mathrm{\&Lambda;}}_j^{j^{\&prime;}}{\mathrm{\&epsiv;}}^{\mathrm{ij}}---\left(15\right)$

${\widetilde{\mathrm{\&mu;}}}^{i^{\&prime;}{j}^{\&prime;}}={\left[\det \left(\mathrm{\&Lambda;}\right)\right]}^{-1}{\mathrm{\&Lambda;}}_i^{i^{\&prime;}}{\mathrm{\&Lambda;}}_j^{j^{\&prime;}}{\mathrm{\&mu;}}^{\mathrm{ij}}---\left(16\right)$

Wherein, with be permittivity tensor and the permeability tensor of conversion medium, ε and μ are permittivity tensor and the permeability tensors of the original medium in the coordinate space not converting, and

${\mathrm{\&Lambda;}}_i^{i^{\&prime;}}=\frac{\&PartialD;x^{i^{\&prime;}}}{\&PartialD;x^i}---\left(17\right)$

The Jacobian matrix corresponding with coordinate transform.In some applications, coordinate transform is position in the coordinate space not converting to the mapping one to one of the position in the coordinate space of conversion, and in other application, coordinate transform is position in the coordinate space not converting to the one-to-many mapping of the position in the coordinate space of conversion.Some coordinate transforms such as one-to-many mapping can be corresponding to the conversion medium with negative index.In some applications, conversion medium is indefinite medium, has the electromagnetic medium (these conversion mediums can be called as " indefinite conversion medium ") of indefinite specific inductive capacity and/or indefinite magnetic permeability.For example, in equation (15) and (16), if original specific inductive capacity matrix ε is indefinite, the specific inductive capacity matrix of conversion also be indefinite; If and/or original magnetic permeability matrix μ is indefinite, the magnetic permeability matrix of conversion also be indefinite.In some applications, only have the selected matrix element of specific inductive capacity and permeability tensor need to meet equation (15) and (16), for example wherein transform optics response is only for the polarization of selecting.In other application, first group of specific inductive capacity and magnetic permeability matrix element meet equation (15) and (16) with the first Jacobi Λ, corresponding with the first transform optics response of electromagnetic the first polarization, and meet equation (15) and (16) with the second Jacobi Λ ' with orthogonal (or complementary) second group of specific inductive capacity and the magnetic permeability matrix element of first group of matrix element, respond corresponding with the second transform optics of electromagnetic the second polarization.And in other application, although use reduced parameter may not meet equation (15) and (16), but retain the product of unit with (16) the middle unit selected of selection in (15), thereby the dispersion relation in reservation conversion medium (is shown in the people (2) such as such as D.Schurig, on seeing, with people such as W.Cai, " Optical cloaking with metamaterials; " Nature Photonics 1,224 (2007), it is incorporated herein by reference).For example, can use reduced parameter to substitute electroresponse with magnetic response, vice versa.Although reduced parameter has retained the dispersion relation in conversion medium (so that ray or ripple track in the ray in conversion medium or ripple track and equation (15) and (16) do not change), but they do not retain the impedance operator of conversion medium, still suffer reflection (and be unreflected in fact according to the conversion medium of equation (15) and (16) conventionally or have the reflection characteristic of original medium in the coordinate space not converting) thereby incide ray on border or the interface of conversion medium or ripple.Can be by selecting suitable coordinate transform to greatly reduce or eliminating the reflection of the conversion medium with reduced parameter or scattering properties (in the coordinate space of not conversion taking any emission characteristics of original medium as mould), the coordinate transform that described selection is suitable, for example, by to select its corresponding Jacobi (or subset of its yuan) be continuous on the border of conversion medium or interface or be in fact continuous coordinate transform (for example, see the people such as W.Cai, " Nonmagnetic cloak with minimized scattering, " Appl.Phys.Lett.91, 111105 (2007), it is incorporated herein by reference).

Can use the material of manual construction to realize the embodiment (comprising the embodiment of indefinite conversion medium) of indefinite medium and/or conversion medium.In general, the electromagnetic property of the material of manual construction obtains from the configuration of its structure, instead of obtains from its material composition, or other aspects except its material composition obtain.

In some embodiments, the material of manual construction is photonic crystal.The people such as the visible J.D.Joannopoulos of photonic crystal that some are exemplary, Photonic Crystals:Molding the Flow of Light, 2nd Edition, Princeton Univ.Press, 2008, it is incorporated herein by reference.In photonic crystal, design photon dispersion relation and/or photon band gap by the pattern that applies spatial variations in for example, combination at electromagnetic material (conduction, magnetic or dielectric substance) or electromagnetic material.Photon dispersion relation is converted to the effective constitution parameter (for example, specific inductive capacity, magnetic permeability, refractive index) of photonic crystal.Spatial variations pattern is normally periodic, quasi periodic or colloid is periodic, and the operation wavelength of its length dimension and photonic crystal can be compared.

In other embodiment, the material of manual construction is anisotropic media.The people's such as the visible R.A.Hyde of anisotropic media that some are exemplary the 11/355th, No. 493 U.S. Patent application " Variable metamaterial apparatus "; The people's such as D.Smith PCT/US2005/026052 international application " Metamaterials "; The people such as D.Smith, " Metamaterials and negative refractive index, " Science 305,788 (2004); The people's such as D.Smith the 10/525th, No. 191 U.S. Patent application " Indefinite materials "; C.Caloz and T.Itoh, Electromagnetic Metamaterials:Transmission Line Theory and Microwave Applications, Wiley-Interscience, 2006; N.Engheta and R.W.Ziolkowski, eds., Metamaterials:Physics and Engineering Explorations, Wiley-Interscience, 2006; And, A.K.Sarychev and V.M.Shalaev, Electrodynamics of Metamaterials, World Scientific, 2007; Wherein each list of references is incorporated herein by reference.

Anisotropic media is conventionally taking sub-wavelength key element as feature, be that textural element has the part that electromagnetism length dimension is less than the operation wavelength of anisotropic media, and sub-wavelength key element has the collective response to electromagnetic radiation corresponding with effectively continuous dielectric response, with effective dielectric constant, Effective permeability with effectively magnetic-electric coefficient or its combination in any characterize.For example, electromagnetic radiation can cause producing electric charge and/or electric current in sub-wavelength key element, and sub-wavelength key element obtains electricity and/or the magnetic dipole moment of non-zero thus.Wherein, the electric component of electromagnetic radiation comprises electric dipole moment, and anisotropic media has effective dielectric constant; Wherein, the magnetic component of electromagnetic radiation comprises magnetic dipole moment, and anisotropic media has Effective permeability; And wherein electricity (magnetic) component causes magnetic (electricity) dipole moment (as the anisotropic media of chirality), anisotropic media has effective magnetic-electric coefficient.Some anisotropic medias provide artificial magnetic response; For example, the open-loop resonator (SRR) set up from non-magnetic conductor-or other LC or plasma resonant vibration device-can present Effective permeability (is shown in the people such as J.B.Pendry, " Magnetism from conductors and enhanced nonlinear phenomena; " IEEE Trans.Micro.Theo.Tech.47,2075 (1999), it is incorporated herein by reference).Some anisotropic medias have part and show " mixing " electromagnetic property by the architectural feature of anisotropic media and part by the inherent characteristic of constituent material.For example, G.Dewar, " A thin wire array and magnetic host structure with n < 0; " J.Appl.Phys.97,10Q101 (2005) (it is incorporated herein by reference) has described the anisotropic media being made up of the wire array (because its structure causes presenting negative magnetoconductivity) being embedded in the main medium of non-conductive Ferrimagnetic (presenting intrinsic negative magnetoconductivity).According to the coupling between the material behavior of constituent material and shape, chirality, configuration, position, orientation and sub-wavelength key element, can design and manufacture anisotropic media to present selected specific inductive capacity, magnetic permeability and/or magnetic-electric coefficient.Selected specific inductive capacity, magnetic permeability and/or magnetic-electric coefficient can be near (for example, the resonance frequency of material) or its combination in any of (having loss or gain), anisotropic (comprising that tensor is indefinite) positive or negative, plural number, (for example gradient index lens) of spatially-variable, time variable (for example, in response to outside or feedback signal), changeable frequency.Can provide selected electromagnetic property at the wavelength that grows to the scope of infrared/visible wavelength from radiowave; A rear wavelength can with such as nano structural material (such as nanometer rods to or nanometer eyed structure (see the people such as S.Linden, " Photonic metamaterials:Magnetism at optical frequencies; " IEEE J.Select.Top.Quam.Elect.12,1097 (2006) and V.Shalaev, " Optical negative-index metamaterials; " Nature Photonics 1,41 (2007), both its incorporated herein by reference)) realize.An example of the three-dimensional anisotropic media of optical frequency: the people such as elongated open loop " match heap " the visible M.S.Rill of structure, " Photonic metamaterials by direct laser writing and silver chemical vapour deposition; " Nature Materials advance online publication, May 11,2008, (doi:10.1038/nmat2197).

Although a lot of exemplary anisotropic medias are described to comprise discrete element, but some realizations of anisotropic media can comprise non-discrete element or structure.For example, anisotropic media can comprise the element being made up of daughter element, wherein daughter element is discrete structure (such as open-loop resonator etc.), or anisotropic media can comprise some elements, described element comprises, gets rid of some continuous structures, or carries out other variations (for example etching in substrate) along some continuous structures.Anisotropic media can comprise and have distributed electrical magnetic response the extended structure of (such as distributed inductance response, distributed capacitor response and the response of distributed inductance-electric capacity).Example comprises the nanostructured (nanometer mesh, elongated SRR match are piled etc.) of the structure being made up of the transmission line loading and/or interconnect (such as microstrips and strip line), artificial aground plane structure (such as artificial desirable magnetic conductor (PMC) surface and electro-magnetic bandgap (EGB) surface) and interconnection/extension.

In some embodiments, anisotropic media can comprise hierarchy.For example, embodiment can provide the adjacent continuous structure of layer, and wherein these layers have the corresponding continuous material behavior that comprises electromagnetic property (such as specific inductive capacity and/or magnetic permeability).Continuous adjacent layer can be continuous adjacent layer alternately or that repeat, the storehouse that the layer of for example first kind and the layer of Second Type are staggered or repeat three or more types layer the storehouse of sequence.For example, when layer is enough when thin (thickness is less than the operation wavelength of anisotropic media), the feature of hierarchy is effective continuous medium with the effective constitution parameter of the electromagnetic property that relates to each layer.For example, (thickness is d to the layer of consideration the first material ₁and there is homogeneity and isotropic electromagnetic parameter ε ₁, μ ₁) (thickness is d with the layer of the second material ₂and there is homogeneity and isotropic electromagnetic parameter ε ₂, μ ₂) staggered plane storehouse; The feature of hierarchy is effective continuous medium with (effectively) anisotropy formation parameter

${\mathrm{\&epsiv;}}_x={\mathrm{\&epsiv;}}_y=\frac{{\mathrm{\&epsiv;}}_1+\mathrm{\&eta;}{\mathrm{\&epsiv;}}_2}{1+\mathrm{\&eta;}},---\left(18\right)$

$\frac{1}{{\mathrm{\&epsiv;}}_z}=\frac{1}{1+\mathrm{\&eta;}}(\frac{1}{{\mathrm{\&epsiv;}}_1}+\frac{\mathrm{\&eta;}}{{\mathrm{\&epsiv;}}_2}),---\left(19\right)$

${\mathrm{\&mu;}}_x={\mathrm{\&mu;}}_y=\frac{{\mathrm{\&mu;}}_1+\mathrm{\&eta;}{\mathrm{\&mu;}}_2}{1+\mathrm{\&eta;}},---\left(20\right)$

$\frac{1}{{\mathrm{\&mu;}}_z}=\frac{1}{1+\mathrm{\&eta;}}(\frac{1}{{\mathrm{\&mu;}}_1}+\frac{\mathrm{\&eta;}}{{\mathrm{\&mu;}}_2})---\left(21\right)$

Wherein, η=d ₂/ d ₁be the ratio of two layers of thickness, z is the direction vertical with layer, and x, y are the directions parallel with layer.In the time comprising that two materials of cross structure have the electromagnetic parameter of contrary sign, forming parameter (18)-(21) can be corresponding to indefinite medium.For example,, when the first material is to have DIELECTRIC CONSTANT ε ₁the material of < 0 and the second material are to have DIELECTRIC CONSTANT ε ₂when the material of > 0, can according to equation (18)-(21) selection ratio η with provide indefinite specific inductive capacity matrix (and, equal in fact for η | ε ₁/ ε ₂|, indefinite dielectric constant dielectric is the indefinite dielectric constant dielectric of degeneracy in essence).Alternatively or additionally, when the first material is to have magnetic permeability μ ₁the material of < 0 and the second material are to have magnetic permeability μ ₂when the material of > 0, can according to equation (20)-(21) selection ratio η with provide indefinite magnetic permeability matrix (and, equal in fact for η | μ ₁/ μ ₂|, indefinite magnetic permeability medium is the indefinite magnetic permeability medium of degeneracy in essence).

