EP2294482A1 - Focusing and sensing apparatus, methods, and systems - Google Patents
Focusing and sensing apparatus, methods, and systemsInfo
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- EP2294482A1 EP2294482A1 EP09758706A EP09758706A EP2294482A1 EP 2294482 A1 EP2294482 A1 EP 2294482A1 EP 09758706 A EP09758706 A EP 09758706A EP 09758706 A EP09758706 A EP 09758706A EP 2294482 A1 EP2294482 A1 EP 2294482A1
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Classifications
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03B—APPARATUS OR ARRANGEMENTS FOR TAKING PHOTOGRAPHS OR FOR PROJECTING OR VIEWING THEM; APPARATUS OR ARRANGEMENTS EMPLOYING ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ACCESSORIES THEREFOR
- G03B17/00—Details of cameras or camera bodies; Accessories therefor
-
- 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
- G02B1/005—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 made of photonic crystals or photonic band gap materials
-
- 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
- G02B1/007—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 made of negative effective refractive index materials
-
- 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
- G02B27/0075—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 with means for altering, e.g. increasing, the depth of field or depth of focus
Definitions
- Applicant has provided above a specific reference to the application(s) from which priority is being claimed as recited by statute. Applicant understands that the statute is unambiguous in its specific reference language and does not require either a serial number or any characterization, such as “continuation” or “continuation-in-part,” for claiming priority to U.S. patent applications.
- the application discloses apparatus, methods, and systems that may relate to electromagnetic responses that include focusing (including negatively-refractive focusing), focus-adjusting, and sensing.
- FIG. 1 depicts a configuration of a focusing structure and a focus-adjusting structure.
- FIG. 2 depicts a coordinate transformation.
- FIG. 3 depicts a configuration of a focusing structure and a focus-adjusting structure.
- FIG. 4 depicts a coordinate transformation
- FIG.5 depicts a focusing structure and a focus-adjusting structure with a spatial separation.
- FIG. 6 depicts a focusing structure and a focus-adjusting structure without a spatial separation.
- FIG. 7 depicts a process flow.
- FIG. 8 depicts a process flow.
- FIG. 9 depicts a system that includes a focus-adjusting unit and a controller.
- FIG. 10 depicts a configuration of a negatively-refractive focusing structure.
- FIG. 11 depicts a coordinate transformation
- FIG. 12 depicts a configuration of a negatively-refractive focusing structure.
- FIG. 13 depicts a coordinate transformation.
- FIG. 14 depicts a negatively-refractive focusing structure with an input surface region.
- FIG. 15 depicts a process flow.
- FIG. 16 depicts a process flow.
- FIG. 17 depicts a system that includes a focusing unit and a controller.
- FIG. 18 depicts a configuration of a negatively-refractive focusing structure.
- FIG. 19 depicts a coordinate transformation
- FIG. 20 depicts a configuration of a negatively-refractive focusing structure.
- FIG. 21 depicts a coordinate transformation
- FIG. 22 depicts a negatively-refractive focusing structure with an input surface region.
- FIG.23 depicts a process flow.
- FIG. 24 depicts a process flow.
- FIG. 25 depicts a system that includes a focusing unit and a controller.
- Transformation optics is an emerging field of electromagnetic engineering. Transformation optics devices include lenses that refract electromagnetic waves, where the refraction imitates the bending of light in a curved coordinate space (a "transformation" of a flat coordinate space), e.g. as described in A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell's equations,” J. Mod. Optics 43, 773 (1996), J. B. Pendry and S. A. Ramakrishna, "Focusing light using negative refraction," J. Phys. [Cond. Matt.] 15, 6345 (2003), 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.
- 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.
- 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). Additional exemplary transformation optics devices are described in D.
- a transformation medium for a selected coordinate transformation, a transformation medium can be identified wherein electromagnetic waves refract as if propagating in a curved coordinate space corresponding to the selected 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, hi some applications, only selected matrix elements of the permittivity and permeability tensors need satisfy equations (1) and (2), e.g. where the transformation optics response is for a selected polarization only.
