EP2419774A1 - Appareil et procédés de conversion d'onde électromagnétique évanescente - Google Patents

Appareil et procédés de conversion d'onde électromagnétique évanescente

Info

Publication number
EP2419774A1
EP2419774A1 EP10764783A EP10764783A EP2419774A1 EP 2419774 A1 EP2419774 A1 EP 2419774A1 EP 10764783 A EP10764783 A EP 10764783A EP 10764783 A EP10764783 A EP 10764783A EP 2419774 A1 EP2419774 A1 EP 2419774A1
Authority
EP
European Patent Office
Prior art keywords
electromagnetic
region
polarization
evanescent
electromagnetic wave
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP10764783A
Other languages
German (de)
English (en)
Other versions
EP2419774A4 (fr
Inventor
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
Jr. Lowell L. Wood
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Searete LLC
Original Assignee
Searete LLC
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from US12/386,522 external-priority patent/US8634141B2/en
Priority claimed from US12/460,137 external-priority patent/US8634144B2/en
Priority claimed from US12/460,122 external-priority patent/US8630044B2/en
Priority claimed from US12/590,010 external-priority patent/US9081123B2/en
Priority claimed from US12/589,913 external-priority patent/US9081202B2/en
Priority claimed from US12/589,925 external-priority patent/US9083082B2/en
Application filed by Searete LLC filed Critical Searete LLC
Publication of EP2419774A1 publication Critical patent/EP2419774A1/fr
Publication of EP2419774A4 publication Critical patent/EP2419774A4/fr
Withdrawn legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/262—Optical details of coupling light into, or out of, or between fibre ends, e.g. special fibre end shapes or associated optical elements
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/56—Optics using evanescent waves, i.e. inhomogeneous waves
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/32—Optical coupling means having lens focusing means positioned between opposed fibre ends
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials

Definitions

  • the present application is related to and claims the benefit of the earliest available effective filing date(s) from the following listed application(s) (the "Related Applications") (e.g. , claims earliest available priority dates for other than provisional patent applications or claims benefits under 35 USC ⁇ 119(e) for provisional patent applications, for any and all parent, grandparent, great-grandparent, etc. applications of the Related Application(s)).
  • the Related Applications e.g. , claims earliest available priority dates for other than provisional patent applications or claims benefits under 35 USC ⁇ 119(e) for provisional patent applications, for any and all parent, grandparent, great-grandparent, etc. applications of the Related Application(s)).
  • AU subject matter of the Related Applications and of any and all parent, grandparent, great-grandparent, etc. applications of the Related Applications is incorporated herein by reference to the extent such subject matter is not inconsistent herewith.
  • the application discloses apparatus and methods that may relate to electromagnetic responses that include electromagnetic near-field lensing and/or conversion of evanescent electromagnetic waves to non-evanescent electromagnetic waves and/or conversion of non-evanescent electromagnetic waves to evanescent electromagnetic waves.
  • FIG. 1 depicts a conversion structure having first and second surface regions that are substantially planar and substantially parallel.
  • FIG. 2 depicts a layered structure as an exemplary implementation of the conversion structure of FIG. 1.
  • FIG. 3 depicts a layered structure as an exemplary implementation of the conversion structure of FIG. 1.
  • FIG. 4 depicts a conversion structure having a first surface region that is substantially planar and a second surface region that is substantially nonplanar.
  • FIG. 5 depicts a layered structure as an exemplary implementation of the conversion structure of FIG.4.
  • FIG. 6 depicts a layered structure as an exemplary implementation of the conversion structure of FIG.4.
  • FIG. 7 depicts a conversion structure having a first surface region that is substantially nonplanar and a second surface region that is substantially planar.
  • FIG. 8 depicts a layered structure as an exemplary implementation of the conversion structure of FIG. 7.
  • FIG. 9 depicts a layered structure as an exemplary implementation of the conversion structure of FIG. 7.
  • FIG. 10 depicts various conversion structures having first and second surface regions that are substantially nonplanar.
  • FIG. 11 depicts a layered structure as an exemplary implementation of a conversion structure as in FIG. 10.
  • FIG. 12 depicts a first process flow.
  • FIG. 13 depicts a second process flow reciprocal to the first process flow.
  • FIG. 14 depicts a system that includes an evanescent conversion unit.
  • Embodiments provide apparatus and methods for converting evanescent electromagnetic waves to non-evanescent electromagnetic waves and/or for converting non-evanescent electromagnetic waves to evanescent electromagnetic waves.
  • an evanescent electromagnetic wave is an electromagnetic wave having an amplitude that decays exponentially with distance, e.g. having a wave vector that is at least partially imaginary.
  • the electric component of an electromagnetic wave may have a 2D Fourier expansion given by
  • E(r,0 ⁇ E ⁇ (k x ,k y )exp(ik : z + ik x x + ik y y-i ⁇ t) .
  • a conventional far-field optical system has a resolution limit ⁇ (sometimes referred to as a diffraction limit or an Abbe-Rayleigh limit) corresponding to a maximum transverse wavevector k max for propagating waves:
  • embodiments disclosed herein provide apparatus and methods that may exceed this resolution limit, by converting evanescent waves to propagating waves (or vice versa) in an indefinite electromagnetic medium.
  • an indefinite electromagnetic medium is an electromagnetic medium having electromagnetic parameters (e.g. permittivity and/or permeability) that include indefinite tensor parameters.
  • electromagnetic parameters e.g. permittivity and/or permeability
  • indefinite is taken to have its algebraic meaning; thus, an indefinite tensor is a tensor that is neither positive definite (having all positive eigenvalues) nor negative definite (having all negative eigenvalues) but instead has at least one positive eigenvalue and at least one negative eigenvalue.
  • an indefinite medium is an electromagnetic medium having an indefinite permeability.
  • An example of an indefinite permeability medium is a planar slab having a z-axis perpendicular to the slab (with x- and y- axes parallel to the slab) and electromagnetic parameters ⁇ y , ⁇ x , and ⁇ . satisfying the inequalities ⁇ , ⁇ x > o, ⁇ j ⁇ .- ⁇ o (3)
  • the permeability is indefinite, with either ⁇ x ⁇ 0 ⁇ ⁇ . or ⁇ x > 0 > ⁇ . ).
  • these electromagnetic parameters provide a hyperbolic dispersion relation that admits propagating electromagnetic waves (real k. ) with large transverse wavevectors k x .
  • an evanescent wave in the adjoining medium e.g.
  • the propagating wave is characterized by group velocities that are substantially perpendicular to the asymptotes of equation (4), i.e. the propagating wave is substantially conveyed along propagation directions in the xz-plane that form an angle O x with respect to the z-axis (e.g. as depicted in Fig. 10 of the previously cited U.S. Patent Application No.
  • the planar slab may alternately or additionally have electromagnetic parameters ⁇ x and ⁇ y , satisfying the alternate or additional inequalities ⁇ x ⁇ y > 0, ⁇ y / ⁇ z ⁇ 0, (5) providing another hyperbolic dispersion relation
  • a propagating wave in the indefinite medium is characterized by group velocities that are substantially perpendicular to the asymptotes of equation (6), i.e.
  • an indefinite permeability medium may define an axial direction that corresponds to a first eigenvector of the indefinite permeability matrix, with first and second transverse directions that correspond to second and third eigenvectors of the indefinite permeability matrix, respectively.
  • the parameters of the indefinite permeability matrix may vary with position within the indefinite permeability medium, and correspondingly the eigenvectors of the indefinite permeability matrix may also vary with position within the indefinite permeability medium.
  • the disclosure of the preceding paragraph may encompass more general embodiments of an indefinite permeability medium, in the following manner: the z-axis shall be understood to refer more generally to an axial direction that may vary throughout the indefinite medium, the x-axis shall be understood to refer more generally to a first transverse direction perpendicular to the axial direction, and the y-axis shall be understood to refer more generally to a second transverse direction mutually perpendicular to the axial direction and the first transverse direction.
  • , the medium is a degenerate indefinite medium, wherein the cone of propagation directions degenerates to a single propagation direction that
  • an indefinite medium is an electromagnetic medium having an indefinite permittivity.
  • An example of an indefinite permittivity medium is a planar slab having a z-axis perpendicular to the slab (with x- and y- axes parallel to the slab), and having electromagnetic parameters ⁇ y , ⁇ x , and ⁇ . satisfying the inequalities
  • the permittivity is indefinite, with either ⁇ x ⁇ 0 ⁇ ⁇ . or ⁇ x > 0 > ⁇ . ).
  • TM- polarized (i.e. p-polarized) electromagnetic waves with a magnetic field directed along the y-axis these electromagnetic parameters provide a hyperbolic dispersion relation that admits propagating electromagnetic waves (real k. ) with large transverse wavevectors k x .
  • an evanescent wave in the adjoining medium e.g.
  • the propagating wave is characterized by group velocities that are substantially perpendicular to the asymptotes of equation (10), i.e.
  • the planar slab may alternately or additionally have electromagnetic parameters ⁇ x and ⁇ y , satisfying the alternative or additional inequalities ⁇ x ⁇ y > 0, ⁇ y / ⁇ : ⁇ 0 , (11) providing another hyperbolic dispersion relation for TM-polarized electromagnetic waves with a magnetic field directed along the x- axis.
  • a propagating wave in the indefinite medium is characterized by group velocities that are substantially perpendicular to the asymptotes of equation (12), i.e.
  • an indefinite permittivity medium may define an axial direction that corresponds to a first eigenvector of the indefinite permittivity matrix, with first and second transverse directions that correspond to second and third eigenvectors of the indefinite permittivity matrix, respectively.
  • the parameters of the indefinite permittivity matrix may vary with position within the indefinite permittivity medium, and correspondingly the eigenvectors of the indefinite permittivity matrix may also vary with position within the indefinite permittivity medium.
  • the disclosure of the preceding paragraph may encompass more general embodiments of an indefinite permittivity medium, in the following manner: the z- axis shall be understood to refer more generally to an axial direction that may vary throughout the indefinite medium, the x-axis shall be understood to refer more generally to a first transverse direction perpendicular to the axial direction, and the y- axis shall be understood to refer more generally to a second transverse direction mutually perpendicular to the axial direction and the first transverse direction.
  • this dispersion relation supports TM-polarized waves that substantially propagate (for sufficiently large transverse wavevectors k ⁇ ) along propagation directions that locally compose a circular cone having a cone axis that coincides with the local axial direction with a cone half-angle ⁇ (and where ⁇ sc ⁇ A , the medium is a degenerate indefinite medium, wherein the cone of propagation directions degenerates to a single propagation direction that substantially coincides with the local axial direction).
  • an indefinite medium is an electromagnetic medium that is "doubly indefinite," i.e. having both an indefinite permittivity and an indefinite permeability.
  • An example of a doubly indefinite medium is a planar slab defining a z-axis perpendicular to the slab (with x- and y- axes parallel to the slab), and having electromagnetic parameters satisfying one or both of equations (3) and (5) (providing indefinite permeability) and one or both of equations (9) and (11) (providing indefinite permittivity).
  • the doubly-indefinite planar slab provides a hyperbolic dispersion relation for at least one TE-polarized wave (as in equations (4) and/or (6)) and further provides a hyperbolic dispersion relation for at least one TM-polarized wave (as in equations (10) and (12)), with wave propagation features as discussed in the preceding paragraphs containing the equations that are referenced here.
  • a doubly-indefinite medium may have an indefinite permittivity matrix and an indefinite permeability matrix that are substantially simultaneously diagonalizable, and the doubly- indefinite medium defines an axial direction that corresponds to a first common eigenvector of the indefinite matrices, with first and second transverse directions that correspond to second and third common eigenvectors of the indefinite matrices, respectively.
  • the parameters of the indefinite matrices may vary with position within the doubly-indefinite medium, and correspondingly the common eigenvectors of the indefinite matrices may also vary with position within the doubly-indefinite medium.
  • the disclosure of the preceding paragraph may encompass more general embodiments of a doubly-indefinite medium, in the following manner: the z-axis shall be understood to refer more generally to an axial direction that may vary throughout the doubly-indefinite medium, the x-axis shall be understood to refer more generally to a first transverse direction perpendicular to the axial direction, and the y- axis shall be understood to refer more generally to a second transverse direction mutually perpendicular to the axial direction and the first transverse direction.
  • Some embodiments provide an indefinite medium that is a transformation medium, i.e. an electromagnetic medium having properties that may be characterized according to transformation optics.
  • Transformation optics is an emerging field of electromagnetic engineering, and transformation optics devices include structures that influence electromagnetic waves, where the influencing imitates the bending of electromagnetic waves in a curved coordinate space (a "transformation" of a flat coordinate space), e.g. as described in A. J. Ward and J. B. Pendry j "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), D. Schurig et al, "Calculation of material properties and ray tracing in transformation media," Optics Express 14, 9794 (2006) ("D.
  • a first exemplary transformation optics device is the electromagnetic cloak that was described, simulated, and implemented, respectively, in J. B. Pendry et al, "Controlling electromagnetic waves," Science 312, 1780 (2006); S. A. Cummer et al, "Full- wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006); and D. Schurig et al, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006) (“D. Schurig et al (2)”); each of which is herein incorporated by reference. See also J. Pendry et al, "Electromagnetic cloaking method," U.S. Patent Application No. 11/459,728, herein incorporated by reference.
  • the curved coordinate space is a transformation of a flat space that has been punctured and stretched to create a hole (the cloaked region), and this transformation corresponds to a set of constitutive parameters (electric permittivity and magnetic permeability) for a transformation medium wherein electromagnetic waves are refracted around the hole in imitation of the curved coordinate space.
  • a second exemplary transformation optics device is illustrated by embodiments of the electromagnetic compression structure described in J. B. Pendry, D. Schurig, and D. R. Smith, "Electromagnetic compression apparatus, methods, and systems," U.S. Patent Application No. 11/982,353; and in J. B. Pendry, D. Schurig, and D. R.
  • an electromagnetic compression structure includes a transformation medium with constitutive parameters corresponding to a coordinate transformation that compresses a region of space intermediate first and second spatial locations, the effective spatial compression being applied along an axis joining the first and second spatial locations.
  • the electromagnetic compression structure thereby provides an effective electromagnetic distance between the first and second spatial locations greater than a physical distance between the first and second spatial locations.
  • a third exemplary transformation optics device is illustrated by embodiments of the electromagnetic cloaking and/or translation structure described in J. T. Kare, "Electromagnetic cloaking apparatus, methods, and systems," U.S.
  • an electromagnetic translation structure includes a transformation medium that provides an apparent location of an electromagnetic transducer different then an actual location of the electromagnetic transducer, where the transformation medium has constitutive parameters corresponding to a coordinate transformation that maps the actual location to the apparent location.
  • embodiments include an electromagnetic cloaking structure operable to divert electromagnetic radiation around an obstruction in a field of regard of the transducer (and the obstruction can be another transducer).