Provide the exemplary plane storehouse of the alternative materials of effective continuous medium with indefinite specific inductive capacity matrix to comprise the people such as B.Wood, " Directed subwavelength imaging using a layered medal-dielectric system, " Phys.Rev.B 74, the silver/silicon dioxide hierarchical system and the A.J.Hoffman that replace described in 115116 (2006), " Negative refraction in semiconductor metamaterials, " Nature Materials 6, the semiconductor hierarchical system of the doping replacing/non-doping described in 946 (2007), wherein each list of references is incorporated herein by reference.More generally, the material with positive specific inductive capacity includes but not limited to: semiconductor (for example, frequency is greater than semi-conductive plasma frequency) and for example, such as insulator, glass, pottery and the polymkeric substance (as photoresist, PMMA) of dielectric crystal (monox, aluminium oxide, calcium fluoride, magnesium fluoride).Conventionally, these materials also have positive magnetic permeability (if material is nonmagnetic in essence, magnetic permeability equals in fact 1).In some embodiments, the material of positive specific inductive capacity is gain media, for example it can be by pumping to reduce or to overcome loss such as ohmic loss (with reference to S.Ramakrishna and J.B.Pendry, " Removal of absorption and increase in resolution in a near-field lens via optical gain; " Phys.Rev.B 67, exemplary silver/gain the hierarchical system replacing that 201101 (R) (2003) are described, it is incorporated herein by reference).The example of gain media comprises insulator laser material (for example rear-earth-doped crystal, glass or pottery) and the Raman gain material of semiconductor laser material (for example GaN, AlGaAs), doping.The material with negative magnetoconductivity includes but not limited to: ferrite, magnetic garnet, spinel, artificial ferrite and other ferromagnetic or ferrimagnetic materials are (for example, in the frequency higher than the ferromagnetic of material or Ferrimagnetic resonance frequency; With reference to No. 11/279/460 U.S. Patent application " Tunable negative refractive index composite " of F.J.Rachford, it is incorporated herein by reference).The material with negative permittivity includes but not limited to: the metal (for example, in the frequency of the plasma frequency lower than metal) that comprises heavy metal (Cu, Au, Ag); Semiconductor (for example, in the frequency lower than semi-conductive plasma frequency); For example, and polar crystal (SiC, LiTaO3, LiF, ZnSe) in frequency in the rejection band of polar crystal is (with reference to G.Schvets, " Photonic approach to making a material with a negative index of refraction; " Phys.Rev.B 67,035109 (2003) and the people such as T.Tauber, " Near-field microscopy through a SiC superlens; " Science 313,1595 (2006), wherein each list of references is incorporated herein by reference).For relating to semi-conductive application, plasma frequency (can be considered to the frequency of semiconductor specific inductive capacity reindexing) relates to the density of the free carrier in semiconductor, and (for example chemical doping, photodoping, temperature variation, carrier injection etc.) controls the density of this free carrier in several ways.Therefore, for example comprise the crossbedded hierarchical system of the second semiconductor material that there is the first semiconductor material of the first plasma frequency and there is the second plasma frequency and can provide the indefinite specific inductive capacity (according to equation (18)-(19)) in the window of intermediate frequency of the first plasma frequency and the second plasma frequency, and can control this window by first and second semiconductor materials that for example differently adulterate.

In some applications, hierarchy comprises it being in fact nonplanar continuous adjacent layer.Exemplary hierarchy is made up of continuous plane layer above, every layer has the layer normal direction (z direction) fixing along the lateral extent of layer and the fixing layer thickness of lateral extent along layer, hierarchy can extend to the nonplanar hierarchy being made up of continuous non planar layer, every layer have along layer revocable layer of normal direction of lateral extent and alternatively along layer the revocable layer thickness of lateral extent.The visible A.Salandrino of some examples and the N.Engheta of cylindrical and/or spherical hierarchy, " Far-field subdiffraction optical microscopy using metamaterial crystals:Theory and simulations; " Phys.Rev.B 74,075103 (2006); The people such as Z.Jacob, " Optical hyperlens:Far-field imaging beyond the diffraction limit, " Opt.Exp.14,8247 (2006); The people such as Z.Liu, " Far field optical hyperlens magnifying sub-diffraction-limited objects, " Science 315,1686 (2007); And H.Lee, " Development of optical hyperlens for imaging below the diffraction limit, " Opt.Exp.15,15886 (2007), wherein each list of references is incorporated herein by reference.More generally, for the on-plane surface hierarchy replacing, the radius-of-curvature of hypothetical layer is much smaller than its thickness separately, and transverse layers thickness gradient is much smaller than 1, being characterized as of nonplanar hierarchy has the effective continuous medium that forms parameter as (effectively) anisotropy in equation (18)-(21), wherein use the layer normal direction changing with the position in hierarchy to substitute z direction, by the alternative x direction of first horizontal direction vertical with layer normal direction, with substituting y direction with layer normal direction and orthogonal the second horizontal direction of the first horizontal direction, and layer thickness is than η=d ₂/ d ₁it is the partial layer thickness d that can change with the position of whole hierarchy ₁and d ₂ratio (therefore η also can change with position).Thereby nonplanar hierarchy can provide the indefinite medium of the axis direction with the spatial variations corresponding with layer normal direction.For example, for scalar potential function phi, suppose the vector field u that equals or be parallel to conventional vector field for axis direction of the spatial variations of indefinite medium _a(r) provide,

$u_A\&Proportional;\&dtri;\mathrm{\&Phi;}---\left(22\right)$

Can provide indefinite medium by nonplanar hierarchy, wherein the interface of adjacent layer is corresponding to the equipotential surface of function phi.

Can manufacture nonplanar hierarchy by several different methods known to those skilled in the art.In the first example, the 7th of J.A.Folta, 062, No. 348 United States Patent (USP)s " Dynamic mask for producing uniform or graded-thickness thin films " (it is incorporated herein by reference) have been described the gas-phase deposition system that adopts mobile mask, and wherein the speed of mobile mask and position can be by computer control accurately to adjust the thickness distribution of deposit film.In the second example, the 6th of Tzu-Yu Wang, 606, No. 199 United States Patent (USP)s " Graded thickness optical element and method of manufacture therefor " (it is incorporated herein by reference) have been described the method for deposit the thick layer of classification through the aperture of mask layer.

Referring now to Fig. 1, illustrative embodiment has been described, this embodiment comprises the transformational structure 100 with indefinite electromagnetic parameter, and this transformational structure has first surface region 111 and second surface region 112, and first surface region is in fact plane and parallel in fact with second surface region.For example, unless pointed out in addition in literary composition, planimetric map or the two-dimentional embodiment (in Fig. 1, wherein transformational structure is arranged in metal or the dielectric plate waveguide perpendicular to the page) of this figure and the three-dimensional embodiment of other figure representations.Transformational structure in response to the electromagnetic wave that suddenly dies in first surface region (schematically illustrated with curve tail 120) so that propagation of electromagnetic waves (schematically illustrated with dotted line 125) is transferred to second surface region from first surface region, and provide in second surface region the non-electromagnetic wave that suddenly dies (with wave 130 schematically illustrated).In some embodiments, the non-electromagnetic wave that suddenly dies providing is the electromagnetic wave of Free propagation, for example, from the ripple (comprise and disperse propagation wave, assemble propagation wave and be essentially the propagation wave of plane) of the transmission of second surface region free radiation.In other embodiment, the non-evanescent wave providing is to propagate limited electromagnetic wave, for example, be transmitted as the ripple (as waveguide, transmission line, optical fiber etc.) of propagating guided wave mode from second surface region.Although figure 1 illustrates the first and second surf zone 111 and 112 outside surfaces as transformational structure 100, but in other embodiment, first surface region and/or second surface region can be positioned at the inside (for example, wherein transformational structure comprises refraction covering, impedance matching layer, inputs or outputs one or more in light parts etc.) of transformational structure at least in part.Description at the use light in Fig. 1 and other places is heuristic ground, and it is convenient to the object of visual explanation, and is not intended to any restriction or the hypothesis of hint to geometrical optics; Further, the element shown in Fig. 1 can have respectively and is less than, is greater than or comparable bulk of intending interested wavelength.On first surface region 111, electromagnetic wave 120 use the first lateral wave vectors suddenly die (corresponding to the surperficial parallel direction in first surface region, with the vector 141 in Fig. 1 represent) characterizes, the first lateral wave vector be greater than the first maximum transversal wave vector of non-evanescent wave (with reference to equation (2) and above related content):

$k_T^{\left(1\right)}>k_{\max }^{\left(1\right)}=\frac{2\mathrm{\&pi;}{n}_{1}f}{c}=\frac{2\mathrm{\&pi;f}}{v_1}---\left(23\right)$

Wherein, f is the electromagnetic frequency that suddenly dies, and v ₁that the first area of transformational structure 100 outsides and the electromagnetic phase velocity (frequency f) that approaches first surface region 111 are (according to being related to v ₁=c/n ₁, phase velocity can be corresponding to the refractive index n of the refracting medium in first area (may be vacuum) ₁).On second surface region 112, non-electromagnetic wave 130 use the second lateral wave vectors that suddenly die (corresponding to the surperficial parallel direction in second surface region, with the vector 142 in Fig. 1 represent) characterizes, and this second lateral wave vector is not more than the second maximum transversal wave vector of non-evanescent wave (with reference to equation (2) and above related content):

$k_T^{\left(2\right)}<k_{\max }^{\left(2\right)}=\frac{2\mathrm{\&pi;}{n}_{2}f}{c}=\frac{2\mathrm{\&pi;f}}{v_2}---\left(24\right)$

Wherein, suddenly die electromagnetic frequency and v of f right and wrong ₂that the second area of transformational structure 100 outsides and the electromagnetic phase velocity (frequency f) that approaches second surface region 112 are (according to being related to v ₂=c/n ₂, phase velocity can be corresponding to the refractive index of the refracting medium in second area (may be vacuum), wherein n ₂can equal n ₁or be different from n ₁).

In the illustrative embodiment of Fig. 1, transformational structure 100 has indefinite electromagnetic parameter, be that (transformational structure provides indefinite medium, as mentioned above, there is the electromagnetic medium of indefinite specific inductive capacity and/or indefinite magnetic permeability), described indefinite dielectric response in the electromagnetic wave 120 that suddenly dies so that propagation of electromagnetic waves is transferred to second surface region 112 from first surface region 111.Indefinite medium has defined axis direction (each position vector 150 in indefinite medium indicates), and as mentioned above, axis direction is corresponding to the first eigenvector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix; And, indefinite medium has also defined horizontal direction (each position vector 151 in indefinite medium indicates), as mentioned above, horizontal direction is perpendicular to axis direction and corresponding to the Second Characteristic vector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix.In the illustrative embodiment of Fig. 1, axis direction 150 is revocable axis directions, and it is the function of the position in transformational structure 100, and axis direction can be considered to vector field (the vector value function of position).And axis direction points to second surface region 112 from first surface region 111 conventionally, that is, extend to second surface region corresponding to the axial field wire of axial vector field from first surface region.In Fig. 1, the dotted line 125 of instruction propagation of electromagnetic waves is also corresponding to axial field wire, this is because illustrative embodiment has been described the indefinite medium of degeneracy, i.e. indefinite medium as above, and this indefinite medium transmits electromagnetic energy along the direction of propagation of the axis direction corresponding to indefinite medium in fact.(this description is not intended to restriction: in other embodiment, indefinite medium is " nondegenerate " the indefinite medium that for example at least transmits in fact electromagnetic energies along multiple directions of propagation along two directions of propagation, at least each in both direction has the substantial common angles about axis direction, or propagate along multiple directions of propagation, described multiple directions of propagation form in fact the circular cone with consistent with axis direction in fact circular cone axis.)

Referring again to Fig. 1, propagate electromagnetic field 125 and can use the lateral wave vector k corresponding to horizontal direction 151 _tcharacterize.In this example, their geometric divergences in the time that axial field wire (corresponding to the vector field of describing axis direction 150) advances to second surface region 112 from first surface region 111, and this geometric divergence can provide the first lateral wave vector from first surface region (as equation (23), for mating the lateral wave vector of the electromagnetic wave 120 that suddenly dies) are to the second lateral wave vector on second surface region the lateral wave vector k of (as equation (24), for mating the lateral wave vector of the non-electromagnetic wave 130 that suddenly dies) _tcontinuous in fact variation.Thereby, there is lateral wave vector from the initial horizontal of maximum wave vector that is greater than non-evanescent wave to wave vector to the propagation of electromagnetic waves 125 of continuous in fact variation of final lateral wave vector of maximum wave vector that is not more than non-evanescent wave by support, the axially geometric divergence of the field wire conversion of electromagnetic wave 120 to the non-electromagnetic wave 130 that suddenly dies that allow suddenly to die.