- a first set of permittivity and permeability matrix elements satisfy equations (1) and (2) 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 (1) and (2) 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 (1) and (2), but preserve products of selected elements in (1) and selected elements in (2), thus preserving dispersion relations inside the transformation medium (see, for example, D. Schurig et al (2), supra, and W.
- Reduced parameters can be used, for example, to substitute a magnetic response for an electric response, or vice versa. While 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 (1) and (2)), 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 (1) and (2) is substantially nonreflective).
- the reflective or scattering characteristics of a transformation medium with reduced parameters can be substantially reduced or eliminated by a suitable choice of coordinate transformation, e.g. by selecting a coordinate transformation for which the corresponding Jacobian ⁇ (or a subset of elements thereof) is continuous or substantially continuous at a boundary or interface of the transformation medium (see, for example, W. Cai et al, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 1 11105 (2007), herein incorporated by reference).
- constitutive parameters such as permittivity and permeability
- a medium responsive to an electromagnetic wave can vary with respect to a frequency of the electromagnetic wave (or equivalently, with respect to a wavelength of the electromagnetic wave in vacuum or in a reference medium).
- a medium can have constitutive parameters ⁇ ⁇ , ⁇ x , etc. at a first frequency, and constitutive parameters ⁇ 2 , ⁇ 2 , etc. at a second frequency; and so on for a plurality of constitutive parameters at a plurality of frequencies.
- constitutive parameters at a first frequency can provide a first response to electromagnetic waves at the first frequency, corresponding to a first selected coordinate transformation
- constitutive parameters at a second frequency can provide a second response to electromagnetic waves at the second frequency, corresponding to a second selected coordinate transformation
- a plurality of constitutive parameters at a plurality of frequencies can provide a plurality of responses to electromagnetic waves corresponding to a plurality of coordinate transformations.
- the first response at the first frequency is substantially nonzero (i.e. one or both of £, and ⁇ , is substantially non-unity), corresponding to a nontrivial coordinate transformation
- a second response at a second frequency is substantially zero (i.e.
- ⁇ 2 and ⁇ 2 are substantially unity), corresponding to a trivial coordinate transformation (i.e. a coordinate transformation that leaves the coordinates unchanged); thus, electromagnetic waves at the first frequency are refracted (substantially according to the nontrivial coordinate transformation), and electromagnetic waves at the second frequency are substantially nonrefracted.
- Constitutive parameters of a medium can also change with, time (e.g. in response to an external input or control signal), so that the response to an electromagnetic wave can vary with respect to frequency and/or time. Some embodiments may exploit this variation with frequency and/or time to provide respective frequency and/or time multiplexing/demultiplexing of electromagnetic waves.
- a transformation medium can have a first response at a frequency at time J 1 , corresponding to a first selected coordinate transformation, and a second response at the same frequency at time t 2 , corresponding to a second selected coordinate transformation.
- a transformation medium can have a response at a first frequency at time t v corresponding to a selected coordinate transformation, and substantially the same response at a second frequency at time t 2 .
- a transformation medium can have, at time t x , a first response at a first frequency and a second response at a second frequency, whereas at time t 2 , the responses are switched, i.e.
- the second response (or a substantial equivalent thereof) is at the first frequency and the first response (or a substantial equivalent thereof) is at the second frequency.
- the second response can be a zero or substantially zero response.
- Other embodiments that utilize frequency and/or time dependence of the transformation medium will be apparent to one of skill in the art.
- Constitutive parameters such as those of equations (1) and (2) (or reduced parameters derived therefrom) can be realized using artificially- structured materials.
- 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 metarnaterials.
- 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 magnetoelectric 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 (c.f. J. B. Pendry et al, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Micro. Theo. Tech.
- Some 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, 10Q101 (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, 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 nanostractured materials such as nanorod pairs or nano-fishnet structures (c.f. 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 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, layers, or other variations along some continuous structure (e.g. etchings on a substrate).
- layered metamaterials include: a structure consisting of alternating doped/intrinsic semiconductor layers (cf.
- 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.).
- FIG. 1 an illustrative embodiment is depicted that includes a focusing structure 110 and a focus-adjusting structure 120.
- 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 transducers are positioned inside a metallic or dielectric slab waveguide oriented normal to the page).