  • a fourth exemplary transformation optics device is illustrated by embodiments of the various focusing and/or focus-adjusting structures described in J. A. Bowers et al, "Focusing and sensing apparatus, methods, and systems," U.S. Patent Application No. 12/156,443; J. A. Bowers et al, “Emitting and focusing apparatus, methods, and systems," U.S. Patent Application No. 12/214,534; J. A. Bowers et al, “Negatively-refractive focusing and sensing apparatus, methods, and systems," U.S. Patent Application No. 12/220,705; J. A. Bowers et al, "Emitting and negatively-refractive focusing apparatus, methods, and systems," U.S. Patent
  • a focusing and/or focusing-structure includes a transformation medium that provides an extended depth of focus/field greater than a nominal depth of focus/field, or an interior focus/field region with an axial magnification that is substantially greater than or less than one. Additional exemplary transformation optics devices are described in D.
  • ⁇ and ⁇ are the permittivity and permeability tensors of the transformation medium
  • ⁇ and // are the permittivity and permeability tensors of the original medium in the untransformed coordinate space
  • the coordinate transformation is the Jacobian matrix corresponding to the coordinate transformation.
  • the coordinate transformation is a one-to-one mapping of locations in the untransformed coordinate space to locations in the transformed coordinate space
  • the coordinate transformation is a one-to-many mapping of locations in the untransformed coordinate space to locations in the transformed coordinate space.
  • Some coordinate transformations, such as one-to-many mappings may correspond to a transformation medium having a negative index of refraction
  • the transformation medium is an indefinite medium, i.e. an electromagnetic medium having an indefinite permittivity and/or an indefinite permeability (these transformation media may be referred to as "indefinite transformation media").
  • equations (15) and (16) if the original permittivity matrix ⁇ is indefinite, then the transformed permittivity matrix ⁇ is also indefinite; and/or if the original permeability matrix ⁇ is indefinite, then the transformed permeability matrix ⁇ is also indefinite.
  • equations (15) and (16) only selected matrix elements of the permittivity and permeability tensors need satisfy equations (15) and (16), e.g. where the transformation optics response is for a selected polarization only.
  • a first set of permittivity and permeability matrix elements satisfy equations (15) and (16) with a first Jacobian ⁇ , corresponding to a first transformation optics response for a first polarization of electromagnetic waves, and a second set of permittivity and permeability matrix elements, orthogonal (or otherwise complementary) to the first set of matrix elements, satisfy equations (15) and (16) with a second Jacobian ⁇ ' , corresponding to a second transformation optics response for a second polarization of electromagnetic waves.
  • reduced parameters are used that may not satisfy equations (15) and (16), but preserve products of selected elements in (15) and selected elements in (16), thus preserving dispersion relations inside the transformation medium (see, for example, D.
  • reduced parameters preserve dispersion relations inside the transformation medium (so that the ray or wave trajectories inside the transformation medium are unchanged from those of equations (15) and (16)), they may not preserve impedance characteristics of the transformation medium, so that rays or waves incident upon a boundary or interface of the transformation medium may sustain reflections (whereas in general a transformation medium according to equations (15) and (16) is substantially nonreflective or sustains the reflection characteristics of the original medium in the untransformed coordinate space).
  • the reflective or scattering characteristics of a transformation medium with reduced parameters can be substantially reduced or eliminated (modulo any reflection characteristics of the original medium in the untransformed coordinate space) by a suitable choice of coordinate transformation, e.g.
  • Embodiments of an indefinite medium and/or a transformation medium can be realized using artificially-structured materials.
  • the electromagnetic properties of artificially-structured materials derive from their structural configurations, rather than or in addition to their material composition.
  • the artificially-structured materials are photonic crystals.
  • Some exemplary photonic crystals are described in J. D. Joannopoulos et al, Photonic Crystals: Molding the Flow of Light, 2 nd Edition, Princeton Univ. Press, 2008, herein incorporated by reference.
  • photonic dispersion relations and/or photonic band gaps are engineered by imposing a spatially- varying pattern on an electromagnetic material (e.g. a conducting, magnetic, or dielectric material) or a combination of electromagnetic materials.
  • the photonic dispersion relations translate to effective constitutive parameters (e.g. permittivity, permeability, index of refraction) for the photonic crystal.
  • the spatially- varying pattern is typically periodic, quasi-periodic, or colloidal periodic, with a length scale comparable to an operating wavelength of the photonic crystal.
  • the artificially-structured materials are metamaterials.
  • Some exemplary metamaterials are described in R. A. Hyde et al, "Variable metamaterial apparatus," U.S. Patent Application No. 11/355,493; D. Smith et al, “Metamaterials,” International Application No. PCT/US2005/026052; D. Smith et al, “Metamaterials and negative refractive index,” Science 305, 788 (2004); D. Smith et al, "Indefinite materials," U.S. Patent Application No. 10/525,191; C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Wiley-Interscience, 2006; N. Engheta and R. W.
  • Metamaterials generally feature subwavelength elements, i.e. structural elements with portions having electromagnetic length scales smaller than an operating wavelength of the metamaterial, and the subwavelength elements have a collective response to electromagnetic radiation that corresponds to an effective continuous medium response, characterized by an effective permittivity, an effective permeability, an effective magnetoelec ' tric coefficient, or any combination thereof.
  • the electromagnetic radiation may induce charges and/or currents in the subwavelength elements, whereby the subwavelength elements acquire nonzero electric and/or magnetic dipole moments.
  • the metamaterial has an effective permittivity; where the magnetic component of the electromagnetic radiation induces magnetic dipole moments, the metamaterial has an effective permeability; and where the electric (magnetic) component induces magnetic (electric) dipole moments (as in a chiral metamaterial), the metamaterial has an effective magnetoelectric coefficient.
  • Some metamaterials provide an artificial magnetic response; for example, split-ring resonators (SRRs) — or other LC or plasmonic resonators — built from nonmagnetic conductors can exhibit an effective magnetic permeability (cf. J. B. Pendry et al, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Micro. Theo. Tech.
  • metamaterials have "hybrid” electromagnetic properties that emerge partially from structural characteristics of the metamaterial, and partially from intrinsic properties of the constituent materials.
  • G. Dewar "A thin wire array and magnetic host structure with n ⁇ 0," J. Appl. Phys. 97, 1OQ 101 (2005), herein incorporated by reference, describes a metamaterial consisting of a wire array (exhibiting a negative permeability as a consequence of its structure) embedded in a nonconducting ferrimagnetic host medium (exhibiting an intrinsic negative permeability).
  • Metamaterials can be designed and fabricated to exhibit selected permittivities, permeabilities, and/or magnetoelectric coefficients that depend upon material properties of the constituent materials as well as shapes, chiralities, configurations, positions, orientations, and couplings between the subwavelength elements.
  • the selected permittivites, permeabilities, and/or magnetoelectric coefficients can be positive or negative, complex (having loss or gain), anisotropic (including tensor-indefinite), variable in space (as in a gradient index lens), variable in time (e.g. in response to an external or feedback signal), variable in frequency (e.g. in the vicinity of a resonant frequency of the metamaterial), or any combination thereof.
  • the selected electromagnetic properties can be provided at wavelengths that range from radio wavelengths to infrared/visible wavelengths; the latter wavelengths are attainable, e.g., with nanostructured materials such as nanorod pairs or nano-fishnet structures (cf. S. Linden et al, "Photonic metamaterials: Magnetism at optical frequencies,” IEEE J. Select. Top. Quant. Elect. 12, 1097 (2006) and V. Shalaev, "Optical negative-index metamaterials,” Nature Photonics 1, 41 (2007), both herein incorporated by reference).
  • metamaterials by direct laser writing and silver chemical vapour deposition
  • a metamaterial may include non-discrete elements or structures.
  • a metamaterial may include elements comprised of sub- elements, where the sub-elements are discrete structures (such as split-ring resonators, etc.), or the metamaterial may include elements that are inclusions, exclusions, or other variations along some continuous structure (e.g. etchings on a substrate).
  • the metamaterial may include extended structures having distributed electromagnetic responses (such as distributed inductive responses, distributed capacitive responses, and distributed inductive-capacitive responses). Examples include structures consisting of loaded and/or interconnected transmission lines (such as microstrips and striplines), artificial ground plane structures (such as artificial perfect magnetic conductor (PMC) surfaces and electromagnetic band gap (EGB) surfaces), and interconnected/extended nanostructures (nano-fishnets, elongated SRR woodpiles, etc.).
  • distributed electromagnetic responses such as distributed inductive responses, distributed capacitive responses, and distributed inductive-capacitive responses.
  • Examples include structures consisting of loaded and/or interconnected transmission lines (such as microstrips and striplines), artificial ground plane structures (such as artificial perfect magnetic conductor (PMC) surfaces and electromagnetic band gap (EGB) surfaces), and interconnected/extended nanostructures (nano-fishnets, elongated SRR woodpiles, etc.).
  • a metamaterial may include a layered structure.
  • embodiments may provide a structure having a succession of adjacent layers, where the layers have a corresponding succession of material properties that include electromagnetic properties (such as permittivity and/or permeability).
  • the succession of adjacent layers may be an alternating or repeating succession of adjacent layers, e.g. a stack of layers of a first type interleaved with layers of a second type, or a stack that repeats a sequence of three or more types of layers.
  • the layers are sufficiently thin (e.g. having thicknesses smaller than an operating wavelength of the metamaterial)
  • the layered structure may be characterized as an effective continuous medium having effective constitutive parameters that relate to the electromagnetic properties of the individual layers.
  • the layered structure may be characterized as an effective continuous medium having (effective) anisotropic constitutive parameters
  • the constitutive parameters (18)-(21) may correspond to an indefinite medium.
  • the ratio ⁇ may be selected to provide an indefinite permittivity matrix according to equations (18)-(19) (moreover, for ⁇ substantially equal to J ⁇ 1 / f 2
  • the ratio ⁇ may be selected to provide an indefinite permeability matrix according to equations (20)-(21) (moreover, for ⁇ substantially equal to I ⁇ 2 ⁇ , the indefinite permeability medium is substantially a degenerate indefinite permeability medium).
  • Exemplary planar stacks of alternating materials providing an effective continuous medium having an indefinite permittivity matrix, include an alternating silver/silica layered system described in B. Wood et al, "Directed subwavelength imaging using a layered medal-dielectric system," Phys. Rev. B 74, 115116 (2006), and an alternating doped/undoped semiconductor layered system described in A. J. Hoffman, “Negative refraction in semiconductor metamaterials,” Nature Materials 6, 946 (2007), each of which is herein incorporated by reference. More generally, materials having a positive permittivity include but are not limited to: semiconductors (e.g. at frequencies higher than a plasma frequency of the semiconductor) and insulators such as dielectric crystals (e.g.
  • a positive permittivity material is a gain medium, which may be pumped, for example, to reduce or overcome other losses such as ohmic losses (cf. an exemplary alternating silver/gain layered system described in 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, 201101(R) (2003), herein incorporated by reference).
  • gain media examples include semiconductor laser materials (e.g. GaN, AlGaAs), doped insulator laser materials (e.g. rare-earth doped crystals, glasses, or ceramics), and Raman gain materials.
  • Materials having a negative permeability include but are not limited to: ferrites, magnetic garnets or spinels, artificial ferrites, and other ferromagnetic or ferrimagnetic materials (e.g. at frequencies above a ferromagnetic or ferrimagnetic resonance frequency of the material; cf. F. J. Rachford, "Tunable negative refractive index composite," U.S. Patent Application No. 11/279/460, herein incorporated by reference).
  • Materials having a negative permittivity include but are not limited to: metals (e.g.
  • the plasma frequency (which may be regarded as a frequency at which the semiconductor permittivity changes sign) is related to the density of free carriers within the semiconductor, and this free carrier density may be controlled in various ways (e.g. by chemical doping, photodoping, temperature change, carrier injection, etc.).
  • a layered system comprising interleaved layers of a first semiconductor material having a first plasma frequency and a second semiconductor material having a second plasma frequency may provide an indefinite permittivity (per equations (18)-(19)) in a window of frequencies intermediate the first plasma frequency and the second plasma frequency, and this window may be controlled, e.g., by differently doping the first and second semiconductor materials.
  • a layered structure includes a succession of adjacent layers that are substantially nonplanar.
  • the preceding exemplary layered structure consisting of successive planar layers, each layer having a layer normal direction (the z direction) that is constant along the transverse extent of the layer and a layer thickness that is constant along the transverse extent of the layer — may be extended to a nonplanar layered structure, consisting of successive nonplanar layers, each layer having a layer normal direction that is non-constant along the transverse extent of the layer and, optionally, a layer thickness that is non-constant along the transverse extent of the layer.
  • Some examples of cylindrical and/or spherical layered structures are described in A. Salandrino and N.
  • the nonplanar layered structure may thus provide an indefinite medium having a spatially-varying axial direction that corresponds to the layer normal direction.