Refer now to Fig. 2 and Fig. 3, described the hierarchy as the exemplary realization of the transformational structure 100 of Fig. 1.In the exemplary realization of Fig. 2 and Fig. 3, transformational structure 100 comprises that (as above) is in fact plane and parallel in fact first surface region 111 and second surface region 112; In the middle of the first and second surf zones, hierarchy provides the effective continuous medium corresponding to indefinite medium.Hierarchy comprises the layer 201 of the first interlaced material and the layer 202 of the second material, and wherein the first and second materials have the electromagnetic parameter that symbol is contrary (for example specific inductive capacity and/or magnetic permeability), as mentioned above.In the exemplary realization of Fig. 2 and 3, layer 201 and 202 is alternately nonplanar in fact, have with the position of whole hierarchy (, from layer to layer and/or along the lateral extent of every layer) and the normal direction of the layer that changes, and the normal direction of this layer corresponding to the axis direction of provided indefinite medium (indicating with the vector 150 in Fig. 1) (equivalently, interface between the layer 201 and 202 replacing is thought of as to the equipotential surface of scalar function Φ, according to equation (22), the gradient local of the Φ direction 150 that parallels to the axis).In the exemplary realization of Fig. 3, the ground floor 301 of hierarchy is consistent in fact with first surface region 111, and last one deck 302 of hierarchy is consistent in fact with second surface region 112, but this is not intended to restriction (for example, in the exemplary realization of Fig. 2, neither first surface region 111 non-second surface region 112 and hierarchy layer consistent in fact again).Nonplanar alternating layer can have identical in fact thickness in the lateral extent of whole layer, as shown in Figure 2; Or the lateral extent at whole layer has the thickness being different in essence, as shown in Figure 3; Or its combination.

Referring now to Fig. 4, illustrative embodiment has been described, this embodiment comprises the transformational structure 100 with indefinite electromagnetic parameter, this transformational structure has to be in fact the first surface region 111 of plane and to be in fact nonplanar second surface region 112.In illustrative embodiment, although (nonplanar in fact second surface region 112 is described to convex surface region, this configuration is " plano-convex " configuration), but this is exemplary configuration and is not intended to restriction: and it is recessed (" plano-concave " configuration) or comprise the first recessed subregion and nonplanar in fact second surface region 112 of protruding the second subregion that other embodiment (not shown) provide.For example, unless pointed out in addition in literary composition, planimetric map or the two-dimentional embodiment (in Fig. 4, transformational structure is arranged in perpendicular to the metal of the page or dielectric plate waveguide) of this figure and the three-dimensional embodiment of other figure representations.This transformational structure in response to the electromagnetic wave that suddenly dies in first surface region (schematically illustrated with curve 120) so that propagation of electromagnetic waves (schematically illustrated with dotted line 125) is transferred to second surface region from first surface region, with provide in second surface region the non-electromagnetic wave that suddenly dies (with wave 130 schematically illustrated).In some embodiments, the non-electromagnetic wave that suddenly dies providing is Free propagation electromagnetic wave, for example, from the ripple (comprise and disperse propagation wave, assemble propagation wave and be essentially the propagation wave of plane) of the second resistance electromagnetic surface transmission free radiation.In other embodiment, the non-evanescent wave providing is to propagate limited electromagnetic wave, for example, be transmitted as from the second resistance electromagnetic surface the ripple (as waveguide, transmission line, optical fiber etc.) of propagating guided wave mode.Although figure 4 illustrates the first and second surf zone 111 and 112 outside surfaces as transformational structure 100, but in other embodiment, first surface region and/or second surface region can be positioned at the inside (for example, wherein transformational structure comprises refraction covering, impedance matching layer, inputs or outputs one or more in light parts etc.) of transformational structure at least in part.Description at the use line in Fig. 4 and other places is heuristic ground, so that the object of visual explanation, and be not intended to any restriction or the hypothesis of hint to geometrical optics; Further, the element shown in Fig. 4 can have respectively and is less than, is greater than or comparable bulk of intending interested wavelength.On first surface region 111, electromagnetic wave 120 use the first lateral wave vectors suddenly die (corresponding to the surperficial parallel direction in first surface region, with the vector 141 in Fig. 4 represent) characterizes, and this first lateral wave vector is greater than the first maximum transversal wave vector of definition in equation (23) on second surface region 112, non-electromagnetic wave 130 use the second lateral wave vectors that suddenly die (corresponding to the surperficial parallel direction in second surface region, with the vector 142 in Fig. 4 represent) characterizes, and this second lateral wave vector is not more than the second maximum transversal wave vector of equation (24) definition

In the illustrative embodiment of Fig. 4, transformational structure 100 has indefinite electromagnetic parameter, be that (transformational structure provides indefinite medium, as mentioned above, there is the electromagnetic medium of indefinite specific inductive capacity and/or indefinite magnetic permeability), described indefinite dielectric response in the electromagnetic wave 120 that suddenly dies so that propagation of electromagnetic waves is transferred to second surface region 112 from first surface region 111.Indefinite medium has defined axis direction (each position vector 150 in indefinite medium indicates), and as mentioned above, this axis direction is corresponding to the first eigenvector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix; And, indefinite medium has also defined horizontal direction (each position vector 151 in indefinite medium indicates), as mentioned above, horizontal direction is perpendicular to axis direction, and corresponding to the Second Characteristic vector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix.In the illustrative embodiment of Fig. 4, axis direction 150 is revocable axis directions, and it is the function of the position in transformational structure 100, and axis direction can be considered to vector field (the vector value function of position).And axis direction points to second surface region 112 from first surface region 111 conventionally, that is, extend to second surface region corresponding to the axial field wire of axial vector field from first surface region.In Fig. 4, the dotted line 125 of instruction propagation of electromagnetic waves is also corresponding to axial field wire, this is because illustrative embodiment has been described the indefinite medium of degeneracy, i.e. indefinite medium as above, and this indefinite medium transmits electromagnetic energy along the direction of propagation of the axis direction corresponding to indefinite medium in fact.(this description is not intended to restriction: in other embodiment, indefinite medium is " nondegenerate " the indefinite medium that for example at least transmits in fact electromagnetic energies along multiple directions of propagation along two directions of propagation, at least each in both direction has the substantial common angles about axis direction, or propagate along multiple directions of propagation, described multiple directions of propagation have formed in fact the circular cone with consistent with axis direction in fact circular cone axis.)

Referring again to Fig. 4, propagate electromagnetic field 125 and can use the lateral wave vector k corresponding to horizontal direction 151 _tcharacterize.In this example, their geometric divergences in the time that axial field wire (corresponding to the vector field of describing axis direction 150) advances to second surface region 112 from first surface region 111, and this geometric divergence can provide lateral wave vector k _tthe first lateral wave vector from first surface region (as equation (23), for mating the lateral wave vector of the electromagnetic wave 120 that suddenly dies) are to the second lateral wave vector on second surface region the continuous in fact variation of (as equation (24), for mating the lateral wave vector of the non-electromagnetic wave 130 that suddenly dies).Thereby, there is lateral wave vector from the initial horizontal of maximum wave vector that is greater than non-evanescent wave to wave vector to the propagation of electromagnetic waves 125 of continuous in fact variation of final lateral wave vector of maximum wave vector that is not more than non-evanescent wave by support, the axially geometric divergence of the field wire conversion of electromagnetic wave 120 to the non-electromagnetic wave 130 that suddenly dies that allow suddenly to die.

Refer now to Fig. 5 and 6, described the hierarchy as the exemplary realization of the transformational structure 100 of Fig. 4.In the exemplary realization of Fig. 5 and 6, transformational structure 100 comprises that (as Fig. 4) is in fact the first surface region 111 of plane and is in fact nonplanar second surface region 112; In the middle of the first and second surf zones, hierarchy provides the effective continuous medium corresponding to indefinite medium.Hierarchy comprises the layer 201 of the first interlaced material and the layer 202 of the second material, and wherein the first and second materials have the electromagnetic parameter that symbol is contrary (for example specific inductive capacity and/or magnetic permeability), as mentioned above.In the exemplary realization of Fig. 5 and 6, layer 201 and 202 is alternately nonplanar in fact, have with the position of whole hierarchy (, from layer to layer and/or along the lateral extent of every layer) and the layer normal direction that change, and this layer of normal direction corresponding to the axis direction of provided indefinite medium (indicating with the vector 150 in Fig. 4) (equivalently, interface between the layer 201 and 202 replacing is thought of as to the equipotential surface of scalar function Φ, according to equation (22), the gradient local of the Φ direction 150 that parallels to the axis).In the exemplary realization of Fig. 6, although the ground floor 301 of hierarchy is consistent in fact with first surface region 111, and last one deck 302 of hierarchy is consistent in fact with second surface region 112, but this (is not for example intended to restriction, in the exemplary realization of Fig. 5, only have the layer 302 of second surface region 112 and hierarchy consistent in fact).Nonplanar cross-stratum can have identical in fact thickness in the lateral extent of whole layer, as shown in Figure 5; Or the lateral extent at whole layer has the thickness being different in essence, as shown in Figure 6; Or its combination.

Referring now to Fig. 7, show illustrative embodiment, this embodiment comprises the transformational structure 100 with indefinite electromagnetic parameter, this transformational structure has to be in fact nonplanar first surface region 111 and to be in fact the second surface region 112 of plane.In illustrative embodiment, although (nonplanar in fact first surface region 111 is described to recessed surf zone, this configuration is " recessed flat " configuration), but this is exemplary configuration and is not intended to restriction: and it is protruding (" convex flat " configuration) or comprise the first recessed subregion and nonplanar in fact first surface region 111 of protruding the second subregion that other embodiment (not shown) provide.For example, unless pointed out in addition in literary composition, planimetric map or the two-dimentional embodiment (in Fig. 7, transformational structure is arranged in perpendicular to the metal of the page or dielectric plate waveguide) of this figure and the three-dimensional embodiment of other figure representations.Transformational structure in response to the electromagnetic wave that suddenly dies in first surface region (schematically illustrated with curve 120) so that propagation of electromagnetic waves (schematically illustrated with dotted line 125) is transferred to second surface region from first surface region, with provide in second surface region the non-electromagnetic wave that suddenly dies (with wave 130 schematically illustrated).In some embodiments, the non-electromagnetic wave that suddenly dies providing is Free propagation electromagnetic wave, for example, from the ripple (comprise and disperse propagation wave, assemble propagation wave and be essentially the propagation wave of plane) of the second resistance electromagnetic surface transmission free radiation.In other embodiment, the non-evanescent wave providing is to propagate limited electromagnetic wave, for example, be transmitted as from the second resistance electromagnetic surface the ripple (as waveguide, transmission line, optical fiber etc.) of propagating guided wave mode.Although figure 7 illustrates the first and second surf zone 111 and 112 outside surfaces as transformational structure 100, but in other embodiment, first surface region and/or second surface region can be positioned at the inside (for example, wherein transformational structure comprises refraction covering, impedance matching layer, inputs or outputs one or more in light parts etc.) of transformational structure at least in part.Description at the use light in Fig. 7 and other places is heuristic ground, so that the object of visual explanation, and be not intended to any restriction or the hypothesis of hint to geometrical optics; Further, the element shown in Fig. 7 can have respectively and is less than, is greater than or comparable bulk of intending interested wavelength.On first surface region 111, electromagnetic wave 120 use the first lateral wave vectors suddenly die (corresponding to the surperficial parallel direction in first surface region, with the vector 141 in Fig. 7 represent) characterizes, the first lateral wave vector be greater than the first maximum transversal wave vector of definition in equation (23) on second surface region 112, non-electromagnetic wave 130 use the second lateral wave vectors that suddenly die (corresponding to the surperficial parallel direction in second surface region, with the vector 142 in Fig. 7 represent) characterizes, the second lateral wave vector be not more than the second maximum transversal wave vector of equation (24) definition

In the illustrative embodiment of Fig. 7, transformational structure 100 has indefinite electromagnetic parameter, be that (transformational structure provides indefinite medium, as mentioned above, there is the electromagnetic medium of indefinite specific inductive capacity and/or indefinite magnetic permeability), described indefinite dielectric response in the electromagnetic wave 120 that suddenly dies so that propagation of electromagnetic waves is transferred to second surface region 112 from first surface region 111.Indefinite medium has defined axis direction (each position vector 150 in indefinite medium indicates), and as mentioned above, axis direction is corresponding to the first eigenvector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix; And, indefinite medium has also defined horizontal direction (each position vector 151 in indefinite medium indicates), and described horizontal direction is perpendicular to axis direction and corresponding to the Second Characteristic vector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix.In the illustrative embodiment of Fig. 7, axis direction 150 is revocable axis directions, and it is the function of the position in transformational structure 100, and axis direction can be considered to vector field (the vector value function of position).And axis direction points to second surface region 112 from first surface region 111 conventionally, that is, extend to second surface region corresponding to the axial field wire of axial vector field from first surface region.In Fig. 7, the dotted line 125 of instruction propagation of electromagnetic waves is also corresponding to axial field wire, this is because illustrative embodiment has been described the indefinite medium of degeneracy, i.e. indefinite medium as above, and this indefinite medium transmits electromagnetic energy along the direction of propagation of the axis direction corresponding to indefinite medium in fact.(this description is not intended to restriction: in other embodiment, indefinite medium is " nondegenerate " the indefinite medium that for example transmits in fact electromagnetic energies along multiple directions of propagation along at least two directions of propagation, each in described at least both direction has the substantial common angles about axis direction, or propagate along multiple directions of propagation, described multiple directions of propagation form in fact the circular cone with consistent with axis direction in fact circular cone axis.)