- the focusing structure receives input electromagnetic energy, depicted as solid rays 102; in this example, the input electromagnetic energy radiates from an electromagnetic source 101 positioned on an optical axis 112 of the focusing structure (the use of a ray description, in FIG.
- the solid rays 103 represent output electromagnetic energy from the focusing structure. This output electromagnetic energy is received by the focus-adjusting structure 120, which influences the propagation of the output electromagnetic energy (e.g. by refracting the rays 103, as depicted).
- the dashed rays 104 represent the "nominal" propagation of the output electromagnetic energy, i.e. the propagation that would occur in the absence of the focus-adjusting structure.
- the focusing structure 110 provides a nominal focusing region 130 having a nominal depth of focus 132; Ln this example, the nominal focusing region 130 is depicted as a slab having a thickness equal to the nominal depth of focus 132 and centered on a nominal focal plane 134 (where the dashed rays converge).
- the focus-adjusting structure 120 influences the propagation of the output electromagnetic energy to provide an actual focusing region 140 different than the nominal focusing region 130, the actual focusing region having an actual depth of focus 142 which is an extended depth of focus greater than the nominal depth of focus; in this example, the actual focusing region 140 is depicted as a slab having a thickness equal to the actual depth of focus 142 and centered on an actual focal plane 144.
- Embodiments optionally include one or more electromagnetic sensors (schematically depicted as ellipses 150) positioned within the actual focusing region.
- the dashed ellipse 152 represents a nominal sensor positioning, i.e. a sensor positioning within the nominal focusing region 130 that could apply in the absence of the focus-adjusting structure (in the present example, sensors are positioned only along the optical axis 112 of the focusing structure, but this is not intended to be limiting).
- the actual depth of focus may, in some embodiments, accommodate more sensors than the nominal depth of focus.
- the focusing structure 110 is depicted in FIG. 1 as having a lens-like shape, but this is a schematic illustration and is not intended to be limiting.
- focusing structures can include reflective structures (e.g. parabolic dish reflectors), refractive structures (e.g. dielectric, microwave, gradient index, or metamaterial lenses), dif ⁇ ractive structures (e.g. Fresnel zone plates), antenna structures (e.g. antenna director elements, antenna arrays), waveguiding structures (e.g. waveguides, transmission lines, and coherent bundles thereof) and various combinations, assemblies, portions, and hybrids thereof (such as an optical assembly or a refractive-diffractive lens), hi general, a focusing structure provides a nominal focusing region wherein electromagnetic energy coupled to the focusing structure is nominally substantially concentrated (i.e.
- reflective structures e.g. parabolic dish reflectors
- refractive structures e.g. dielectric, microwave, gradient index, or metamaterial lenses
- dif ⁇ ractive structures e.g. Fresnel zone plates
- antenna structures e.g. antenna director elements, antenna arrays
- waveguiding structures e.g. waveguides,
- the nominal focusing region may be a planar or substantially planar slab (e.g. 130 in FIG. 1) having a thickness corresponding to a nominal depth of focus of the focusing structure (e.g. 132 in FIG. 1) and centered on a nominal focal plane (e.g. 134 in FIG. 1).
- the nominal focusing region may be a non-planar region, e.g.
- the focusing structure defines an optical axis (such as that depicted as element 112 in FIG. 1) as a symmetry or central axis of the focusing structure, and the optical axis provides an axial direction (such as the axial unit vector 160 in FIG. 1), with transverse directions defined perpendicular thereto (such as the transverse unit vectors 161 and 162 in FIG. 1).
- the nominal focusing region is a planar slab
- the axial direction corresponds to a unit vector normal to the slab.
- the axial direction can vary along the transverse extent of the focusing region.
- the axial direction corresponds to a radius unit vector (and the transverse directions correspond to height/azimuth unit vectors or azimuth/zenith unit vectors, respectively); where the nominal focusing region is an otherwise-curved slab, the axial direction corresponds to a vector locally normal to the slab surface (and the transverse directions correspond to orthogonal unit vectors locally tangent to the slab surface).