  • the spatially-varying axial direction of an indefinite medium is given by a vector field u A (r) that is equal to or parallel to a conservative vector field, i.e. u, oc V ⁇ (22) for a scalar potential function ⁇ ;
  • the indefinite medium may be provided by a nonplanar layered structure where the interfaces of adjacent layers correspond to equipotential surfaces of the function ⁇ .
  • Nonplanar layered structures may be fabricated by various methods that are known to those of skill in the art.
  • J. A. Folta "Dynamic mask for producing uniform or graded-thickness thin films," U.S. Patent No. 7,062,348 (herein incorporated by reference)
  • Tzu-Yu Wang “Graded thickness optical element and method of manufacture therefor," U.S. Patent No. 6,606,199 (herein incorporated by reference) describes methods for depositing graded thickness layers through apertures in a masking layer.
  • an illustrative embodiment is depicted that includes a conversion structure 100 with indefinite electromagnetic parameters, the conversion structure having a first surface region 111 and a second surface region 112, the first surface region and the second surface region being substantially planar and,substantially parallel.
  • This and other drawings can represent a planar view of a three-dimensional embodiment, or a two-dimensional embodiment (e.g. in FIG. 1 where the conversion structure is placed inside a metallic or dielectric slab waveguide oriented normal to the page).
  • the conversion structure is responsive to an evanescent electromagnetic wave (depicted schematically as exponential tails 120) at the first surface region to convey a propagating electromagnetic wave (depicted schematically as dashed rays 125) from the first surface region to the second surface region, and to provide a non-evanescent electromagnetic wave (depicted schematically as the wavy rays 130) at the second surface region.
  • the provided non-evanescent electromagnetic wave is a freely-propagating electromagnetic wave, e.g. a wave that is transmitted by and freely radiates from the second surface region (including diverging propagating waves, converging propagating waves, and substantially planar propagating waves).
  • the provided non-evanescent wave is a confinedly-propagating electromagnetic wave, e.g. a wave that is transmitted by the second surface region into a propagating guided wave mode (as in a waveguide, transmission line, optical fiber, etc.)
  • the first and second surface regions 111 and 112 are depicted in FIG. 1 as exterior surfaces of the conversion structure 100, in other embodiments the first surface region and/or the second surface region may be at least partially interior to the conversion structure (e.g. where the conversion structure includes one or more of a refractive cladding, an impedance-matching layer, input or output optical components, etc.).
  • the evanescent electromagnetic wave 120 may be characterized by a first transverse wavevector k ⁇ (corresponding to a surface parallel direction of the first surface region indicated as the vectors 141 in FIG. 1) that exceeds a first maximum transverse wavevector k ⁇ for non-evanescent waves (cf. equation (2) and related preceding text):
  • the non-evanescent electromagnetic wave 130 may be characterized by a second transverse wavevector k ⁇ 2) (corresponding to a surface parallel direction of the second surface region indicated as the vectors 142 in FIG. 1) that does not exceed a second maximum transverse wavevector k ⁇ for non- evanescent waves (cf. equation (2) and related preceding text):
  • the conversion structure 100 has indefinite electromagnetic parameters, i.e. the conversion structure provides an indefinite medium (i.e. an electromagnetic medium having an indefinite permittivity and/or an indefinite permeability, as discussed above) that is responsive to the evanescent electromagnetic wave 120 to convey a propagating electromagnetic wave from the first surface region 111 to the second surface region 112.
  • an indefinite medium i.e. an electromagnetic medium having an indefinite permittivity and/or an indefinite permeability, as discussed above
  • the indefinite medium defines an axial direction (indicated by the vectors 150 at various positions within the indefinite medium), which, as previously discussed, corresponds to a first eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix; and the indefinite medium further defines a transverse direction (indicated by the vectors 151 at various positions within the indefinite medium) that is perpendicular to the axial direction and corresponds to a second eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix.
  • the axial direction 150 is a non-constant axial direction that is a function of location within the conversion structure 100, i.e.
  • the axial direction may be regarded as a vector field (a vector- valued function of location). Moreover, the axial direction is generally directed from the first surface region 111 to the second surface region 112, i.e. axial field lines corresponding to the axial direction vector field extend from the first surface region to the second surface region.
  • the dashed rays 125 indicating the propagating electromagnetic wave, also correspond to axial field lines, because the illustrative embodiment depicts a degenerate indefinite medium, i.e. an indefinite medium, as described previously, that substantially conveys electromagnetic energy along a propagation direction that corresponds to the axial direction of the indefinite medium.
  • the indefinite medium is a "non- degenerate" indefinite medium that substantially conveys electromagnetic energy along multiple propagation directions — e.g. along at least two propagation directions, each of the at least two directions having a substantially common angle with respect to the axial direction, or along a plurality of propagation directions, the plurality of propagation directions substantially composing a cone having a cone axis that substantially coincides with the axial direction.
  • the propagating electromagnetic field 125 may be characterized by a transverse wavevector k ⁇ that corresponds to the transverse direction 151.
  • the axial field lines (corresponding to the vector field that describes the axial direction 150) diverge geometrically as they proceed from the first surface region 111 to the second surface region 112, and this geometric divergence may provide a substantially continuous variation of the transverse wavevector k ⁇ , from a first transverse wavevector k ⁇ at the first surface region (as in equation (23), to match the transverse wavevector of the evanescent electromagnetic wave 120) to a second transverse wavevector k ⁇ 2) at the second surface region (as in equation (24), to match the transverse wavevector of the non- evanescent electromagnetic wave 130).
  • the geometric divergence of the axial field lines admits the conversion of an evanescent electromagnetic wave 120 to a non- evanescent electromagnetic wave 130, by supporting a propagating electromagnetic wave 125 having a substantially continuous variation of transverse wavevector from an initial transverse wavevector that exceeds a maximum wavevector for non- evanescent waves to a final transverse wavevector that does not exceed a maximum wavevector for non-evanescent waves.
  • FIGS. 2 and 3 layered structures are depicted as exemplary implementations of the conversion structure 100 of FIG. 1. In the exemplary implementations of FIGS.
  • the conversion structure 100 includes (as above) a first surface region 111 and a second surface region 112 that are substantially planar and substantially parallel; intermediate the first and second surface regions, a layered structure provides an effective continuous medium that corresponds to an indefinite medium.
  • the layered structure includes layers of a first material 201 interleaved with layers of a second material 202, where the first and second materials have electromagnetic parameters (e.g. permittivities and/or permeabilities) that are oppositely-signed, as described previously.
  • the alternating layers 201 and 202 are substantially nonplanar, having a layer normal direction that varies with position throughout the layered structure (i.e.
  • a first layer 301 of the layered structure substantially coincides with the first surface region 111
  • a last layer 302 of the layered structure substantially coincides with the second surface region 112, but this is not intended to be limiting (e.g. in the exemplary implementation of FIG.
  • the nonplanar alternating layers may have substantially uniform thickness throughout the transverse extents of the layers, as in FIG. 2; or substantially non-uniform thicknesses throughout the transverse extents of the layers, as in FIG. 3; or a combination thereof.
  • an illustrative embodiment is depicted that includes a conversion structure 100 with indefinite electromagnetic parameters, the conversion structure having a first surface region 111 that is substantially planar and a second surface region 112 that is substantially nonplanar.
  • the substantially nonplanar second surface region 112 is depicted as a convex surface region (i.e. the configuration is a "plano-convex" configuration), but this is an exemplary configuration and is not intended to be limiting: other embodiments (not depicted) provide a substantially nonplanar second surface region 112 that is concave (a "plano-concave" configuration), or that includes a first subregion that is concave and a second subregion that is convex.
  • FIG. 4 can represent a planar view of a three- dimensional embodiment, or a two-dimensional embodiment (e.g. in FIG. 4 where the conversion structure is placed inside a metallic or dielectric slab waveguide oriented normal to the page).
  • the conversion structure is responsive to an evanescent electromagnetic wave (depicted schematically as exponential tails 120) at the first surface region to convey a propagating electromagnetic wave (depicted schematically as dashed rays 125) from the first surface region to the second surface region, and to provide a non-evanescent electromagnetic wave (depicted schematically as the wavy rays 130) at the second surface region.
  • the provided non- evanescent electromagnetic wave is a freely-propagating electromagnetic wave, e.g. a wave that is transmitted by and freely radiates from the second electromagnetic surface (including diverging propagating waves, converging propagating waves, and substantially planar propagating waves).
  • the provided non- evanescent wave is a conflnedly-propagating electromagnetic wave, e.g. a wave that is transmitted by the second electromagnetic surface into a propagating guided wave mode (as in a waveguide, transmission line, optical fiber, etc.)
  • the first and second surface regions 111 and 112 are depicted in FIG. 4 as exterior surfaces of the conversion structure 100, in other embodiments the first surface region and/or the second surface region may be at least partially interior to the conversion structure
  • the evanescent electromagnetic wave 120 may be characterized by a first transverse wavevector kTM (corresponding to a surface parallel direction of the first surface region indicated as the vectors 141 in FIG.
  • the non-evanescent electromagnetic wave 130 may be characterized by a second transverse wavevector kTM (corresponding to a surface parallel direction of the second surface region indicated as the vectors 142 in FIG. 4) that does not exceed a second maximum transverse wavevector k ⁇ defined as in equation (24).
  • the conversion structure 100 has indefinite electromagnetic parameters, i.e. the conversion structure provides an indefinite medium (i.e.
  • the indefinite medium defines an axial direction (indicated by the vectors 150 at various positions within the indefinite medium), which, as previously discussed, corresponds to a first eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix; and the indefinite medium further defines a transverse direction (indicated by the vectors 151 at various positions within the indefinite medium) that is perpendicular to the axial direction and corresponds to a second eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix.
  • the axial direction 150 is a non-constant axial direction that is a function of location within the conversion structure 100, i.e. the axial direction may be regarded as a vector field (a vector-valued function of location).
  • the axial direction is generally directed from the first surface region 111 to the second surface region 112, i.e. axial field lines corresponding to the axial direction vector field extend from the first surface region to the second surface region.
  • the dashed rays 125 indicating the propagating electromagnetic wave, also correspond to axial field lines, because the illustrative embodiment depicts a degenerate indefinite medium, i.e.
  • the indefinite medium is a "non- degenerate" indefinite medium that substantially conveys electromagnetic energy along multiple propagation directions — e.g. along at least two propagation directions, each of the at least two directions having a substantially common angle with respect to the axial direction, or along a plurality of propagation directions, the plurality of propagation directions substantially composing a cone having a cone axis that substantially coincides with the axial direction.
  • the. propagating electromagnetic field 125 may be characterized by a transverse wavevector k ⁇ that corresponds to the transverse direction 151.
  • the axial field lines (corresponding to the vector field that describes the axial direction 150) diverge geometrically as they proceed from the first surface region 111 to the second surface region 112, and this geometric divergence may provide a substantially continuous variation of the transverse wavevector k ⁇ , from a first transverse wavevector kTM at the first surface region (as in equation (23), to match the transverse wavevector of the evanescent electromagnetic wave 120) to a second transverse wavevector kTM at the second surface region(as in equation (24), to match the transverse wavevector of the non- evanescent electromagnetic wave 130).
  • the geometric divergence of the axial field lines admits the conversion of an evanescent electromagnetic wave 120 to a non- evanescent electromagnetic wave 130, by supporting a propagating electromagnetic wave 125 having a substantially continuous variation of transverse wavevector from an initial transverse wavevector that exceeds a maximum wavevector for non- evanescent waves to a final transverse wavevector that does not exceed a maximum wavevector for non-evanescent waves.
  • the conversion structure 100 includes (as in FIG. 4) a first surface region 111 that is substantially planar and a second surface region 112 that substantially nonplanar; intermediate the first and second surface regions, a layered structure provides an effective continuous medium that corresponds to an indefinite medium.
  • the layered structure includes layers of a first material 201 interleaved with layers of a second material 202, where the first and second materials have electromagnetic parameters (e.g. permittivities and/or permeabilities) that are oppositely-signed, as described previously.
  • electromagnetic parameters e.g. permittivities and/or permeabilities
  • the alternating layers 201 and 202 are substantially nonplanar, having a layer normal direction that varies with position throughout the layered structure (i.e. from layer to layer and/or along the transverse extent of each layer), and this layer normal direction corresponds to the axial direction (as depicted by the vectors 150 in FIG. 4) of the provided indefinite medium (equivalently, regarding the interfaces between alternating layers 201 and 202 as equipotential surfaces of a scalar function ⁇ , the gradient of ⁇ is locally parallel to the axial direction 150 as per equation (22)).