Referring again to Fig. 7, propagate electromagnetic field 125 and can use the lateral wave vector k corresponding to horizontal direction 151 _tcharacterize.In this example, their geometric divergences in the time that axial field wire (corresponding to the vector field of describing axis direction 150) advances to second surface region 112 from first surface region 111, and this geometric divergence can provide lateral wave vector k _tthe first lateral wave vector from first surface region (as equation (23), for mating the lateral wave vector of the electromagnetic wave 120 that suddenly dies) are to the second lateral wave vector on second surface region the continuous in fact variation of (as equation (24), for mating the lateral wave vector of the non-electromagnetic wave 130 that suddenly dies).Thereby, there is lateral wave vector from the initial horizontal of maximum wave vector that is greater than non-evanescent wave to wave vector to the propagation of electromagnetic waves 125 of continuous in fact variation of final lateral wave vector of maximum wave vector that is not more than non-evanescent wave by support, the axially geometric divergence of the field wire conversion of electromagnetic wave 120 to the non-electromagnetic wave 130 that suddenly dies that allow suddenly to die.

Refer now to Fig. 8 and 9, show the hierarchy as the exemplary realization of the transformational structure 100 of Fig. 7.In the exemplary realization of Fig. 8 and 9, transformational structure 100 comprises that (as Fig. 7) is in fact nonplanar first surface region 111 and is in fact the second surface region 112 of plane; In the middle of the first and second surf zones, hierarchy provides the effective continuous medium corresponding to indefinite medium.Hierarchy comprises the layer 201 of the first interlaced material and the layer 202 of the second material, and wherein the first and second materials have the electromagnetic parameter that symbol is contrary (for example specific inductive capacity and/or magnetic permeability), as mentioned above.In the exemplary realization of Fig. 8 and 9, layer 201 and 202 is alternately nonplanar in fact, have with the position in whole hierarchy (, from layer to layer and/or along the lateral extent of every layer) and the layer normal direction that change, and this layer of normal direction corresponding to the axis direction of provided indefinite medium (indicating with the vector 150 in Fig. 7) (equivalently, interface between the layer 201 and 202 replacing is thought of as to the equipotential surface of scalar function Φ, according to equation (22), the gradient local of the Φ direction 150 that parallels to the axis).In the exemplary realization of Fig. 9, although the ground floor 301 of hierarchy is consistent in fact with first surface region 111, and last one deck 302 of hierarchy is consistent in fact with second surface region 112, but this is not intended to restriction (for example, in the exemplary realization of Fig. 8, only having the layers 301 consistent in fact of first surface region 112 and hierarchy).Nonplanar cross-stratum can have identical in fact thickness in the lateral extent of whole layer, as shown in Figure 8; Or the lateral extent at whole layer has the thickness being different in essence, as shown in Figure 9; Or its combination.

Referring now to Figure 10, it shows multiple illustrative embodiments, these embodiments comprise the transformational structure 100 with indefinite electromagnetic parameter, this transformational structure has first surface region 111 and second surface region 112, and described first surface region and second surface region are in fact nonplanar and are in fact nonconcentric(al).Conventionally, if: first surface region has revocable curvature, and/or second surface region has revocable curvature, and/or the center of the osculating circle in first surface region different from the center of the osculating circle in second surface region (osculating circle is coplanar), first surface region and second surface region are nonconcentric(al).Embodiment 1001 shows that to have be all the first surface region 111 of protruding (" biconvex " configuration) and the transformational structure 100 in second surface region 112.Embodiment 1002 shows that to have be all the first surface region 111 of recessed (" concave-concave " configuration) and the transformational structure 100 in second surface region 112.Embodiment 1003 shows the transformational structure 100 with recessed first surface region 111 and protruding second surface region 112, wherein right-hand-nearer apart from transformational structure than the flexural center in second surface region in the flexural center in second surface region, the flexural center in first surface region, , recessed-protruding " negative bent moon " configuration (another exemplary embodiment-not shown-provide recessed-protruding " positive bent moon " to configure, wherein the flexural center in first surface region is at the left of the flexural center in second surface region-farther apart from transformational structure than the flexural center in second surface region).Embodiment 1004 shows the transformational structure 100 with protruding first surface region 111 and recessed second surface region 112, wherein the flexural center in first surface region is at the left of the flexural center in second surface region-nearer apart from transformational structure than the flexural center in second surface region, , male-female " positive bent moon " configuration (another exemplary embodiment-not shown-provide male-female " negative bent moon " to configure, wherein right-hand-farther apart from transformational structure than the flexural center in second surface region in the flexural center in second surface region, the flexural center in first surface region).Embodiment 1005 show there is the first surface region 111 that the protruding and part of part is recessed and part is protruding and the transformational structure in the second surface region 112 that part is recessed (in other embodiment, not shown, first surface region 111 is only protruding or is only recessed, and second surface region 112 is that the protruding and part of part is recessed, or first surface region 111 is that part is protruding and part is recessed and second surface region 112 only for protruding or only for recessed).In other place, the explanation in Figure 10 can represent planimetric map or the two-dimentional embodiment (for example, wherein transformational structure 100 is arranged in metal or the dielectric plate waveguide perpendicular to the page) of three-dimensional embodiment.

In each embodiment of Figure 10, transformational structure 100 in response to the electromagnetic wave that suddenly dies in first surface region 111 (schematically illustrated with curve 120) so that propagation of electromagnetic waves (schematically illustrated with dotted line 125) is transferred to second surface region from first surface region, with provide in second surface region 112 the non-electromagnetic wave that suddenly dies (with wave 130 schematically illustrated).In some applications, the non-electromagnetic wave that suddenly dies providing is the electromagnetic wave of Free propagation, for example, from the ripple (comprise and disperse propagation wave, assemble propagation wave and be essentially the propagation wave of plane) of the second resistance electromagnetic surface transmission free radiation.In other realization, the non-evanescent wave providing is to propagate limited electromagnetic wave, for example, be transmitted as from the second resistance electromagnetic surface the ripple (as waveguide, transmission line, optical fiber etc.) of propagating guided wave mode.Although figure 10 illustrates the first and second surf zone 111 and 112 outside surfaces as transformational structure 100, but in other embodiment, first surface region and/or second surface region can be positioned at the inside (for example, wherein transformational structure comprises refraction covering, impedance matching layer, inputs or outputs one or more in light parts etc.) of transformational structure at least in part.Description at the use light in Figure 10 and other places is heuristic ground, so that the object of visual explanation, and be not intended to any restriction or the hypothesis of hint to geometrical optics; Further, the element shown in Figure 10 can have respectively and is less than, is greater than or comparable bulk of intending interested wavelength.On first surface region 111, the electromagnetic wave 120 that suddenly dies can be with the first lateral wave vector (corresponding to the surperficial parallel direction in first surface region, in order to simplify, the surperficial parallel direction in first surface region is not shown in the embodiment of Figure 10, but should can be obviously from the similar components 141 shown in Fig. 1,4 and 7) sign, the first lateral wave vector be greater than the first maximum transversal wave vector of definition in equation (23) on second surface region 112, the non-electromagnetic wave 130 that suddenly dies can be with the second lateral wave vector (corresponding to the surperficial parallel direction in second surface region, again in order to simplify, the surperficial parallel direction in second surface region is not shown in the embodiment of Figure 10, but should can be obviously from the similar components 142 shown in Fig. 1,4 and 7) sign, the second lateral wave vector be not more than the second maximum transversal wave vector of definition in equation (24)

In the illustrative embodiment of Figure 10, transformational structure 100 has indefinite electromagnetic parameter, be that (transformational structure provides indefinite medium, as mentioned above, there is the electromagnetic medium of indefinite specific inductive capacity and/or indefinite magnetic permeability), described indefinite dielectric response in the electromagnetic wave 120 that suddenly dies so that propagation of electromagnetic waves is transferred to second surface region 112 from first surface region 111.Indefinite medium has defined axis direction (again in order to simplify, although not shown this axis direction in the embodiment of Figure 10, but should be obviously from the similar components 150 shown in Fig. 1,4 and 7), as mentioned above, axis direction is corresponding to the first eigenvector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix; And indefinite medium has also defined horizontal direction (again in order to simplify, although not shown this horizontal direction in the embodiment of Figure 10, but should be obviously according to the similar components 151 shown in Fig. 1,4 and 7), horizontal direction is perpendicular to axis direction, and corresponding to the Second Characteristic vector of indefinite specific inductive capacity matrix and/or indefinite magnetic permeability matrix.In the illustrative embodiment of Figure 10, axis direction 150 is revocable axis directions, and it is the function of the position in transformational structure 100, and axis direction can be considered to vector field (the vector value function of position).And axis direction points to second surface region 112 from first surface region 111 conventionally, that is, extend to second surface region corresponding to the axial field wire of axis direction vector field from first surface region.In Fig. 1, the dotted line 125 of instruction propagation of electromagnetic waves is also corresponding to axial field wire, this is because illustrative embodiment has been described the indefinite medium of degeneracy, i.e. indefinite medium as above, and this indefinite medium transmits electromagnetic energy along the direction of propagation of the axis direction corresponding to indefinite medium in fact.(this description is not intended to restriction: in other embodiment, indefinite medium is " nondegenerate " the indefinite medium that for example transmits in fact electromagnetic energies along multiple directions of propagation along at least two directions of propagation, each in described at least both direction has the common angles in fact about axis direction, or propagate along multiple directions of propagation, described multiple directions of propagation form in fact the circular cone with consistent with axis direction in fact circular cone axis.)

Referring again to Figure 10, propagate electromagnetic field 125 by the lateral wave vector k corresponding to horizontal direction _tcharacterize (again in order to simplify, although in the embodiment of Figure 10 not shown this horizontal direction, should be obviously according to the similar components 151 shown in Fig. 1,4 and 7).In this example, their geometric divergences in the time that axial field wire (corresponding to the vector field of describing axis direction) advances to second surface region 112 from first surface region 111, and this geometric divergence can provide lateral wave vector k _tthe first lateral wave vector from first surface region (as equation (23), for mating the lateral wave vector of the electromagnetic wave 120 that suddenly dies) are to the second lateral wave vector on second surface region the continuous in fact variation of (as equation (24), for mating the lateral wave vector of the non-electromagnetic wave 130 that suddenly dies).Thereby, there is lateral wave vector from the initial horizontal of maximum wave vector that is greater than non-evanescent wave to wave vector to the propagation of electromagnetic waves 125 of continuous in fact variation of final lateral wave vector of maximum wave vector that is not more than non-evanescent wave by support, the axially geometric divergence of the field wire conversion of electromagnetic wave 120 to the non-electromagnetic wave 130 that suddenly dies that allow suddenly to die.

Refer now to Figure 11, show the hierarchy as the exemplary realization of the transformational structure 100 in Figure 10.In the exemplary realization of Figure 11, transformational structure 100 comprises it being in fact on-plane surface and nonconcentric(al) in fact first surface region 111 and second surface region 112; In the centre of the first and second surf zones, hierarchy provides the effective continuous medium corresponding to indefinite medium.Hierarchy comprises the layer 201 of the first interlaced material and the layer 202 of the second material, and wherein the first and second materials have the electromagnetic parameter that symbol is contrary (for example specific inductive capacity and/or magnetic permeability), as mentioned above.In the exemplary realization of Figure 11, layer 201 and 202 is alternately nonplanar in fact, have with the position in whole hierarchy (, from layer to layer and/or along the lateral extent of every layer) and the layer normal direction that change, and this layer of normal direction corresponding to the axis direction of provided indefinite medium (equivalently, interface between the layer 201 and 202 replacing is thought of as to the equipotential surface of scalar function Φ, according to equation (22), the gradient local of the Φ direction that parallels to the axis).In the exemplary realization of Fig. 3, although the ground floor 301 of hierarchy is consistent in fact with first surface region 111, and last one deck 302 of hierarchy is consistent in fact with second surface region 112, but this is not intended to restriction (in other embodiments, do not illustrate, first surface region 111 is inconsistent with the layer of hierarchy, and/or second surface region 112 is inconsistent with the layer of hierarchy).Nonplanar alternating layer can have identical in fact thickness in the lateral extent of whole layer; Or the lateral extent at whole layer has the thickness being different in essence; Or its combination, as shown in figure 11.