- the nominal depth of focus of a focusing structure may be related to an f-number //# of the focusing structure, and/or to a resolution length £ in a transverse direction of the nominal focusing region.
- the f-number can correspond to a ratio of focal length to aperture diameter for the focusing structure, and may (inversely) characterize the convergence of electromagnetic energy towards the nominal focusing region; moreover, the convergence can correspond to a ratio of nominal depth of focus to transverse resolution length; so the following general relation may apply for the focusing structure: where d N is the nominal depth of focus.
- (smaller) nominal depth of focus corresponds to a larger (smaller) resolution length.
- the resolution length may corresponds to a circle of confusion (CoC) diameter limit for image blur perception, and/or the resolution length may correspond to a transverse extent of (the sensitive area of) an individual sensor or multiplet of sensors, as further discussed below.
- a focus-adjusting structure e.g. 120 in FIG.
- the actual focusing region may be a planar or substantially planar slab (e.g. 140 in FIG. 1) having a thickness corresponding to an actual depth of focus of the focusing structure (e.g. 142 in FIG. 1) and centered on an actual focal plane (e.g. 144 in FIG. 1).
- the actual focusing region may be a non-planar region, e.g.
- the non-planar region may enclose a non-planar focal surface (such as a Petzval, sagittal, or transverse focal surface).
- the nominal focusing region and the actual focusing region are substantially parallel (for substantially planar slabs), substantially concentric/confocal (for substantially cylindrically-, spherically, or ellipsoidally-curved slabs), or otherwise substantially co-curved
- the axial and transverse directions (defined previously for the nominal focusing region) also apply to the geometry of the actual focusing region; i.e. the axial direction corresponds to both the nominal and axial depths of focus (with transverse directions perpendicular thereto), and the actual depth of focus is equivalent to a actual axial dimension of the actual focusing region as measured along the axial dimension defined previously.
- a focus-adjusting structure such as that depicted in FIG. 1, includes a transformation medium.
- the ray trajectories 103 in FIG. 1 correspond to a coordinate transformation that is a uniform spatial dilation along the axial direction 160 (within the axial extent of the focus-adjusting structure 120); this coordinate transformation can be used to identify constitutive parameters for a corresponding transformation medium (e.g. as provided in equations (1) and (2), or reduced parameters obtained therefrom) that responds to electromagnetic radiation as in FIG. 1.
- a transformation medium e.g. as provided in equations (1) and (2), or reduced parameters obtained therefrom
- the uniform spatial dilation of FIGS. 1-2 corresponds to a transformation medium that is a uniform uniaxial medium.
- the focus-adjusting structure includes a transformation medium that provides a non-uniform spatial dilation.
- a focusing structure 110 provides a nominal focusing region 130 having a nominal depth of field 132
- the focus-adjusting structure 120 provides an actual focusing region 140 having an actual depth of field 142, where the actual depth of field is an extended depth of field greater than the nominal depth of field.
- FIG. 1 a focusing structure 110 provides a nominal focusing region 130 having a nominal depth of field 132
- the focus-adjusting structure 120 provides an actual focusing region 140 having an actual depth of field 142, where the actual depth of field is an extended depth of field greater than the nominal depth of field.
- FIG.3 provides an actual focal plane 144 coincident with the nominal focal plane 134; moreover, after exiting the focus-adjusting structure, the actual rays 103 and the nominal rays 104 propagate identically (implying that an optical path length through the focus-adjusting structure is equal to a nominal optical path length where the focus-adjusting structure is replaced by an ambient medium).
- embodiments of a focus-adjusting structure operable to provide an extended depth of focus for output electromagnetic energy greater than the nominal depth of focus, may comprise a transformation medium, the transformation medium corresponding to a coordinate transformation that maps a nominal focusing region (with a nominal depth of focus) to an actual focusing region (with an actual depth of focus greater than the nominal depth of focus); and the constitutive relations of this transformation medium may be implemented with an artificially-structured material (such as a metamaterial), as described previously.
- an artificially-structured material such as a metamaterial
- the coordinate transformation from the nominal focusing region to the actual focusing region includes a spatial dilation along an axial direction of the nominal focusing region, and a scale factor of the spatial dilation (within the actual focusing region) may correspond to a ratio of the actual depth of focus to the nominal depth of focus.