  • FIG. 1 the exemplary implementation of FIG.
  • a first layer 301 of the layered structure substantially coincides with the first surface region 111, and a last layer 302 of the layered structure substantially coincides with the second surface region 112, but this is not intended to be limiting (e.g. in the exemplary implementation of FIG. 5, only the second surface region 112 substantially coincides with a layer 302 of the layered structure).
  • the nonplanar alternating layers may have substantially uniform thickness throughout the transverse extents of the layers, as in FIG. 5; or substantially nonuniform thicknesses throughout the transverse extents of the layers, as in FIG. 6; or a combination thereof.
  • an illustrative embodiment is depicted that includes a conversion structure 100 with indefinite electromagnetic parameters, the conversion structure having a first surface region 111 that is substantially nonplanar and a second surface region 112 that is substantially planar.
  • the substantially nonplanar first surface region 111 is depicted as a concave surface region (i.e. the configuration is a "concave-piano" configuration), but this is an exemplary configuration and is not intended to be limiting: other embodiments (not depicted) provide a substantially nonplanar first surface region 111 that is convex (a "convex-piano" configuration), or that includes a first subregion that is concave and a second subregion that is convex.
  • FIG. 7 can represent a planar view of a three-dimensional embodiment, or a two-dimensional embodiment (e.g. in FIG. 7 where the conversion structure is placed inside a metallic or dielectric slab waveguide oriented normal to the page).
  • the conversion structure is responsive to an evanescent electromagnetic wave (depicted schematically as exponential tails 120) at the first surface region to convey a propagating electromagnetic wave (depicted schematically as dashed rays 125) from the first surface region to the second surface region, and to provide a non- evanescent electromagnetic wave (depicted schematically as the wavy rays 130) at the second surface region.
  • the provided non-evanescent electromagnetic wave is a freely-propagating electromagnetic wave, e.g. a wave that is transmitted by and freely radiates from the second electromagnetic surface (including diverging propagating waves, converging propagating waves, and substantially planar propagating waves).
  • the provided non- evanescent wave is a confinedly-propagating electromagnetic wave, e.g. a wave that is transmitted by the second electromagnetic surface into a propagating guided wave mode (as in a waveguide, transmission line, optical fiber, etc.) While the first and second surface regions 111 and 112 are depicted in FIG.
  • the first surface region and/or the second surface region may be at least partially interior to the conversion structure (e.g. where the conversion structure includes one or more of a refractive cladding, an impedance-matching layer, input or output optical components, etc.).
  • the conversion structure includes one or more of a refractive cladding, an impedance-matching layer, input or output optical components, etc.
  • the use of a ray description, in FIG. 7 and elsewhere, is a heuristic convenience for purposes of visual illustration, and is not intended to connote any limitations or assumptions of geometrical optics; further, the elements depicted in FIG. 7 can have spatial dimensions that are variously less than, greater than, or comparable to a wavelength of interest.
  • the evanescent electromagnetic wave 120 may be characterized by a first transverse wavevector k ⁇ (corresponding to a surface parallel direction of the first surface region indicated as the vectors 141 in FIG. 7) that exceeds a first maximum transverse wavevector k ⁇ defined as in equation (23).
  • the non-evanescent electromagnetic wave 130 may be characterized by a second transverse wavevector k ⁇ 2) (corresponding to a surface parallel direction of the second surface region indicated as the vectors 142 in FIG. 7) that does not exceed a second maximum transverse wavevector k ⁇ defined as in equation (24).
  • the conversion structure 100 has indefinite electromagnetic parameters, i.e. the conversion structure provides an indefinite medium (i.e. an electromagnetic medium having an indefinite permittivity and/or an indefinite permeability, as discussed above) that is responsive to the evanescent electromagnetic wave 120 to convey a propagating electromagnetic wave from the first surface region 111 to the second surface region 112.
  • an indefinite medium i.e. an electromagnetic medium having an indefinite permittivity and/or an indefinite permeability, as discussed above
  • the indefinite medium defines an axial direction (indicated by the vectors 150 at various positions within the indefinite medium), which, as previously discussed, corresponds to a first eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix; and the indefinite medium further defines a transverse direction (indicated by the vectors 151 at various positions within the indefinite medium) that is perpendicular to the axial direction and corresponds to a second eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix.
  • the axial direction 150 is a non-constant axial direction that is a function of location within the conversion structure 100, i.e.
  • the axial direction may be regarded as a vector field (a vector-valued function of location). Moreover, the axial direction is generally directed from the first surface region 111 to the second surface region 112, i.e. axial field lines corresponding to the axial direction vector field extend from the first surface region to the second surface region.
  • the dashed rays 125 indicating the propagating electromagnetic wave, also correspond to axial field lines, because the illustrative embodiment depicts a degenerate indefinite medium, i.e. an indefinite medium, as described previously, that substantially conveys electromagnetic energy along a propagation direction that corresponds to the axial direction of the indefinite medium.
  • the indefinite medium is a "non- degenerate" indefinite medium that substantially conveys electromagnetic energy along multiple propagation directions — e.g. along at least two propagation directions, each of the at least two directions having a substantially common angle with respect to the axial direction, or along a plurality of propagation directions, the plurality of propagation directions substantially composing a cone having a cone axis that substantially coincides with the axial direction.
  • the propagating electromagnetic field 125 may be characterized by a transverse wavevector k ⁇ that corresponds to the transverse direction 151.
  • the axial field lines (corresponding to the vector field that describes the axial direction 150) diverge geometrically as they proceed from the first surface region 111 to the second surface region 112, and this geometric divergence may provide a substantially continuous variation of the transverse wavevector k ⁇ , from a first transverse wavevector k ⁇ at the first surface region (as in equation (23), to match the transverse wavevector of the evanescent electromagnetic wave 120) to a second transverse wavevector k ⁇ at the second surface region (as in equation (24), to match the transverse wavevector of the non- evanescent electromagnetic wave 130).
  • the geometric divergence of the axial field lines admits the conversion of an evanescent electromagnetic wave 120 to a non- evanescent electromagnetic wave 130, by supporting a propagating electromagnetic wave 125 having a substantially continuous variation of transverse wavevector from an initial transverse wavevector that exceeds a maximum wavevector for non- evanescent waves to a final transverse wavevector that does not exceed a maximum wavevector for non-evanescent waves.
  • FIGS. 8 and 9 layered structures are depicted as exemplary implementations of the conversion structure 100 of FIG. 7.
  • the conversion structure 100 includes (as in FIG.
  • a layered structure provides an effective continuous medium that corresponds to an indefinite medium.
  • the layered structure includes layers of a first material 201 interleaved with layers of a second material 202, where the first and second materials have electromagnetic parameters (e.g. permittivities and/or permeabilities) that are oppositely-signed, as described previously.
  • the alternating layers 201 and 202 are substantially nonplanar, having a layer normal direction that varies with position throughout the layered structure (i.e.
  • a first layer 301 of the layered structure substantially coincides with the first surface region 111, and a last layer 302 of the layered structure substantially coincides with the second surface region 112, but this is not intended to be limiting (e.g. in the exemplary implementation of FIG.
  • the nonplanar alternating layers may have substantially uniform thickness throughout the transverse extents of the layers, as in FIG. 8; or substantially non-uniform thicknesses throughout the transverse extents of the layers, as in FIG. 9; or a combination thereof.
  • a conversion structure 100 with indefinite electromagnetic parameters having a first surface region 111 and a second surface region 112, the first surface region and the second surface region being substantially nonplanar and substantially non-concentric.
  • a first surface region and a second surface region are non-concentric if: the first surface region has a non- constant curvature, and/or the second surface region has a non-constant curvature, and/or a center of an osculating circle of the first surface region is different than a center of an osculating circle of the second surface region (where the osculating circles are coplanar).
  • Embodiment 1001 depicts a conversion structure 100 having a first surface region 111 and a second surface region 112 that are both convex (a "bi- convex" configuration).
  • Embodiment 1002 depicts a conversion structure 100 having a first surface region 111 and a second surface region 112 that are both concave (a "bi-concave” configuration).
  • Embodiment 1003 depicts a conversion structure 100 having a first surface region 111 that is concave and a second surface region 112 that is convex, where a center of curvature of the first surface region is to the right of — i.e. nearer to the conversion structure than — a center of curvature of the second surface region, i.e.
  • Embodiment 1004 depicts a conversion structure 100 having a first surface region 111 that is convex and a second surface region 112 that is concave, where a center of curvature of the first surface region is to the left of — i.e. nearer to the conversion structure than — a center of curvature of the second surface region, i.e.
  • Embodiment 1005 depicts a conversion structure having a first surface region 111 that is partially convex and partially concave and a second surface region 112 that is partially convex and partially concave (in other embodiments, not shown, the first surface region 111 is convex only or concave only and the second surface region 112 is partially convex and partially concave, or the first surface region 111 is partially convex and partially concave and the second surface region 112 is convex only or concave only).
  • the depictions in FIG. 10 can represent planar views of three-dimensional embodiments, or a two- dimensional embodiment (e.g. where the conversion structure 100 is placed inside a metallic or dielectric slab waveguide oriented normal to the page).
  • the conversion structure 100 is responsive to an evanescent electromagnetic wave (depicted schematically as exponential tails 120) at the first surface region 111 to convey a propagating electromagnetic wave (depicted schematically as dashed rays 125) from the first surface region to the second surface region, and to provide a non-evanescent electromagnetic wave (depicted schematically as the wavy rays 130) at the second surface region 112.
  • the provided non-evanescent electromagnetic wave is a freely- propagating electromagnetic wave, e.g. a wave that is transmitted by and freely radiates from the second electromagnetic surface (including diverging propagating waves, converging propagating waves, and substantially planar propagating waves).
  • the provided non-evanescent wave is a confinedly-propagating electromagnetic wave, e.g. a wave that is transmitted by the second electromagnetic surface into a propagating guided wave mode (as in a waveguide, transmission line, optical fiber, etc.)
  • the first and second surface regions 111 and 112 are depicted in FIG. 10 as exterior surfaces of the conversion structure 100, in other embodiments the first surface region and/or the second surface region may be at least partially interior to the conversion structure (e.g. where the conversion structure includes one or more of a refractive cladding, an impedance-matching layer, input or output optical components, etc.).
  • FIG. 10 is a heuristic convenience for purposes of visual illustration, and is not intended to connote any limitations or assumptions of geometrical optics; further, the elements depicted in FIG. 10 can have spatial dimensions that are variously less than, greater than, or comparable to a wavelength of interest.
  • the evanescent electromagnetic wave 120 may be characterized by a first transverse wavevector k ⁇ (corresponding to a surface parallel direction of the first surface region — for simplicity this surface parallel direction of the first surface region is not depicted in the embodiments of FIG. 10, but should be apparent from the analogous elements 141 depicted in FIGS. 1, 4, and 7) that exceeds a first maximum transverse wavevector Jc ⁇ x defined as in equation (23).
  • k ⁇ corresponding to a surface parallel direction of the first surface region — for simplicity this surface parallel direction of the first surface region is not depicted in the embodiments of FIG. 10, but should be apparent from the analogous elements 141 depicted in FIGS. 1, 4, and 7) that exceeds a first maximum transverse wavevector Jc ⁇ x defined as in equation (23).
  • the non-evanescent electromagnetic wave 130 may be characterized by a second transverse wavevector k ⁇ 2) (corresponding to a surface parallel direction of the second surface region — again for simplicity this surface parallel direction of the second surface region is not depicted in the embodiments of FIG. 10, but should be apparent from the analogous elements 142 depicted in FIGS. 1, 4, and 7) that does not exceed a second maximum transverse wavevector k ⁇ (defined as in equation (24).
  • the conversion structure 100 has indefinite electromagnetic parameters, i.e. the conversion structure provides an indefinite medium (i.e.
  • an electromagnetic medium having an indefinite permittivity and/or an indefinite permeability, as discussed above) that is responsive to the evanescent electromagnetic wave 120 to convey a propagating electromagnetic wave from the first surface region 111 to the second surface region 112.
  • the indefinite medium defines an axial direction (again for simplicity this axial direction is not depicted in the embodiments of FIG. 10, but should be apparent from the analogous elements 150 depicted in FIGS. 1, 4, and 7), which, as previously discussed, corresponds to a first eigenvector of the indefinite permittivity matrix and/or the indefinite permeability matrix; and the indefinite medium further defines a transverse direction (again for simplicity this transverse direction is not depicted in the embodiments of FIG.