In some embodiments, those transformational structures shown in Fig. 1-11 comprise indefinite conversion medium, have the conversion medium of indefinite electromagnetic parameter.For example, along the geometric divergence of the axial field wire of the dotted line 125 in Fig. 1,4,7 and 10 can meet from for example wherein axially field wire there is no the not coordinate transform of the coordinate space of conversion of geometric divergence.Recall the previous exemplary surface plate of indefinite medium (, the document of equation (3), (5), (9) and/or (11) and these equatioies of enclosing is described), surface plate has the axis direction corresponding to z axle; Therefore, the axial field wire of surface plate is to be parallel to z axle and perpendicular to the straight line of plate face (for illustrative purposes, supposing plate face-its first and second surf zone-lay respectively at z=0 and z=d).In order to obtain indefinite conversion medium, suppose that this surface plate is considered to the original not conversion medium in equation (15) and (16), and consider exemplary coordinate transform, this coordinate transform is mapped to a part of surperficial z=0 the first surface region 111 of transformational structure 100 and a part of surperficial z=d is mapped to the second surface region 112 of transformational structure 100, fixing z (, is arrived to the continuous surface in coordinate transforming space for the part mapping of 0 < z < intermediate surface d) thereby the series of continuous surface in the coordinate space of conversion, cross over the middle region in first surface region and second surface region.Further, the coordinate transform of hypothetical examples provides the magnification increasing progressively on continuous fixing z surface according to amplification coefficient m (z), therefore, two lines that are for example parallel to z axle in the coordinate space of not conversion should scatter in the coordinate space of conversion, and the geodesic distance between two lines is on surface on be proportional to m (z).For the transformational structure 100 of Fig. 1, it has parallel in fact and is in fact the first and second surf zones 111 and 112 of plane, and exemplary coordinate transform is arrived fixing z ' according to equation (25) by the Planar Mapping of fixing z

x′＝m(z)x

y′＝m(z)y (25)

z′＝z

Wherein, m (z) is the amplification coefficient (for example, the m=M > 1 from the m=1 in first surface region to second surface region) increasing with z.In this example, the first and second surf zones of indefinite conversion medium correspond respectively to the first and second surf zones 111 and 112 of the transformational structure 100 of Fig. 1 at z '=0 and z '=d place.According to amplifying coordinate transform (25), the formation parameter of indefinite conversion medium (obtaining in conjunction with the Jacobian matrix (17) corresponding to coordinate transform (25) according to equation (15) and (16)) provides the indefinite medium with the axial field wire disperseing to second surface region geometry from first surface region.Then, for by lateral wave vector k _tthe propagation of electromagnetic waves 125 characterizing, in the time that propagation of electromagnetic waves advances to second surface region 112 from first surface region 111, lateral wave vector and amplification coefficient m (z ') are inversely proportional to, at the first lateral wave vector of the electromagnetic wave 120 that suddenly dies (in first surface region) the second lateral wave vector with the non-electromagnetic wave 130 that suddenly dies (in second surface region) between comprise following relation

$\frac{k_T^{\left(1\right)}}{k_T^{\left(2\right)}}=\frac{m(z^{\&prime;}=d)}{m(z^{\&prime;}=0)}=M---\left(26\right)$

Therefore, transformational structure 100 is for the lateral wave vector of certain limit the electromagnetic wave 120 that will suddenly die is converted to the non-electromagnetic wave 130 that suddenly dies (with reference to equation (23) and (24)); Or, reciprocity ground, transformational structure 100 is for the lateral wave vector of certain limit the non-electromagnetic wave 130 that suddenly dies is converted to the electromagnetic wave 120 that suddenly dies.

In some embodiments, the surface plate of indefinite medium of conversion is not the indefinite medium of degeneracy, provide TM polarized wave (| ε _x| and/or | ε _y| much smaller than | ε _z|), TE polarized wave (| μ _x| and/or | μ _y| much smaller than | μ _z|) or both degeneracy propagate.For example, surface plate can have specific inductive capacity matrix

$\mathrm{\&epsiv;}=\left(\begin{array}{ccc}{\mathrm{\&epsiv;}}_x& 0& 0\\ 0& {\mathrm{\&epsiv;}}_y& 0\\ 0& 0& {\mathrm{\&epsiv;}}_z\end{array}\right)\&ap;\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& {\mathrm{\&epsiv;}}_z\end{array}\right)---\left(27\right)$

(wherein, symbol " ≈ " represents that cross stream component is about zero).In the coordinate space of conversion, new permittivity tensor is

${\widetilde{\mathrm{\&epsiv;}}}^{i^{\&prime;}{j}^{\&prime;}}\&ap;{\left|\det \left(\mathrm{\&Lambda;}\right)\right|}^{-1}{\mathrm{\&Lambda;}}_z^{i^{\&prime;}}{\mathrm{\&Lambda;}}_z^{j^{\&prime;}}{\mathrm{\&epsiv;}}_z---\left(28\right)$

In new coordinate space, can be turned to by diagonal angle

$\widetilde{\mathrm{\&epsiv;}}\&ap;\frac{{\mathrm{\&epsiv;}}_z}{\left|\det \left(\mathrm{\&Lambda;}\right)\right|}\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& {\mathrm{\&Sigma;}}_{i^{\&prime;}}{\mathrm{\&Lambda;}}_z^{i^{\&prime;}}{\mathrm{\&Lambda;}}_z^{i^{\&prime;}}\end{array}\right).---\left(29\right)$

Conversion medium is the new indefinite medium of degeneracy, and it has the axis direction of new spatial variations, is provided by equation (30)

$u_A\&Proportional;(\frac{\&PartialD;x^{\&prime;}}{\&PartialD;z},\frac{\&PartialD;y^{\&prime;}}{\&PartialD;z},\frac{\&PartialD;z^{\&prime;}}{\&PartialD;z})\&Proportional;(x^{\&prime;},y^{\&prime;},\frac{m\left(z^{\&prime;}\right)}{m^{\&prime;}\left(z^{\&prime;}\right)})---\left(30\right)$

(in coordinate base (x ', y ', z ')), wherein the latter's proportional obtains by substituting equation (25).In some embodiments, this conversion medium can be embodied as to nonplanar hierarchy (with reference to previously discussed hierarchy) by vector field (30) being associated with to scalar potential Φ according to equation (22), the interface of the adjacent layer in nonplanar hierarchy is so as to the equipotential surface corresponding to function phi.In the first example, amplification coefficient can increase along with z is linear, for example

$m\left(z\right)=1+(M-1)\frac{z}{d};---\left(31\right)$

The axial vector field (30) producing is corresponding to the scalar potential Φ of equipotential surface with homocentric sphere centered by z '=-d/ (M-1) (or cylinder) in two-dimentional embodiment.The hierarchy of Fig. 2 is similar to the configuration of this class; And, the hierarchy of Fig. 5 and Fig. 8 is similar to the configuration of Fig. 2, although do not exist selected layer to there is nonplanar first surface region or nonplanar second surface region of transformational structure, similar indefinite dielectric property be provided in the inside of transformational structure.In the second example, amplification coefficient can for example, along with the non-linear increase of z,

$m\left(z\right)=1+\frac{M-1}{2}(1-\cos \frac{\mathrm{\&pi;z}}{d})---\left(32\right)$

(choice function dependence is there to be m ' (0)=m ' (d)=0); The axial vector field (30) producing corresponding to have plane from z '=0 by a series of curved surfaces the scalar potential Φ to the continuous equipotential surface of another plane of z '=d.The hierarchy of Fig. 3 is similar to the configuration of this class; And, the hierarchy of Fig. 6 and Fig. 9 is similar to the configuration of Fig. 3, although do not exist selected layer to there is nonplanar first surface region or nonplanar second surface region of transformational structure, similar indefinite dielectric property be provided in the inside of transformational structure.

Fig. 1,4,7 and 10 exemplary transformational structure provide and have been shown as in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic indefinite medium that suddenly dies to be provided.(for example, wherein indefinite medium is the electromagnetic medium of reciprocity) in some embodiments, indefinite medium has reciprocity response alternatively or additionally, indefinite dielectric response in the non-electromagnetic wave that suddenly dies so that the electromagnetic wave that suddenly dies to be provided.In the reciprocity response of the transformational structure 100 in Fig. 1,4,7 and 10, can think that (non-electromagnetic wave 130 and the propagation of electromagnetic waves 125 of suddenly dying have the reverse direction of propagation, space, propagate from right to left in the drawings) and can think that (the electromagnetic wave 120 that suddenly dies has the reverse exponential damping in space, there is exponential damping from right to left, instead of shown exponential damping from left to right).Therefore, in reciprocity situation, transformational structure 100 in second surface region 112 in response to (propagate left) non-electromagnetic wave 130 that suddenly dies so that propagation of electromagnetic waves 125 is transferred to first surface region 111 from second surface region, and (decay left) is provided on first surface region, and electromagnetic wave 120 suddenly dies.As above, suddenly dying electromagnetic wave 120 can be by the first lateral wave vector in equation (23) sign and the non-electromagnetic wave 130 that suddenly dies can be by the second lateral wave vectors in equation (24) characterize.In reciprocity situation, in the time that indefinite medium is the indefinite medium of degeneracy, propagation of electromagnetic waves 125 can be along corresponding to propagating with the direction of propagation of the antiparallel direction of axis direction of indefinite medium.In the time that indefinite medium is the indefinite medium of nondegenerate, propagation of electromagnetic waves 125 can for example be propagated along at least two directions of propagation along multiple directions of propagation, each in described at least both direction have about with the substantial common angles of the antiparallel direction of axis direction, or propagate along multiple directions of propagation, described multiple directions of propagation form in fact the circular cone with consistent with the antiparallel direction of axis direction in fact circular cone axis.In Fig. 1,4,7 and 10 description, in the time that advancing to second surface region 112 from first surface region 111, axial field wire occurs to disperse for how much; Equivalently, occur during to first surface 111 from second surface 112 to assemble for how much.In reciprocity situation, this how much assemble for by lateral wave vector k _tthe propagation of electromagnetic waves 125 characterizing can provide from lateral wave vector k _tsecond surface region (as equation (24), to mate the lateral wave vector of the non-electromagnetic wave 130 that suddenly dies) arrive first surface region the continuous in fact variation of (as equation (23), to mate the lateral wave vector of the electromagnetic wave 120 that suddenly dies).Thereby, there is lateral wave vector from the initial horizontal of maximum wave vector that is not more than non-evanescent wave to wave vector to the propagation of electromagnetic waves of continuous in fact variation of final lateral wave vector of maximum wave vector that is greater than non-evanescent wave by support, axially assemble for how much of field wire and allow the non-conversions of electromagnetic wave 130 to the electromagnetic wave 120 that suddenly dies of suddenly dying.

Some embodiments in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic wave that suddenly dies (and/or vice versa in reciprocity situation) in selected frequency/frequency band and/or selected polarization to be provided.Selected frequency or frequency band can for example, be selected from the scope that comprises radio frequency, microwave frequency, millimeter wave or submillimeter wave frequency, THZ ripple frequency, optical frequency (, corresponding respectively to grenz ray, far ultraviolet, ultraviolet ray, visible ray, near infrared, infrared or far red light) etc.Selected polarization can be TE polarization, TM polarization, circular polarisation etc.(other embodiments in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic wave that suddenly dies of any polarization (for example, for non-polarised electromagnetic energy) to be provided, and/or in reciprocity situation, vice versa).