- a scale factor of the spatial dilation may correspond to a ratio of the actual depth of focus to the nominal depth of focus.
- a substantially cylindrically- or spherically-curved actual focusing region may be a (uniform or non-uniform) radial dilation of a substantially cylindrically- or spherically-curved nominal focusing region; a substantially ellipsoidally-curved actual focusing region may be a (uniform or non-uniform) confocal dilation of a substantially ellipsoidally-curved nominal focusing region; etc.
- the influence of the focus-adjusting structure provides a modified relationship (as compared to equation (4)) between the f-number, the nominal depth of focus, and the resolution length £ . Namely, some embodiments provide the relation
- d A is the actual depth of focus and s is a scale factor for a spatial dilation applied along the axial direction.
- the f-number is here defined independently of the focus-adjusting structure: it is a ratio of the nominal focal path length to aperture diameter for the focusing structure (however, some embodiments provide an actual focal path length equal or substantially equal to the nominal focal path length, notwithstanding that the actual focal distance may be substantially different than the nominal focal distance).
- Combining equations (4) and (7) recovers the relation d A ⁇ sd N discussed in the preceding paragraph.
- the focus-adjusting structure 120 is depicted in FIGS. 1 and 3 as a planar slab, but this is a schematic illustration and is not intended to be limiting.
- the focus-adjusting structure can be a cylindrically-, spherically-, or ellipsoidally-curved slab, or any other slab- or non-slab-like structure configured to receive the output electromagnetic energy and provide an extended depth of focus greater than the nominal depth of focus.
- the focus-adjusting structure 120 and the focusing structure 110 may have a spatial separation, defining an intermediate region 500 between the structures; in other embodiments, such as that depicted in FIG. 6, the focus-adjusting structure 120 and the focusing structure 110 may define a composite or contiguous unit.
- Embodiments may define an input surface region (e.g. region 510 in FIGS. 5 and 6) as a surface region of the focus-adjusting structure that receives output electromagnetic radiation from the focusing structure, and this input surface region maybe substantially nonreflective of the output electromagnetic radiation.
- this input surface region may be substantially nonreflective by virtue of a substantial impedance-matching to the adjacent medium.
- the adjacent medium corresponds to the intermediate region (e.g. 500 in FIG. 5).
- the adjacent medium corresponds to an output surface region 600 (e.g. as depicted in FIG. 6) of the focusing structure.
- a wave impedance of the input surface region is substantially equal to a wave impedance of the adjacent medium.
- the wave impedance of an isotropic medium is
- an impedance-matching is a substantial matching of every matrix element of the wave impedance tensor (i.e. to provide a substantially nonrefiective interface for all incident polarizations); in other embodiments an impedance-matching is a substantial matching of only selected matrix elements of the wave impedance tensor (e.g.
- the adjacent medium defines a permittivity S 1 and a permeability ⁇ , where either or both parameters may be substantially unity or substantially non-unity;
- the input surface region defines a permittivity ⁇ 2 and a permeability ⁇ 2 , where either or both parameters may be substantially unity or substantially non-unity; and the impedance- matching condition implies
- ⁇ 2 and ⁇ 2 may be tensor quantities.
- a surface normal direction and a surface parallel direction e.g. depicted as elements 521 and 522, respectively, in FIGS. 5 and 6
- some embodiments provide a input surface region that defines: a surface normal permittivity ⁇ 2 corresponding to the surface normal direction and a surface parallel permittivity corresponding to the surface parallel direction; and/or a surface normal permeability ⁇ 2 corresponding to the surface normal direction and a surface parallel permeability corresponding to the surface parallel direction; and the impedance-matching condition may imply (in addition to equation (9)) one or both of the following conditions:
- the surface normal direction and the surface parallel direction can vary with position along the input surface region.
- Some embodiments provide one or more electromagnetic sensors positioned within the actual focusing region of the focusing structure.
- electromagnetic sensors such as those depicted FIG. 1 and in other embodiments, are electromagnetic devices having a detectable response to received or absorbed electromagnetic energy.