  • the axial direction 150 is a non-constant axial direction that is a function of location within the conversion structure 100, i.e. the axial direction may be regarded as a vector field (a vector-valued function of location).
  • the axial direction is generally directed from the first surface region 111 to the second surface region 112, i.e. axial field lines corresponding to the axial direction vector field extend from the first surface region to the second surface region.
  • the dashed rays 125 indicating the propagating electromagnetic wave, also correspond to axial field lines, because the illustrative embodiment depicts a degenerate indefinite medium, i.e. an indefinite medium, as described previously, that substantially conveys electromagnetic energy along a propagation direction that corresponds to the axial direction of the indefinite medium.
  • the indefinite medium is a "non-degenerate" indefinite medium that substantially conveys electromagnetic energy along multiple propagation directions — e.g.
  • each of the at least two directions having a substantially common angle with respect to the axial direction, or along a plurality of propagation directions, the plurality of propagation directions substantially composing a cone having a cone axis that substantially coincides with the axial direction.
  • the propagating electromagnetic field 125 may be characterized by a transverse wavevector k ⁇ that corresponds to the transverse direction (again for simplicity this transverse direction is not depicted in the embodiments of FIG. 10, but should be apparent from the analogous elements 151 depicted in FIGS. 1, 4, and 7).
  • the axial field lines (corresponding to the vector field that describes the axial direction) diverge geometrically as they proceed from the first surface region 111 to the second surface region 112, and this geometric divergence may provide a substantially continuous variation of the transverse wavevector k ⁇ , from a first transverse wavevector k ⁇ at the first surface region (as in equation (23), to match the transverse wavevector of the evanescent electromagnetic wave 120) to a second transverse wavevector k ⁇ 2) at the second surface region(as in equation (24), to match the transverse wavevector of the non-evanescent electromagnetic wave 130).
  • the geometric divergence of the axial field lines admits the conversion of an evanescent electromagnetic wave 120 to a non-evanescent electromagnetic wave 130, by supporting a propagating electromagnetic wave 125 having a substantially continuous variation of transverse wavevector from an initial transverse wavevector that exceeds a maximum wavevector for non-evanescent waves to a final transverse wavevector that does not exceed a maximum wavevector for non-evanescent waves.
  • a layered structure is depicted as an exemplary implementation of a conversion structure 100 as in FIG. 10.
  • the conversion structure 100 includes a first surface region 111 and a second surface region 112 that are substantially nonplanar and substantially non-concentric; intermediate the first and second surface regions, a layered structure provides an effective continuous medium that corresponds to an indefinite medium.
  • the layered structure includes layers of a first material 201 interleaved with layers of a second material 202, where the first and second materials have electromagnetic parameters (e.g. permittivities and/or permeabilities) that are oppositely-signed, as described previously.
  • electromagnetic parameters e.g. permittivities and/or permeabilities
  • the alternating layers 201 and 202 are substantially nonplanar, having a layer normal direction that varies with position throughout the layered structure (i.e. from layer to layer and/or along the transverse extent of each layer), and this layer normal direction corresponds to the axial direction of the provided indefinite medium (equivalently, regarding the interfaces between alternating layers 201 and 202 as equipotential surfaces of a scalar function ⁇ , the gradient of ⁇ is locally parallel to the axial direction as per equation (22)).
  • a layer normal direction that varies with position throughout the layered structure (i.e. from layer to layer and/or along the transverse extent of each layer)
  • this layer normal direction corresponds to the axial direction of the provided indefinite medium (equivalently, regarding the interfaces between alternating layers 201 and 202 as equipotential surfaces of a scalar function ⁇ , the gradient of ⁇ is locally parallel to the axial direction as per equation (22)).
  • a first layer 301 of the layered structure substantially coincides with the first surface region 111
  • a last layer 302 of the layered structure substantially coincides with the second surface region 112, but this is not intended to be limiting (in other embodiments, not depicted, the first surface region 111 does not coincide with a layer of the layered structure, and/or the second surface region 112 does not coincide with a layer of the layered structure).
  • the nonplanar alternating layers may have substantially uniform thickness throughout the transverse extents of the layers; or substantially non-uniform thicknesses throughout the transverse extents of the layers; or a combination thereof, as in FIG. 11.
  • a conversion structure such as those depicted in FIGS. 1-11, includes an indefinite transformation medium, i.e. a transformation medium that has indefinite electromagnetic parameters.
  • an indefinite transformation medium i.e. a transformation medium that has indefinite electromagnetic parameters.
  • the geometric divergence of the axial field lines, along the dashed rays 125 in FIGS. 1, 4, 7, and 10 may accord with a coordinate transformation, e.g. from an untransformed coordinate space in which the axial field lines do not have a geometric divergence.
  • a coordinate transformation e.g. from an untransformed coordinate space in which the axial field lines do not have a geometric divergence.
  • the exemplary coordinate transformation provides an increasing magnification of the successive constant-z surfaces according to a magnification factor m(z) so that, for example, two lines that are parallel to the z-axis in the untransformed coordinate space shall diverge in the transformed coordinate space, with a geodesic distance between the two lines being proportional to m ⁇ z) on the surface S..
  • m(z) magnification factor
  • Constitutive parameters of the indefinite transformation medium (obtained from equations (15) and (16) with the Jacobian matrix (17) corresponding to coordinate transformation (25)) provide an indefinite medium with axial field lines that diverge geometrically as they proceed from the first surface region to the second surface region, in accordance with the magnifying coordinate transformation (25). Then, for a propagating electromagnetic wave 125 characterized by a transverse wavevector k ⁇ , the transverse wavevector varies in inverse proportion to the magnification factor m ⁇ z ") as the propagating electromagnetic wave advances from the first surface region 111 to the second surface region 112, implying the connection
  • the conversion structure 100 will convert an evanescent electromagnetic wave 120 to a non-evanescent electromagnetic wave 130 for a range of transverse wavevectors k? e ( ⁇ w '- ⁇ TM ⁇ ) (°f- equations (23) and (24)); or, reciprocally, the conversion structure 100 will convert a non-evanescent electromagnetic wave 130 to an evanescent electromagnetic wave 120 for a range of transverse wavevectors
  • the planar slab of untransformed indefinite medium is a degenerate indefinite medium, i.e. providing degenerate propagation for TM- polarized waves (with and/or ⁇ substantially less than TE-polarized waves (with ⁇ x and/or ⁇ substantially less than ⁇ . ⁇ ), or both.
  • the planar slab may have a permittivity matrix
  • the new permittivity tensor is which may be diagonalized in the new coordinate space as
  • the transformation medium is a new degenerate indefinite medium, with a new spatially-varying axial direction given by (dx' dy' dz ⁇ ( , , m(z') "l ,,, deliberately, " ⁇ ⁇ Tdz 1 P dz T ⁇ z J T y J 'T tnXzt 1 )) (30)
  • this transformation medium may be implemented as a nonplanar layered structure (cf. the preceding discussion of layered structures), by relating the vector field (30) to a scalar potential ⁇ according to equation (22) whereby the interfaces of adjacent layers in the nonplanar layered structure correspond to equipotential surfaces of the function ⁇ .
  • the magnification factor may increase linearly with z, e.g.
  • the layered structure of FIG. 2 resembles a configuration of this sort; moreover the layered structures of FIGS. 5 and 8 resemble the configuration of FIG. 2, absent selected layers so as to have either a nonplanar first surface region or a nonplanar second surface region of the conversion structure, but providing similar indefinite medium properties within the interior of the conversion structure.
  • the magnification factor may increase nonlinearly with z, e.g.
  • the layered structure of FIG. 3 resembles a configuration of this sort; moreover the layered structures of FIGS. 6 and 9 resemble the configuration of FIG. 3, absent selected layers so as to have either a nonplanar first surface region or a nonplanar second surface region of the conversion structure, but providing similar indefinite medium properties within the interior of the conversion structure.
  • the exemplary conversion structures 100 in FIGS. 1, 4, 7, and 10 provide an indefinite medium that is depicted as responding to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave.
  • the indefinite medium alternately or additionally has a reciprocal response, i.e. the indefinite medium responds to a non-evanescent electromagnetic wave to provide an evanescent electromagnetic wave .
  • the non-evanescent electromagnetic wave 130 and the propagating electromagnetic wave 125 may be regarded as having spatially-reversed propagation directions (i.e.
  • the conversion structure 100 is responsive to a (leftwards-propagating) non-evanescent electromagnetic wave 130 at the second surface region 112 to convey a propagating electromagnetic wave 125 from the second surface region to the first surface region 111 and to provide an (leftwards-decaying) evanescent electromagnetic wave 120 at the first surface region.
  • the evanescent electromagnetic wave 120 may be characterized by a first transverse wavevector kTM as in equation (23) and the non-evanescent electromagnetic wave 130 may be characterized by a second transverse wavevector k ⁇ 2) as in equation (24).
  • the propagating electromagnetic wave 125 may propagate along a propagation direction that corresponds to a direction antiparallel to the axial direction of the indefinite medium; when the indefinite medium is a non- degenerate indefinite medium, the propagating electromagnetic wave 125 may propagate along multiple propagation directions — e.g.
  • the axial field lines diverge geometrically as they proceed from the first surface region 111 to the second surface region 112; equivalently, the axial field lines converge geometrically from the second surface 112 to the first surface 111.
  • this geometric convergence may provide — for a propagating electromagnetic wave 125 characterized by a transverse wavevector k ⁇ — a substantially continuous variation of the transverse wavevector k ⁇ , from k ⁇ 2) at the second surface region (as in equation (24), to match the transverse wavevector of the non-evanescent electromagnetic wave 130) to kTM at the first surface region (as in equation (23), to match the transverse wavevector of the evanescent electromagnetic wave 120).
  • the geometric convergence of the axial field lines admits the conversion of a non-evanescent electromagnetic wave 130 to an evanescent electromagnetic wave 120, by supporting a propagating electromagnetic wave having a substantially continuous variation of transverse wavevector from an initial transverse wavevector that does not exceed a maximum wavevector for non- evanescent waves to a final transverse wavevector that exceeds a maximum wavevector for non-evanescent waves.
  • Some embodiments are responsive to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave (and/or vice versa, in a reciprocal scenario) at a selected frequency/frequency band and/or a selected polarization.
  • the selected frequency or frequency band may be selected from a range that includes radio frequencies, microwave frequencies, millimeter- or submillimeter-wave frequencies, THz-wave frequencies, optical frequencies (e.g. variously corresponding to soft x-rays, extreme ultraviolet, ultraviolet, visible, near-infrared, infrared, or far infrared light), etc.
  • the selected polarization may be a TE polarization, a TM polarization, a circular polarization, etc.
  • Some embodiments are responsive to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave — and/or vice versa, in a reciprocal scenario — for any polarization, e.g. for unpolarized electromagnetic energy).
  • Some embodiments are responsive to an evanescent electromagnetic wave to a provide a non-evanescent electromagnetic wave (and/or vice versa, in a reciprocal scenario) at a first frequency, and further responsive to an evanescent electromagnetic wave to a provide a non-evanescent electromagnetic wave (and/or vice versa, in a reciprocal scenario) at a second frequency different than the first frequency.
  • the first and second frequencies may be selected from the frequency categories in the preceding paragraph.
  • first and second frequencies may generally be replaced by a recitation of first and second frequency bands, again selected from the above frequency categories.
  • These embodiments responsive at first and second frequencies may include a indefinite medium having adjustable electromagnetic properties.
  • the indefinite medium may have electromagnetic properties that are adjustable (e.g. in response to an external input or control signal) between first electromagnetic properties and second electromagnetic properties, the first electromagnetic properties providing an indefinite medium responsive to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave (and/or vice versa) at the first frequency, and the second electromagnetic properties providing an indefinite medium responsive to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave (and/or vice versa) at the second frequency.
  • An indefinite medium with an adjustable electromagnetic response may be implemented with variable metamaterials, e.g. as described in R. A. Hyde et al, supra.
  • Other embodiments responsive at first and second frequencies may include an indefinite medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters.
  • the frequency-dependent response at a first frequency may be a response to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave (and/or vice versa) at the first frequency
  • the frequency-dependent response at a second frequency may be a response to an evanescent electromagnetic wave to provide a non-evanescent electromagnetic wave (and/or vice versa) at the second frequency.
  • An indefinite medium having a frequency-dependent response to electromagnetic radiation can be implemented with artificially-structured materials such as metamaterials; for example, a first set of metamaterial elements having a response at the first frequency may be interleaved with a second set of metamaterial elements having a response at the second frequency.
  • Flow 1200 includes operation 1210 — coupling to an evanescent electromagnetic wave at an input region.