Some embodiments in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic wave that suddenly dies (and/or vice versa in reciprocity situation) of first frequency to be provided, and further in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic wave that suddenly dies (and/or vice versa in reciprocity situation) of the second frequency different from first frequency to be provided.For the embodiment of narration the first and second frequencies, the first and second frequencies can be selected from the frequency categorization of above paragraph.And for these embodiments, the narration of the first and second frequencies can substitute with the narration of the first and second frequency bands conventionally, again selects from above frequency categorization.These embodiments that respond in the first and second frequencies can comprise the indefinite medium with adjustable electromagnetic property.For example, indefinite medium can have the adjustable electromagnetic property (for example, in response to outside input or control signal) between the first electromagnetic property and the second electromagnetic property, the first electromagnetic property provides in response to the electromagnetic wave that suddenly dies so that the indefinite medium of the non-electromagnetic wave (and/or vice versa) that suddenly dies of first frequency to be provided, and the second electromagnetic property provides in response to the electromagnetic wave that suddenly dies so that the indefinite medium of the non-electromagnetic wave (and/or vice versa) that suddenly dies of second frequency to be provided.The indefinite medium with adjustable electromagnetic response can be realized with variable anisotropic media, for example, as people such as R.A.Hyde, above described in.Can comprise the indefinite medium with the frequency dependence response (forming parameter corresponding to frequency dependence) to electromagnetic radiation at other embodiments of the first and second frequency responses.For example, the frequency dependence response of first frequency can be in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic wave (and/or vice versa) that suddenly dies of first frequency to be provided, and the response of the frequency dependence of second frequency can be in response to the electromagnetic wave that suddenly dies so that the non-electromagnetic wave (and/or vice versa) that suddenly dies of second frequency to be provided.The indefinite medium with the frequency dependence response to electromagnetic radiation can be used such as the material of the manual construction of anisotropic media and realize; For example, having can be with to have second group of anisotropic media element in the response of second frequency staggered at first group of anisotropic media element of the response of first frequency.

Process flow diagram in Figure 12 shows illustrative embodiment.Flow process 1200 comprises that operation 1210-is coupled at input area the electromagnetic wave that suddenly dies.For example, shown in Fig. 1,4,7 and 10, the transformational structure for element 100 is coupled to the electromagnetic wave 120 that suddenly dies on the first surface region 111 of transformational structure.Flow process 1200 comprises that operation 1220-, in response to coupling, propagates into the second surface in output area by the electromagnetic energy of elect magnetic field from the first surface in input area.For example, the transformational structure 100 in Fig. 1,4,7 and 10 is transferred to second surface region 112 by propagation of electromagnetic waves 125 from first surface region 111.First surface can be the outside surface of input area or the inside (for example,, corresponding to the transformational structure having at least partially in the input surface region 111 of transformational structure inside) at least partially in input area.Second surface can be the outside surface of output area or the inside (for example,, corresponding to the transformational structure having at least partially in the output surface region 112 of transformational structure inside) at least partially in output area.Operation 1220 comprises that child-operation 1221-produces the first polarization at first direction, and the first polarization is just corresponding with the first component of the electromagnetic field of first direction; And child-operation 1222-produces the second polarization in the second direction vertical with first direction, the second polarization is born corresponding with the second component of the electromagnetic field of second direction.For example, transformational structure 100 in Fig. 1,4,7 and 10 can provide the indefinite medium with indefinite specific inductive capacity, and this indefinite specific inductive capacity can corresponding at first direction be just and second direction be negative electric susceptibility (wherein, the first and second directions can be corresponding to the axis direction in Fig. 1,4 and 7 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa).Then, propagation of electromagnetic waves 125 can produce electric polarization at first direction, described electric polarization is just corresponding to the electric field component of the propagation of electromagnetic waves of (according to positive electric susceptibility) first direction, and produce electric polarization in second direction further, the electric field component of the negative propagation of electromagnetic waves corresponding to (according to negative electric susceptibility) second direction of described electric polarization.In optional example, transformational structure 100 in Fig. 1,4,7 and 10 can provide the indefinite medium with indefinite magnetic permeability, and indefinite magnetic permeability can corresponding at first direction be just and second direction be negative magnetic polarizability (wherein, the first and second directions can be corresponding to the axis direction in Fig. 1,4 and 7 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa).Then, propagation of electromagnetic waves 125 can produce magnetic polarization at first direction, described magnetic polarization is just corresponding to the magnetic-field component of the propagation of electromagnetic waves of (according to positive magnetic polarizability) first direction, and produce magnetic polarization in second direction further, the magnetic-field component of the negative propagation of electromagnetic waves corresponding to (according to negative magnetic polarizability) second direction of described magnetic polarization.Alternatively, operation 1220 also comprises that child-operation 1223-produces the 3rd polarization at third direction, and the 3rd polarization is just corresponding with the three-component of the electromagnetic field of third direction; And child-operation 1224-produces the 4th polarization in the fourth direction vertical with third direction, the 4th polarization is born corresponding with the 4th component of the electromagnetic field of fourth direction.For example, Fig. 1, 4, transformational structure 100 in 7 and 10 can provide the indefinite medium with indefinite specific inductive capacity and indefinite magnetic permeability, described indefinite specific inductive capacity corresponding at first direction be just and second direction be negative electric susceptibility (wherein, the first and second directions can be corresponding to Fig. 1, 4, axis direction in 7 and 10 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa), and indefinite magnetic permeability corresponding at third direction be just and fourth direction be negative magnetic polarizability (wherein, the third and fourth direction can be corresponding to Fig. 1, 4, axis direction in 7 and 10 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa).Then, propagation of electromagnetic waves 125 can produce: the electric polarization of (1) first direction, (according to positive electric susceptibility) is just corresponding with the electric field component of the propagation of electromagnetic waves of first direction, (2) electric polarization of second direction, (according to negative electric susceptibility) is negative corresponding with the electric field component of the propagation of electromagnetic waves of second direction, (3) magnetic polarization of third direction, (according to positive magnetic polarizability) is just corresponding with the magnetic-field component of the propagation of electromagnetic waves of second direction, and the magnetic polarization of (4) fourth direction, (according to negative magnetic polarizability) is negative corresponding with the magnetic-field component of the propagation of electromagnetic waves of fourth direction.Flow process 1200 comprises that operation 1230-provides the electromagnetic energy of propagation as the non-electromagnetic wave that suddenly dies of output area.For example, the transformational structure 100 in Fig. 1,4,7 and 10 provides the non-electromagnetic wave 130 that suddenly dies on second surface region 112; Electromagnetic wave that the non-electromagnetic wave that suddenly dies can the be Free propagation ripple of the second resistance electromagnetic surface transmitting free radiation (for example from) or propagate limited electromagnetic wave (be for example transmitted as from second surface region and propagate guided wave mode etc.).

Process flow diagram in Figure 13 shows illustrative embodiment.Flow process 1300 comprises that operation 1310-receives the non-electromagnetic wave that suddenly dies in input area.For example, such as in Fig. 1,4,7 and 10 as the transformational structure shown in element 100 on second surface region 112, receive (with Fig. 1 as above, 4,7 and 10 in reciprocity situation) the non-electromagnetic wave 130 that suddenly dies.Flow process 1300 comprises that operation 1320-, in response to reception, propagates into the second surface in output area by the electromagnetic energy of elect magnetic field from the first surface in input area.For example, the transformational structure 100 in Fig. 1,4,7 and 10 (with the reciprocity situation of Fig. 1 as above, 4,7 and 10 situation under) propagation of electromagnetic waves 125 is transferred to first surface region 111 from second surface region 112.First surface can be the outside surface of input area or the inside (for example,, corresponding to the transformational structure having at least partially in the second surface region 112 of transformational structure inside) at least partially in input area.Second surface can be the outside surface of output area or the inside (for example,, corresponding to the transformational structure having at least partially in the first surface region 111 of transformational structure inside) at least partially in output area.Operation 1320 comprises that child-operation 1321-produces the first polarization at first direction, and the first polarization is just corresponding with the first component of the electromagnetic field of first direction; And child-operation 1322-produces the second polarization in the second direction vertical with first direction, the second polarization is born corresponding with the second component of the electromagnetic field of second direction.For example, transformational structure 100 in Fig. 1,4,7 and 10 can provide the indefinite medium with indefinite specific inductive capacity, and indefinite specific inductive capacity can corresponding at first direction be just and second direction be negative electric susceptibility (wherein, the first and second directions can be corresponding to the axis direction in Fig. 1,4 and 7 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa).Then, propagation of electromagnetic waves 125 can produce electric polarization at first direction, described electric polarization is just corresponding to the electric field component of the propagation of electromagnetic waves of (according to positive electric susceptibility) first direction, and produce electric polarization in second direction further, the electric field component of the negative propagation of electromagnetic waves corresponding to (according to negative electric susceptibility) second direction of described electric polarization.In optional example, transformational structure 100 in Fig. 1,4,7 and 10 can provide the indefinite medium with indefinite magnetic permeability, and indefinite magnetic permeability can corresponding at first direction be just and second direction be negative magnetic polarizability (wherein, the first and second directions can be corresponding to the axis direction in Fig. 1,4 and 7 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa).Then, propagation of electromagnetic waves 125 can produce magnetic polarization at first direction, described magnetic polarization is just corresponding to the magnetic-field component of the propagation of electromagnetic waves of (according to positive magnetic polarizability) first direction, and produce magnetic polarization in second direction further, the magnetic-field component of the negative propagation of electromagnetic waves corresponding to (according to negative magnetic polarizability) second direction of described magnetic polarization.Alternatively, operation 1320 also comprises that child-operation 1323-produces the 3rd polarization at third direction, and the 3rd polarization is just corresponding with the three-component of the electromagnetic field of third direction; And child-operation 1324-produces the 4th polarization in the fourth direction vertical with third direction, the 4th polarization is born corresponding with the 4th component of the electromagnetic field of fourth direction.For example, Fig. 1, 4, transformational structure 100 in 7 and 10 can provide the indefinite medium with indefinite specific inductive capacity and indefinite magnetic permeability, described indefinite specific inductive capacity corresponding at first direction be just and second direction be negative electric susceptibility (wherein, the first and second directions can be corresponding to Fig. 1, 4, axis direction in 7 and 10 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa), and indefinite magnetic permeability corresponding at third direction be just and fourth direction be negative magnetic polarizability (wherein, the third and fourth direction can be corresponding to Fig. 1, 4, axis direction in 7 and 10 and horizontal direction 150 and 151, or be parallel or perpendicular to the direction of the light 125 in Figure 10, or vice versa).Then, propagation of electromagnetic waves 125 can produce: the electric polarization of (1) first direction, (according to positive electric susceptibility) is just corresponding with the electric field component of the propagation of electromagnetic waves of first direction, (2) electric polarization of second direction, (according to negative electric susceptibility) is negative corresponding with the electric field component of the propagation of electromagnetic waves of second direction, (3) magnetic polarization of third direction, (according to positive magnetic polarizability) is just corresponding with the magnetic-field component of the propagation of electromagnetic waves of second direction, and the magnetic polarization of (4) fourth direction, (according to negative magnetic polarizability) is negative corresponding with the magnetic-field component of the propagation of electromagnetic waves of fourth direction.Flow process 1300 comprises that operation 1330-is coupled to the electromagnetic energy of propagation the electromagnetic wave that suddenly dies of output area.For example, transformational structure 100 in Fig. 1,4,7 and 10 provides (with the situation that is reciprocity of the situation in previously described Fig. 1,4, the 7 and 10) electromagnetic wave 120 that suddenly dies (for this reciprocity situation on first surface region 111, evanescent wave has the exponential damping away from transformational structure, instead of the described decay that approaches transformational structure).

Referring now to Figure 14, illustrative embodiment is depicted as to system chart.System 1400 comprises the converting unit 1420 that suddenly dies that is coupled to alternatively control module 1440.The converting unit that suddenly dies 1420 can comprise such as the transformational structure that is described as the element 100 in Fig. 1-11.Transformational structure can be variable transformational structure, such as in response to one or more control inputs to change the variable anisotropic media of one or more operating characteristic (effective coordinate transform of the polarization of frequency of operation, operating wave, conversion medium etc.), and control module 1440 can comprise the control circuit that one or more control inputs are provided to variable transformational structure.The converting unit that suddenly dies 1420 can also comprise having for example, location structure (for example one or more piezoelectric working platforms with respect to one or more control inputs of the location/position of transformational structure (suddenly dying in scope in transformational structure) of the location/position for changing transformational structure and/or change sample or target, nanometer positioning device, conveyor/turntable or other drivers), and control module 1440 can comprise alternatively for example, in response to the feedback signal (cantilever force feedback) of carrying out self positioning structure, the control circuit of one or more control inputs is provided to location structure.The converting unit that suddenly dies 1420 can comprise one or more opticses, for example be positioned electromagnetic energy to be sent to the input surface of transformational structure, receive electromagnetic energy from the output surface of transformational structure, electromagnetic energy is sent to sample or the target of the scope that suddenly dies that is positioned at transformational structure, and/or receives electromagnetic energy from the sample of the scope that suddenly dies or the target that are positioned at transformational structure; Control module 1440 can comprise provides the control circuit (for example,, for control azimuth, focus characteristics, aperture size etc.) of one or more control inputs to one or more opticses.System comprises the input block 1410 (for example,, for electromagnetic energy being sent to the converting unit 1420 that suddenly dies) that is coupled to the converting unit 1420 that suddenly dies alternatively; Input block can comprise electromagnet source (such as antenna, laser instrument or transducer) and input circuit and/or the optics such as modulator, phase regulator etc.System comprises the output unit 1430 (for example,, for receiving electromagnetic energy from the converting unit 1420 that suddenly dies) that is coupled to the converting unit 1420 that suddenly dies alternatively; Output unit can comprise electromagnetic detector (such as ccd array, photomultiplier etc.) and output circuit and/or the optics such as detuner, phase regulator, spectroanalysis instrument, image processing circuit etc.

Above United States Patent (USP), United States Patent (USP) that in this instructions, relate to and/or that in any request for data table, list are open, U.S. Patent application, foreign patent, foreign patent application and the disclosed full content of non-patent be by being incorporated into this with quoting in consistent degree herein.

It will be understood by those of skill in the art that parts described herein (for example step), equipment and target and their discussion of enclosing as being convenient to make the example of clear concept, with and the scope that is modified in those skilled in the art of various configurations in.Therefore, as used herein, described instantiation and appended discussion are intended to represent that it more generally classifies.Conventionally, the use of any instantiation herein is also intended to represent its classification, and the expression that should not be considered to not comprising of such concrete parts (for example step), equipment and target is expected its restriction herein.

About the use of considerable any plural number and/or singular references herein, in the time being suitable for this content and/or application, those skilled in the art can be odd number and/or be converted to plural number from odd number from complex conversion.For simplicity, various singular/plural conversion are not specially described herein.

Although illustrated and described the concrete aspect of described theme herein, but those skilled in the art it is evident that, according to instruction herein, do not depart from herein described theme and wider aspect prerequisite under can change and revise, therefore, claims are for being included in all of these changes and modifications that fall in true spirit and the scope of theme described herein within the scope of it.And, should be understood that the present invention is defined by the following claims.It will be understood by those of skill in the art that, conventionally the term herein and especially for example, using in claims (main body of claim) is intended to that (for example term " comprises (including) " should be interpreted as " including but not limited to " as " open " term conventionally, term " has " should be interpreted as " at least having ", term " comprise (includes) " and should be interpreted as " including but not limited to " etc.).Those skilled in the art will be further understood that, if wish the concrete quantity that refers to that introduced claim describes in detail, and the clearly statement in the claims of such intention, and while lacking such statement, will not there is not such intention.For example, for the ease of understanding, below claims can comprise introductory phrase " at least one " and " one or more " use to introduce claim detailed description.But, the use of such phrase should not be interpreted as claim that hint introduces by indefinite article " " and any concrete right that the claim that comprises introduction like this is described in detail is described in detail in detail requires to be restricted to the invention that only comprises this detailed description, comprises introductory phrase " one or more " or " at least one " and the indefinite article (for example " " should be interpreted as " at least one " or " one or more " conventionally) such as " " even if work as identical claim; Use for the indefinite article in the time introducing claim detailed description is suitable for this principle equally.In addition, even if the concrete quantity that the claim of introducing describes in detail is clearly explained, but will be appreciated that such detailed description, those skilled in the art conventionally should be construed as the quantity (for example, in the situation that there is no other amendments, the literal meaning of " two detailed descriptions " is at least two detailed descriptions or two or more detailed descriptions normally) that at least described in detail.And, in these cases, wherein use the idiom that is similar to " at least one in A, B and C etc. ", conventionally such structure is intended to mean and it should be appreciated by those skilled in the art that idiom (for example, " system has at least one in A, B and C " will include but not limited to system only have A, only have B, only have C, have A and B, have A and C, have B and C and/or have A, B and C etc.).In these cases, wherein use the idiom that is similar to " at least one in A, B and C etc. ", conventionally such structure is intended to mean and it should be appreciated by those skilled in the art that idiom (for example, " system has at least one in A, B and C " will include but not limited to system only have A, only have B, only have C, have A and B, have A and C, have B and C and/or have A, B and C etc.).Antisense conjunction and/or the phrase of what those skilled in the art will be further understood that is nearly all two or more optional terms of description, no matter in instructions, claim or accompanying drawing, all should be understood to comprise any one or two terms in term one, term.For example, phrase " A or B " will be understood to comprise " A " or " B " or " A and B ".

About claims, those skilled in the art will understand operation detailed in this article and conventionally can carry out in any order.Unless pointed out in addition in literary composition, that the example of so optional order can comprise is overlapping, interlock, interrupt, resequence, increase progressively, prepare, supplement, synchronous, oppositely or other modification sequences.About content, unless in literary composition, point out in addition, even if be similar to " in response to " " relating to " or other preterite adjectives be not intended to get rid of its modification conventionally.

Although disclose many aspects and embodiment herein, other aspects and embodiment are apparent for those skilled in the art.Many aspects disclosed herein and embodiment are only for the object that illustrates and be not intended to restriction, by the scope and spirit of following claim instruction essence.

Claims (52)

1. a calutron, comprising:

Transformational structure, described transformational structure has the electromagnetic parameter that comprises indefinite tensor parameter, described transformational structure in response to the electromagnetic wave that suddenly dies in first surface region so that the non-electromagnetic wave that suddenly dies to be provided in second surface region, wherein said first surface region is in fact plane and parallel in fact with described second surface region

Wherein said transformational structure is in response to the electromagnetic wave that suddenly dies of first frequency with the first wave number so that the non-electromagnetic wave that suddenly dies of the first frequency with the second wave number to be provided, and described the first wave number is the surperficial parallel direction corresponding to described second surface region corresponding to the surperficial parallel direction in described first surface region and described the second wave number;

Wherein first area outside in described transformational structure and next-door neighbour described first surface region defines the first-phase bit rate of electromagnetic radiation, and described the first wave number is greater than the business of described first frequency and described first-phase bit rate;

Wherein second area outside in described transformational structure and next-door neighbour described second surface region defines the second-phase bit rate of electromagnetic radiation, and described the second wave number is less than the business of described first frequency and described second-phase bit rate.

2. a calutron, comprising:

Transformational structure, described transformational structure has the electromagnetic parameter that comprises indefinite tensor parameter, described transformational structure in response to the electromagnetic wave that suddenly dies in first surface region so that the non-electromagnetic wave that suddenly dies to be provided in second surface region, in wherein said first surface region and described second surface region one is the surf zone of plane in fact, and another in described first surface region and described second surface region is nonplanar in fact surf zone

Wherein said transformational structure is in response to the electromagnetic wave that suddenly dies of first frequency with the first wave number so that the non-electromagnetic wave that suddenly dies of the first frequency with the second wave number to be provided, and described the first wave number is the surperficial parallel direction corresponding to described second surface region corresponding to the surperficial parallel direction in described first surface region and described the second wave number;

Wherein first area outside in described transformational structure and next-door neighbour described first surface region defines the first-phase bit rate of electromagnetic radiation, and described the first wave number is greater than the business of described first frequency and described first-phase bit rate;

Wherein second area outside in described transformational structure and next-door neighbour described second surface region defines the second-phase bit rate of electromagnetic radiation, and described the second wave number is less than the business of described first frequency and described second-phase bit rate.

3. calutron according to claim 2, wherein said first surface region is the surf zone of plane in fact.

4. calutron according to claim 2, wherein said second surface region is the surf zone of plane in fact.

5. calutron according to claim 2, the surf zone that wherein said nonplanar in fact surf zone is essence fovea superior or the surf zone of essence epirelief.

6. a calutron, comprising:

Transformational structure, described transformational structure has the electromagnetic parameter that comprises indefinite tensor parameter, described transformational structure in response to the electromagnetic wave that suddenly dies in first surface region so that the non-electromagnetic wave that suddenly dies to be provided in second surface region, wherein said first surface region and described second surface region are nonplanar in fact and nonconcentric(al) in fact

Wherein said transformational structure is in response to the electromagnetic wave that suddenly dies of first frequency with the first wave number so that the non-electromagnetic wave that suddenly dies of the first frequency with the second wave number to be provided, and described the first wave number is the surperficial parallel direction corresponding to described second surface region corresponding to the surperficial parallel direction in described first surface region and described the second wave number;

Wherein first area outside in described transformational structure and next-door neighbour described first surface region defines the first-phase bit rate of electromagnetic radiation, and described the first wave number is greater than the business of described first frequency and described first-phase bit rate;

Wherein second area outside in described transformational structure and next-door neighbour described second surface region defines the second-phase bit rate of electromagnetic radiation, and described the second wave number is less than the business of described first frequency and described second-phase bit rate.

7. calutron according to claim 6, wherein said first surface region and described second surface region are essence fovea superiors.

8. calutron according to claim 6, wherein said first surface region and described second surface region are essence epireliefs.

9. calutron according to claim 6, the center of first osculating circle in wherein said first surface region is different from the center of second osculating circle in described second surface region, and described the second osculating circle and described the first osculating circle are coplanar.

10. calutron according to claim 9, wherein said first surface region is that second surface essence fovea superior and described region is essence epirelief.

11. calutrons according to claim 9, wherein said first surface region is that second surface essence epirelief and described region is essence fovea superior.

12. according to the calutron described in claim 1,2 or 6, and wherein said indefinite tensor parameter comprises indefinite permittivity tensor parameter.

13. according to the calutron described in claim 1,2 or 6, and wherein said indefinite tensor parameter comprises indefinite permeability tensor parameter.

14. according to the calutron described in claim 1,2 or 6, and wherein said transformational structure comprises continuous adjacent layer.

15. calutrons according to claim 14, wherein said continuous adjacent layer is that the first alternative materials and the second alternative materials replace continuous adjacent layer.

16. calutrons according to claim 15, wherein said the first alternative materials is that metal and described the second alternative materials are dielectric or gain media.

17. calutrons according to claim 15, wherein said the first alternative materials is that the first semiconductor material and described the second alternative materials are the second semiconductor materials.

18. according to the calutron described in claim 1,2 or 6, and wherein said indefinite tensor parameter comprises the indefinite tensor property value corresponding to indefinite tensor property vector, and described electromagnetic parameter comprises:

Corresponding to the axial magnetic parameter of axis direction, described axis direction is selected from described indefinite tensor property vector; And

Corresponding to the transverse-electromagnetic parameter of horizontal direction, described horizontal direction is vertical in fact with described axis direction.

19. calutrons according to claim 18, wherein said transformational structure is transferred to described second surface region by the electromagnetic wave of propagation from described first surface region with the direction of propagation consistent in fact with described axis direction, edge in response to the electromagnetic wave that suddenly dies on described first surface region.

20. calutrons according to claim 18, wherein said transformational structure is in response to the electromagnetic wave that suddenly dies on described first surface region to be transferred to described second surface region by the electromagnetic wave of propagation from described first surface region along both direction at least, and each in described at least both direction has in fact the common angles about described axis direction.

21. calutrons according to claim 18, wherein said axial magnetic parameter comprises axial specific inductive capacity, and described transverse-electromagnetic parameter comprises transverse magnetic conductance and horizontal specific inductive capacity.

22. calutrons according to claim 21, wherein said axial specific inductive capacity is less than zero, and described horizontal specific inductive capacity is more than or equal to zero, and described transverse magnetic conductance is more than or equal to zero.

23. calutrons according to claim 21, wherein said axial specific inductive capacity is greater than zero, and described horizontal specific inductive capacity is less than or equal to zero, and described transverse magnetic conductance is less than or equal to zero.

24. calutrons according to claim 18, wherein said axial magnetic parameter comprises axial magnetic conductance, and described transverse-electromagnetic parameter comprises transverse magnetic conductance and horizontal specific inductive capacity.

25. calutrons according to claim 24, wherein said axial magnetic conductance is less than zero, and described horizontal specific inductive capacity is more than or equal to zero, and described transverse magnetic conductance is more than or equal to zero.

26. calutrons according to claim 24, wherein said axial magnetic conductance is greater than zero, and described horizontal specific inductive capacity is less than or equal to zero, and described transverse magnetic conductance is less than or equal to zero.

27. according to the calutron described in claim 1,2 or 6, and wherein said transformational structure comprises the material having corresponding to the manual construction of effective electromagnetic response of described electromagnetic parameter.

28. calutrons according to claim 27, the material of wherein said manual construction comprises anisotropic media.

29. calutrons according to claim 28, wherein said anisotropic media comprises the multiple electromagnetic response elements that are arranged on multiple locus and have multiple independent responses, described multiple independent responses form described effective electromagnetic response.

30. calutrons according to claim 29, wherein said electromagnetic response element comprises discrete circuit element, integrated circuit component, printed circuit elements, metal construction, LC resonator, plasma resonance device, nanostructured or open-loop resonator.