  • a conversion structure such as that depicted as element 100 in FIGS. 1, 4, 7, and 10, couples to an evanescent electromagnetic wave 120 at a first surface region 111 of the conversion structure.
  • Flow 1200 includes operation 1220 — responsive to the coupling, propagating electromagnetic energy in an electromagnetic field from a first surface within the input region to a second surface within an output region.
  • the conversion structure 100 in FIGS. 1, 4, 7, and 10 conveys a propagating electromagnetic wave 125 from the first surface region 111 to the second surface region 112.
  • the first surface maybe an exterior surface of the input region, or at least partially within an interior portion of the input region (e.g. corresponding to a conversion structure having an input surface region 111 that is at least partially interior to the conversion structure).
  • the second surface may be an exterior surface of the output region, or at least partially within an interior portion of the output region (e.g. corresponding to a conversion structure having an output surface region 112 that is at least partially interior to the conversion structure).
  • Operation 1220 includes sub-operation 1221 — inducing a first polarization in a first direction, the first polarization positively corresponding to a first component of the electromagnetic field in the first direction — and sub-operation 1222 — inducing a second polarization in a second direction perpendicular to the first direction, the second polarization negatively corresponding to a second component of the electromagnetic field in the second direction.
  • a conversion structure 100 as in FIGS. 1, 4, 7, and 10 may provide an indefinite medium having an indefinite permittivity, and the indefinite permittivity may correspond to an electric susceptibility that is positive in a first direction and negative in a second direction (where the first and second directions may correspond to the axial and transverse directions 150 and 151 as in in FIGS.
  • the propagating electromagnetic wave 125 may induce an electric polarization in the first direction that positively corresponds (in accordance with the positive electric susceptibility) to an electric field component of the propagating electromagnetic wave in the first direction, and further induce an electric polarization in the second direction that negatively corresponds (in accordance with the negative electric susceptibility) to an electric field component of the propagating electromagnetic wave in the second direction.
  • 1, 4, 7, and 10 may provide an indefinite medium having an indefinite permeability, and the indefinite permeability may correspond to a magnetic susceptibility that is positive in a first direction and negative in a second direction (where the first and second directions may correspond to the axial and transverse directions 150 and 151 in
  • the propagating electromagnetic wave 125 may induce a magnetic polarization in the first direction that positively corresponds (in accordance with the positive magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the first direction, and further induce a magnetic polarization in the second direction that negatively corresponds (in accordance with the negative magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the second direction.
  • Operation 1220 optionally further includes sub-operation 1223 — inducing a third polarization in a third direction, the third polarization positively corresponding to a third component of the electromagnetic field in the third direction — and sub-operation 1224 — inducing a fourth polarization in a fourth direction perpendicular to the third direction, the fourth polarization negatively corresponding to a fourth component of the electromagnetic field in the fourth direction.
  • sub-operation 1223 inducing a third polarization in a third direction, the third polarization positively corresponding to a third component of the electromagnetic field in the third direction
  • sub-operation 1224 inducing a fourth polarization in a fourth direction perpendicular to the third direction, the fourth polarization negatively corresponding to a fourth component of the electromagnetic field in the fourth direction.
  • 1, 4, 7, and 10 may provide an indefinite medium having both an indefinite permittivity and an indefinite permeability, the indefinite permittivity corresponding to a electric susceptibility that is positive in a first direction and negative in a second direction (where the first and second directions may correspond to the axial and transverse directions 150 and 151 in FIGS. 1, 4,and 7, or directions parallel and perpendicular to the rays 125 in FIG. 10, or vice versa) and the indefinite permeability corresponding to a magnetic susceptibility that is positive in a third direction and negative in a fourth direction (where the third and fourth directions may correspond to the axial and transverse directions 150 and 151 of FIGS. 1, 4,and 7, or directions parallel and perpendicular to the rays 125 in FIG.
  • the propagating electromagnetic wave 125 may induce: (1) an electric polarization in the first direction that positively corresponds (in accordance with the positive electric susceptibility) to an electric field component of the propagating electromagnetic wave in the first direction, (2) an electric polarization in the second direction that negatively corresponds (in accordance with the negative electric susceptibility) to an electric field component of the propagating electromagnetic wave in the second direction, (3) a magnetic polarization in the third direction that positively corresponds (in accordance with the positive magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the second direction, and (4) a magnetic polarization in the fourth direction that negatively corresponds (in accordance with the negative magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the fourth direction.
  • Flow 1200 includes operation 1230 — providing the propagated electromagnetic energy as a non- evanescent electromagnetic wave at the output region.
  • the conversion structure 100 of FIGS. 1, 4, 7, and 10 provides a non-evanescent electromagnetic wave 130 at the second surface region 112;
  • the non-evanescent electromagnetic wave may be a freely-propagating electromagnetic wave, e.g. a wave that is emitted by and freely radiates from the second electromagnetic surface, or a confinedly-propagating electromagnetic wave, e.g. a wave that is transmitted by the second surface region into a propagating guided wave mode (as in a waveguide, transmission line, optical fiber, etc.).
  • An illustrative embodiments is depicted as a process flow diagram in FIG. 13.
  • Flow 1300 includes operation 1310 — receiving a non-evanescent electromagnetic wave at an input region.
  • a conversion structure such as that depicted as element 100 in FIGS. 1, 4, 7, and 10 , receives (in a reciprocal scenario to that of FIGS. 1, 4, 7, and 10, as described previously) a non-evanescent electromagnetic wave 130 at the second surface region 112.
  • Flow 1300 includes operation 1320 — responsive to the receiving, propagating electromagnetic energy in an electromagnetic field from a first surface within the input region to a second surface within an output region.
  • the conversion structure 100 in FIGS. 1, 4, 7, and 10 conveys (in a reciprocal scenario to that of FIGS.
  • the first surface may be an exterior surface of the input region, or at least partially within an interior portion of the input region (e.g. corresponding to a conversion structure having a second surface region 112 that is at least partially interior to the conversion structure).
  • the second surface may be an exterior surface of the output region, or at least partially within an interior portion of the output region (e.g. corresponding to a conversion structure having an first surface region 111 that is at least partially interior to the conversion structure).
  • Operation 1320 includes sub- operation 1321 — inducing a first polarization in a first direction, the first polarization positively corresponding to a first component of the electromagnetic field in the first direction — and sub-operation 1322 — inducing a second polarization in a second direction perpendicular to the first direction, the second polarization negatively corresponding to a second component of the electromagnetic field in the second direction.
  • a conversion structure 100 as in FIGS. 1, 4, 7, and 10 may provide an indefinite medium having an indefinite permittivity, and the indefinite permittivity may correspond to an electric susceptibility that is positive in a first direction and negative in a second direction (where the first and second directions may correspond to the axial and transverse directions 150 and 151 in FIGS.
  • the propagating electromagnetic wave 125 may induce an electric polarization in the first direction that positively corresponds (in accordance with the positive electric susceptibility) to an electric field component of the propagating electromagnetic wave in the first direction, and further induce an electric polarization in the second direction that negatively corresponds (in accordance with the negative electric susceptibility) to an electric field component of the propagating electromagnetic wave in the second direction.
  • 1, 4, 7, and 10 may provide an indefinite medium having an indefinite permeability, and the indefinite permeability may correspond to a magnetic susceptibility that is positive in a first direction and negative in a second direction (where the first and second directions may correspond to the axial and transverse directions 150 and 151 in FIGS. 1, 4,and 7, or directions parallel and perpendicular to the rays 125 in FIG. 10, or vice versa).
  • the propagating electromagnetic wave 125 may induce a magnetic polarization in the first direction that positively corresponds (in accordance with the positive magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the first direction, and further induce a magnetic polarization in the second direction that negatively corresponds (in accordance with the negative magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the second direction.
  • Operation 1320 optionally further includes sub-operation 1323 — inducing a third polarization in a third direction, the third polarization positively corresponding to a third component of the electromagnetic field in the third direction — and sub-operation 1324 — inducing a fourth polarization in a fourth direction perpendicular to the third direction, the fourth polarization negatively corresponding to a fourth component of the electromagnetic field in the fourth direction.
  • sub-operation 1323 inducing a third polarization in a third direction, the third polarization positively corresponding to a third component of the electromagnetic field in the third direction
  • sub-operation 1324 inducing a fourth polarization in a fourth direction perpendicular to the third direction, the fourth polarization negatively corresponding to a fourth component of the electromagnetic field in the fourth direction.
  • 1, 4, 7, and 10 may provide an indefinite medium having both an indefinite permittivity and an indefinite permeability, the indefinite permittivity corresponding to a electric susceptibility that is positive in a first direction and negative in a second direction (where the first and second directions may correspond to the axial and transverse directions 150 and 151 in FIGS. 1, 4, and 7, or directions parallel and perpendicular to the rays 125 in FIG. 10, or vice versa) and the indefinite permeability corresponding to a magnetic susceptibility that is positive in a third direction and negative in a fourth direction (where the third and fourth directions may correspond to the axial and transverse directions 150 and 151 of FIGS. 1, 4,and 7, or directions parallel and perpendicular to the rays 125 in FIG.
  • the propagating electromagnetic wave 125 may induce: (1) an electric polarization in the first direction that positively corresponds (in accordance with the positive electric susceptibility) to an electric field component of the propagating electromagnetic wave in the first direction, (2) an electric polarization in the second direction that negatively corresponds (in accordance with the negative electric susceptibility) to an electric field component of the propagating electromagnetic wave in the second direction, (3) a magnetic polarization in the third direction that positively corresponds (in accordance with the positive magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the second direction, and (4) a magnetic polarization in the fourth direction that negatively corresponds (in accordance with the negative magnetic susceptibility) to a magnetic field component of the propagating electromagnetic wave in the fourth direction.
  • Flow 1300 includes operation 1330 — coupling the propagated electromagnetic energy to an evanescent electromagnetic wave at the output region.
  • the conversion structure 100 of FIGS. 1, 4, 7, and 10 provides (in a reciprocal scenario to that of FIGS. 1, 4, 7, and 10, as described previously) an evanescent electromagnetic wave 120 at the first surface region 111 (the evanescent wave having an exponential decay away from the conversion structure for this reciprocal scenario, not decaying towards the conversion structure as depicted).
  • FIG. 14 an illustrative embodiment is depicted as a system block diagram.
  • the system 1400 includes an evanescent conversion unit 1420 optionally coupled to a control unit 1440.
  • the evanescent conversion unit 1420 may include a conversion structure such as that depicted as element 100 in FIGS. 1-11.
  • the conversion structure may be a variable conversion structure, such as a variable metamaterial responsive to one or more control inputs to vary one or more operating characteristics (operating frequency, operating wave polarization, effective coordinate transformation for a transformation medium, etc), and the control unit 1440 may include control circuitry that provides one or more control inputs to the variable conversion structure.
  • the evanescent conversion unit 1420 may further include a positioning structure (e.g.
  • control unit 1440 may include control circuitry that provides the one or more control inputs to the positioning structure, optionally in response to a feedback signal from the positioning structure (e.g. a cantilever force feedback).
  • the evanescent conversion unit 1420 may include one or more optical components, e.g.
  • control unit 1440 may include control circuitry that provides one or more control inputs to the one or more optical components (e.g. to control orientations, focusing characteristics, aperture sizes, etc.).
  • the system optionally includes an input unit 1410 coupled to the evanescent conversion unit 1420 (e.g. to deliver electromagnetic energy to the evanescent conversion unit 1420); the input unit may include an electromagnetic source (e.g.
  • the system optionally includes an output unit 1430 coupled to the evanescent conversion unit 1420 (e.g. to receive electromagnetic energy from the evanescent conversion unit 1420); the output unit may include an electromagnetic detector (e.g. a CCD array, photomultiplier, etc.) as well as output circuitry and/or optical components such as demodulators, phase adjusters, spectral analyzers, image processing circuitry, etc.
  • an electromagnetic detector e.g. a CCD array, photomultiplier, etc.
  • optical components such as demodulators, phase adjusters, spectral analyzers, image processing circuitry, etc.