31. 1 kinds are transformed into the non-electromagnetic method that suddenly dies for the electromagnetic wave that will suddenly die, comprise:

Be coupled at input area the electromagnetic wave that suddenly dies;

In response to described coupling, the electromagnetic energy of elect magnetic field is propagated into the second surface in output area from the first surface in described input area, wherein said first surface is in fact plane and parallel in fact with described second surface, and wherein said propagation comprises:

Produce the first polarization at first direction, the first component on described first direction is just corresponding with described electromagnetic field in described the first polarization; And

Produce the second polarization in the second direction vertical with described first direction, described the second polarization is negative corresponding with the second component of described electromagnetic field in described second direction;

And

At described output area, provide propagated electromagnetic energy as the non-electromagnetic wave that suddenly dies;

The wherein said electromagnetic wave that suddenly dies that is coupled to is the electromagnetic wave that suddenly dies that is coupled to the first frequency with the first wave number, and the non-electromagnetic wave that suddenly dies that provides the described non-electromagnetic wave that suddenly dies to be to provide the first frequency with the second wave number, described the first wave number is the surperficial parallel direction corresponding to described second surface corresponding to the surperficial parallel direction of described first surface and described the second wave number;

Wherein said first surface and described second surface limit the interior zone in the middle of described first surface and described second surface, the first perimeter outside at described interior zone and that be close to described first surface limits the first-phase bit rate of electromagnetic radiation, and described the first wave number is greater than the business of described first frequency and described first-phase bit rate;

Wherein the second perimeter outside at described interior zone and the described second surface of next-door neighbour limits the second-phase bit rate of electromagnetic radiation, and described the second wave number is less than the business of described first frequency and described second-phase bit rate.

32. 1 kinds are transformed into the non-electromagnetic method that suddenly dies for the electromagnetic wave that will suddenly die, comprise:

Be coupled at input area the electromagnetic wave that suddenly dies;

In response to described coupling, the electromagnetic energy of elect magnetic field is propagated into the second surface in output area from the first surface in described input area, in wherein said first surface and described second surface one is that another in surface and described first surface and the described second surface of plane is in fact nonplanar in fact surface, and wherein said propagation comprises:

Produce the first polarization at first direction, the first component on described first direction is just corresponding with described electromagnetic field in described the first polarization; And

Produce the second polarization in the second direction vertical with described first direction, described the second polarization is negative corresponding with the second component of described electromagnetic field in described second direction;

And

At described output area, provide propagated electromagnetic energy as the non-electromagnetic wave that suddenly dies;

The wherein said electromagnetic wave that suddenly dies that is coupled to is the electromagnetic wave that suddenly dies that is coupled to the first frequency with the first wave number, and the non-electromagnetic wave that suddenly dies that provides the described non-electromagnetic wave that suddenly dies to be to provide the first frequency with the second wave number, described the first wave number is the surperficial parallel direction corresponding to described second surface corresponding to the surperficial parallel direction of described first surface and described the second wave number;

Wherein said first surface and described second surface limit the interior zone in the middle of described first surface and described second surface, the first perimeter outside at described interior zone and that be close to described first surface limits the first-phase bit rate of electromagnetic radiation, and described the first wave number is greater than the business of described first frequency and described first-phase bit rate;

Wherein the second perimeter outside at described interior zone and the described second surface of next-door neighbour limits the second-phase bit rate of electromagnetic radiation, and described the second wave number is less than the business of described first frequency and described second-phase bit rate.

33. 1 kinds are transformed into the non-electromagnetic method that suddenly dies for the electromagnetic wave that will suddenly die, comprise:

Be coupled at input area the electromagnetic wave that suddenly dies;

In response to described coupling, the electromagnetic energy of elect magnetic field is propagated into the second surface in output area from the first surface in described input area, wherein said first surface and described second surface are nonplanar in fact and are nonconcentric(al) in fact, and wherein said propagation comprises:

Produce the first polarization at first direction, the first component on described first direction is just corresponding with described electromagnetic field in described the first polarization; And

Produce the second polarization in the second direction vertical with described first direction, described the second polarization is negative corresponding with the second component of described electromagnetic field in described second direction;

And

At described output area, provide propagated electromagnetic energy as the non-electromagnetic wave that suddenly dies;

The wherein said electromagnetic wave that suddenly dies that is coupled to is the electromagnetic wave that suddenly dies that is coupled to the first frequency with the first wave number, and the non-electromagnetic wave that suddenly dies that provides the described non-electromagnetic wave that suddenly dies to be to provide the first frequency with the second wave number, described the first wave number is the surperficial parallel direction corresponding to described second surface corresponding to the surperficial parallel direction of described first surface and described the second wave number;

Wherein said first surface and described second surface limit the interior zone in the middle of described first surface and described second surface, the first perimeter outside at described interior zone and that be close to described first surface limits the first-phase bit rate of electromagnetic radiation, and described the first wave number is greater than the business of described first frequency and described first-phase bit rate;

Wherein the second perimeter outside at described interior zone and the described second surface of next-door neighbour limits the second-phase bit rate of electromagnetic radiation, and described the second wave number is less than the business of described first frequency and described second-phase bit rate.

34. 1 kinds for being transformed into by the non-electromagnetic wave that suddenly dies the electromagnetic method that suddenly dies, and comprising:

Receive the non-electromagnetic wave that suddenly dies at input area;

In response to described reception, the electromagnetic energy of elect magnetic field is propagated into the second surface in output area from the first surface in described input area, wherein said first surface is in fact plane and parallel in fact with described second surface, and wherein said propagation comprises:

Produce the first polarization at first direction, the first component on described first direction is just corresponding with described electromagnetic field in described the first polarization; And

Produce the second polarization in the second direction vertical with described first direction, described the second polarization is negative corresponding with the second component of described electromagnetic field in described second direction;

And

At described output area, propagated electromagnetic energy is coupled to the electromagnetic wave that suddenly dies;

The non-electromagnetic wave that suddenly dies of wherein said reception is the non-electromagnetic wave that suddenly dies that receives the first frequency with the first wave number, and described in to be coupled to the electromagnetic wave that suddenly dies be the electromagnetic wave that suddenly dies that is coupled to the first frequency with the second wave number, described the first wave number is the surperficial parallel direction corresponding to described second surface corresponding to the surperficial parallel direction of described first surface and described the second wave number;

Wherein said first surface and described second surface limit the interior zone in the middle of described first surface and described second surface, the first perimeter outside at described interior zone and that be close to described first surface limits the first-phase bit rate of electromagnetic radiation, and described the first wave number is less than the business of described first frequency and described first-phase bit rate;

Wherein the second perimeter outside at described interior zone and that be close to described second surface limits the second-phase bit rate of electromagnetic radiation, and described the second wave number is greater than the business of described first frequency and described second-phase bit rate.

35. 1 kinds for being transformed into by the non-electromagnetic wave that suddenly dies the electromagnetic method that suddenly dies, and comprising:

Receive the non-electromagnetic wave that suddenly dies at input area;

In response to described reception, the electromagnetic energy of elect magnetic field is propagated into the second surface in output area from the first surface in described input area, in wherein said first surface and described second surface one is that another in surface and described first surface and the described second surface of plane is in fact nonplanar in fact surface, and wherein said propagation comprises:

Produce the first polarization at first direction, the first component on described first direction is just corresponding with described electromagnetic field in described the first polarization; And

Produce the second polarization in the second direction vertical with described first direction, described the second polarization is negative corresponding with the second component of described electromagnetic field in described second direction;

And

At described output area, propagated electromagnetic energy is coupled to the electromagnetic wave that suddenly dies;

The non-electromagnetic wave that suddenly dies of wherein said reception is the non-electromagnetic wave that suddenly dies that receives the first frequency with the first wave number, and described in to be coupled to the electromagnetic wave that suddenly dies be the electromagnetic wave that suddenly dies that is coupled to the first frequency with the second wave number, described the first wave number is the surperficial parallel direction corresponding to described second surface corresponding to the surperficial parallel direction of described first surface and described the second wave number;

Wherein said first surface and described second surface limit the interior zone in the middle of described first surface and described second surface, the first perimeter outside at described interior zone and that be close to described first surface limits the first-phase bit rate of electromagnetic radiation, and described the first wave number is less than the business of described first frequency and described first-phase bit rate;

Wherein the second perimeter outside at described interior zone and that be close to described second surface limits the second-phase bit rate of electromagnetic radiation, and described the second wave number is greater than the business of described first frequency and described second-phase bit rate.

36. 1 kinds for being transformed into by the non-electromagnetic wave that suddenly dies the electromagnetic method that suddenly dies, and comprising:

Receive the non-electromagnetic wave that suddenly dies at input area;

In response to described reception, the electromagnetic energy of elect magnetic field is propagated into the second surface in output area from the first surface in described input area, wherein said first surface and described second surface are in fact on-plane surfaces and non-in fact concentric, and wherein said propagation comprises:

Produce the first polarization at first direction, the first component on described first direction is just corresponding with described electromagnetic field in described the first polarization; And

Produce the second polarization in the second direction vertical with described first direction, described the second polarization is negative corresponding with the second component of described electromagnetic field in described second direction;

And

At described output area, propagated electromagnetic energy is coupled to the electromagnetic wave that suddenly dies;

The non-electromagnetic wave that suddenly dies of wherein said reception is the non-electromagnetic wave that suddenly dies that receives the first frequency with the first wave number, and described in to be coupled to the electromagnetic wave that suddenly dies be the electromagnetic wave that suddenly dies that is coupled to the first frequency with the second wave number, described the first wave number is the surperficial parallel direction corresponding to described second surface corresponding to the surperficial parallel direction of described first surface and described the second wave number;

Wherein said first surface and described second surface limit the interior zone in the middle of described first surface and described second surface, the first perimeter outside at described interior zone and that be close to described first surface limits the first-phase bit rate of electromagnetic radiation, and described the first wave number is less than the business of described first frequency and described first-phase bit rate;

Wherein the second perimeter outside at described interior zone and that be close to described second surface limits the second-phase bit rate of electromagnetic radiation, and described the second wave number is greater than the business of described first frequency and described second-phase bit rate.

37. according to the method described in claim 32 or 35, and wherein said first surface is the surface of plane in fact.

38. according to the method described in claim 32 or 35, and wherein said second surface is the surface of plane in fact.

39. according to the method described in claim 32 or 35, wherein said nonplanar in fact surperficial essence fovea superior to or essence epirelief to the surface of described plane in fact.

40. according to the method described in claim 33 or 36, and wherein said first surface essence fovea superior is to described second surface and described second surface essence fovea superior to described first surface.

41. according to the method described in claim 33 or 36, and wherein said first surface essence epirelief is to described second surface and described second surface essence epirelief to described first surface.

42. according to the method described in claim 33 or 36, and the center of the first osculating circle of wherein said first surface is different from the center of the second osculating circle of described second surface, and described the second osculating circle and described the first osculating circle are coplanar.

43. according to the method described in claim 42, and wherein said first surface essence fovea superior is to described second surface and described second surface essence epirelief to described first surface.

44. according to the method described in claim 42, and wherein said first surface essence epirelief is to described second surface and described second surface essence fovea superior to described first surface.

45. according to the method described in any one in claim 31-36, and wherein said the first polarization is the first electric polarization, and described the first component is the first electric component, and described the second polarization is the second electric polarization, and described second component is the second electric component.

46. according to the method described in any one in claim 31-36, and wherein said the first polarization is the first magnetic polarization, and described the first component is the first magnetic component, and described the second polarization is the second magnetic polarization, and described second component is the second magnetic component.

47. according to the method described in any one in claim 31-36, and wherein said propagation also comprises:

Produce the 3rd polarization at third direction, described the 3rd polarization is just corresponding with the three-component of described electromagnetic field on described third direction; And

Produce the 4th polarization in the fourth direction vertical with described third direction, the 4th component in described fourth direction is negative corresponding with described electromagnetic field in described the 4th polarization.

48. according to the method described in claim 47, and wherein said third direction and described first direction are equal in fact or are equal in fact with described second direction, or in fact mutually vertical with described second direction with described first direction.

49. according to the method described in claim 47, and wherein said fourth direction and described first direction are equal in fact or are equal in fact with described second direction, or in fact mutually vertical with described second direction with described first direction.

50. according to the method described in claim 47, wherein said the first polarization is the first electric polarization, described the first component is the first electric component, described the second polarization is the second electric polarization, described second component is the second electric component, and described the 3rd polarization is the first magnetic polarization, and described three-component is the first magnetic component, described the 4th polarization is the second magnetic polarization, and described the 4th component is the second magnetic component.

51. according to the method described in any one in claim 31-36, and wherein said propagation is the propagation along the direction of propagation consistent in fact with the direction of selecting from described first direction and described second direction.

52. according to the method described in any one in claim 31-36, wherein said propagation is the propagation along at least two directions of propagation, and each in described at least two directions of propagation has in fact the common angles about the direction of selecting from described first direction and described second direction.