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Aerials With Secondary Devices (AREA)
  • Shielding Devices Or Components To Electric Or Magnetic Fields (AREA)

Abstract

L'invention porte sur un appareil, sur des procédés et sur des systèmes pour réaliser une conversion d'ondes électromagnétiques évanescentes en ondes électromagnétiques non évanescentes et/ou une conversion d'ondes électromagnétiques non évanescentes en ondes électromagnétiques évanescentes. Dans certaines approches, la conversion comprend la propagation d'ondes électromagnétiques à l'intérieur d'un milieu électromagnétique indéfini, et le milieu indéfini peut comprendre un matériau à structure artificielle, tel qu'une structure à couches ou autre métamatériau.
EP10764783.6A 2009-04-17 2010-04-16 Appareil et procédés de conversion d'onde électromagnétique évanescente Withdrawn EP2419774A4 (fr)

Applications Claiming Priority (10)

Application Number Priority Date Filing Date Title
US12/386,522 US8634141B2 (en) 2009-04-17 2009-04-17 Evanescent electromagnetic wave conversion apparatus I
US12/386,523 US8634142B2 (en) 2009-04-17 2009-04-17 Evanescent electromagnetic wave conversion apparatus II
US12/386,521 US8634140B2 (en) 2009-04-17 2009-04-17 Evanescent electromagnetic wave conversion apparatus III
US12/460,137 US8634144B2 (en) 2009-04-17 2009-07-13 Evanescent electromagnetic wave conversion methods I
US12/460,136 US8634143B2 (en) 2009-04-17 2009-07-13 Evanescent electromagnetic wave conversion methods II
US12/460,122 US8630044B2 (en) 2009-04-17 2009-07-13 Evanescent electromagnetic wave conversion methods III
US12/590,010 US9081123B2 (en) 2009-04-17 2009-10-30 Evanescent electromagnetic wave conversion lenses II
US12/589,913 US9081202B2 (en) 2009-04-17 2009-10-30 Evanescent electromagnetic wave conversion lenses I
US12/589,925 US9083082B2 (en) 2009-04-17 2009-10-30 Evanescent electromagnetic wave conversion lenses III
PCT/US2010/001154 WO2010120383A1 (fr) 2009-04-17 2010-04-16 Appareil et procédés de conversion d'onde électromagnétique évanescente

Publications (2)

Publication Number Publication Date
EP2419774A1 true EP2419774A1 (fr) 2012-02-22
EP2419774A4 EP2419774A4 (fr) 2014-06-18

Family

ID=42982777

Family Applications (1)

Application Number Title Priority Date Filing Date
EP10764783.6A Withdrawn EP2419774A4 (fr) 2009-04-17 2010-04-16 Appareil et procédés de conversion d'onde électromagnétique évanescente

Country Status (3)

Country Link
EP (1) EP2419774A4 (fr)
CN (1) CN102460253B (fr)
WO (1) WO2010120383A1 (fr)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9436182B2 (en) 2014-05-23 2016-09-06 Google Inc. Autonomous vehicles
US9631933B1 (en) 2014-05-23 2017-04-25 Google Inc. Specifying unavailable locations for autonomous vehicles
WO2018208964A1 (fr) * 2017-05-09 2018-11-15 Forelux Inc. Appareil optique pour applications de lumière non visibles
CN110412667B (zh) * 2019-07-17 2022-06-21 深圳市隆利科技股份有限公司 多层结构光学薄膜
CN111897126B (zh) * 2020-07-31 2022-05-31 杭州电子科技大学 基于有限厚度手征原子媒质的Faraday偏振转换分析方法

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20010038325A1 (en) * 2000-03-17 2001-11-08 The Regents Of The Uinversity Of California Left handed composite media
US20060238897A1 (en) * 2005-04-21 2006-10-26 Kimihiko Nishioka Lens and optical system
WO2008069837A2 (fr) * 2006-05-16 2008-06-12 The Trustees Of The University Of Pennsylvania Lentilles optiques à sous-diffraction en champ éloigné (fasdol)
US20090086322A1 (en) * 2005-05-16 2009-04-02 Northeastern University Photonic Crystal Devices Using Negative Refraction

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2004020186A2 (fr) * 2002-08-29 2004-03-11 The Regents Of The University Of California Materiaux indefinis
US7072555B1 (en) * 2003-05-01 2006-07-04 The Regents Of The University Of California Systems and methods for transmitting electromagnetic energy in a photonic device
CN101389998B (zh) * 2004-07-23 2012-07-04 加利福尼亚大学董事会 特异材料
JP4712004B2 (ja) * 2007-06-21 2011-06-29 パナソニック株式会社 微小径光作製装置

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20010038325A1 (en) * 2000-03-17 2001-11-08 The Regents Of The Uinversity Of California Left handed composite media
US20060238897A1 (en) * 2005-04-21 2006-10-26 Kimihiko Nishioka Lens and optical system
US20090086322A1 (en) * 2005-05-16 2009-04-02 Northeastern University Photonic Crystal Devices Using Negative Refraction
WO2008069837A2 (fr) * 2006-05-16 2008-06-12 The Trustees Of The University Of Pennsylvania Lentilles optiques à sous-diffraction en champ éloigné (fasdol)

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
See also references of WO2010120383A1 *
Z. LIU ET AL: "Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects", SCIENCE, vol. 315, no. 5819, 23 March 2007 (2007-03-23), pages 1686-1686, XP055116481, ISSN: 0036-8075, DOI: 10.1126/science.1137368 *
Zubin Jacob ET AL: "Optical Hyperlens: Far-field imaging beyond the diffraction limit References and links", Science Opt. Lett. Opt. Lett. Appl. Phys. Lett. Phys. Rev. E Phys. Rev. B Phys. Rev. B V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov J. Mod. Opt. Phys. Rev. BPhys. Rev. Lett, 1 January 2006 (2006-01-01), pages 77-79, XP055116479, Retrieved from the Internet: URL:http://www.opticsinfobase.org/DirectPDFAccess/2D8905D0-C18F-EE9E-1A4482A7442C868E_97943/oe-14-18-8247.pdf?da=1&id=97943&seq=0&mobile=no [retrieved on 2014-05-06] *

Also Published As

Publication number Publication date
EP2419774A4 (fr) 2014-06-18
WO2010120383A1 (fr) 2010-10-21
CN102460253A (zh) 2012-05-16
CN102460253B (zh) 2014-08-13

Similar Documents

Publication Publication Date Title
US8634143B2 (en) Evanescent electromagnetic wave conversion methods II
US8773777B2 (en) Focusing and sensing apparatus, methods, and systems
US7777962B2 (en) Negatively-refractive focusing and sensing apparatus, methods, and systems
US7830618B1 (en) Negatively-refractive focusing and sensing apparatus, methods, and systems
US8531782B2 (en) Emitting and focusing apparatus, methods, and systems
US7872812B2 (en) Emitting and focusing apparatus, methods, and systems
US9081202B2 (en) Evanescent electromagnetic wave conversion lenses I
US8638505B2 (en) Negatively-refractive focusing and sensing apparatus, methods, and systems
US9081123B2 (en) Evanescent electromagnetic wave conversion lenses II
WO2010120383A1 (fr) Appareil et procédés de conversion d'onde électromagnétique évanescente
US9083082B2 (en) Evanescent electromagnetic wave conversion lenses III
US8634144B2 (en) Evanescent electromagnetic wave conversion methods I
US8164837B2 (en) Negatively-refractive focusing and sensing apparatus, methods, and systems
US8630044B2 (en) Evanescent electromagnetic wave conversion methods III
US8817380B2 (en) Emitting and negatively-refractive focusing apparatus, methods, and systems
US8730591B2 (en) Negatively-refractive focusing and sensing apparatus, methods, and systems
US9019632B2 (en) Negatively-refractive focusing and sensing apparatus, methods, and systems
EP2294482A1 (fr) Appareil, procédés, et systèmes de mise au point et de détection
US20090299683A1 (en) Emitting and focusing apparatus, methods, and systems

Legal Events

Date Code Title Description
PUAI Public reference made under article 153(3) epc to a published international application that has entered the european phase

Free format text: ORIGINAL CODE: 0009012

17P Request for examination filed

Effective date: 20111109

AK Designated contracting states

Kind code of ref document: A1

Designated state(s): AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HR HU IE IS IT LI LT LU LV MC MK MT NL NO PL PT RO SE SI SK SM TR

DAX Request for extension of the european patent (deleted)
A4 Supplementary search report drawn up and despatched

Effective date: 20140519

RIC1 Information provided on ipc code assigned before grant

Ipc: G02B 6/26 20060101AFI20140513BHEP

RAP1 Party data changed (applicant data changed or rights of an application transferred)

Owner name: SEARETE LLC

RAP1 Party data changed (applicant data changed or rights of an application transferred)

Owner name: SEARETE LLC

17Q First examination report despatched

Effective date: 20160224

STAA Information on the status of an ep patent application or granted ep patent

Free format text: STATUS: EXAMINATION IS IN PROGRESS

STAA Information on the status of an ep patent application or granted ep patent

Free format text: STATUS: THE APPLICATION IS DEEMED TO BE WITHDRAWN

18D Application deemed to be withdrawn

Effective date: 20180404