- Electromagnetic sensors can include antennas (such as wire/loop antennas, horn antennas, reflector antennas, patch antennas, phased array antennas, etc.), solid-state photodetectors (such as photodiodes, CCDs, and photoresistors), vacuum photodetectors (such as phototubes and photomultipliers) chemical photodetectors (such as photographic emulsions), cryogenic photodetectors (such as bolometers), photoluminescent detectors (such as phosphor powders or fluorescent dyes/markers), MEMS detectors (such as microcantilever arrays with electromagnetically responsive materials or elements) or any other devices operable to detect and/or transduce electromagnetic energy.
- antennas such as wire/loop antennas, horn antennas, reflector antennas, patch antennas, phased array antennas, etc.
- solid-state photodetectors such as photodiodes, CCDs, and photoresistors
- vacuum photodetectors such as phototubes and photomultipliers
- Some embodiments include a plurality of electromagnetic sensors positioned within the actual focusing region.
- a first example is a multiplet of sensors operable at a corresponding multiplet of wavelengths or wavelength bands, i.e. a first sensor operable at a first wavelength/wavelength band, a second sensor operable at a second wavelength/wavelength band, etc.
- a second example is a focal plane array of sensors or sensor multiplets (e.g. a Bayer or Foveon sensor).
- a third example is a phased array of antennas.
- the plurality of sensors can be axially distributed (as in FIG. 1); for example, the extended depth of focus may admit a plurality of parallel focal plane sensor arrays.
- a transverse extent of the sensitive area of a sensor can provide a resolution length in the transverse direction (e.g. 136 in FIG. 1), and may bear a relation to the depth of focus (as in equations (4) and (7)).
- the focus-adjusting structure provides an extended depth of focus for output electromagnetic energy 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.
- the selected polarization may be a particular TE polarization (e.g. where the electric field is in a particular direction transverse to the axial direction, as with s-polarized electromagnetic energy), a particular TM polarization (e.g. where the magnetic field is in a particular direction transverse to the axial direction, as with p-polarized electromagnetic energy), a circular polarization, etc. (other embodiments provide an extended depth of focus for output electromagnetic energy that is substantially the same extended depth of focus for any polarization, e.g. for unpolarized electromagnetic energy).
- the focus-adjusting structure provides a first extended depth of focus for output electromagnetic energy at a first frequency and a second extended depth of focus for output electromagnetic energy at a second frequency, where the second extended depth of focus may be different than or substantially equal to the first extended depth of focus.
- the first and second frequencies may be selected from the frequency categories in the preceding paragraph.
- the recitation of 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 providing a focus-adjusting structure operable at first and second frequencies may include a transformation medium having an adjustable response to electromagnetic radiation.
- the transformation medium may have a response to electromagnetic radiation that is adjustable (e.g.
- a transformation 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 of a focus-adjusting structure operable at first and second frequencies may include transformation medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters.
- the frequency-dependent response at a first frequency may provide a first extended depth of focus for output electromagnetic energy at the first frequency
- the frequency-dependent response at a second frequency may provide second extended depth of focus for output electromagnetic energy at the second frequency
- a transformation 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.
- the focusing structure provides a first nominal depth of focus for output electromagnetic energy at a first frequency and a second nominal depth of focus for output electromagnetic energy at a second frequency, where the second nominal depth of focus may he different than or substantially equal to the first nominal depth of focus.
- Examples of focusing structures providing different first and second nominal depths of focus include: dichroic lenses or mirrors, frequency- selective surfaces, diffractive gratings; metamaterials having a frequency-dependent response; etc.; or, generally, any focusing structure having a chromatic dispersion or aberration.
- a focusing structure that provides first and second nominal depths of focus for output electromagnetic energy at first and second frequencies can be combined with a focus-adjusting structure that provides first and second extended depths of focus for output electromagnetic energy at the first and second frequencies.
- a particular embodiment provides different first and second nominal depths of focus but substantially equal first and second extended depths of focus (thus, for example, compensating for a chromatic aberration of the focusing structure).
- An illustrative embodiment is depicted as a process flow diagram in FIG.7.
- Flow 700 optionally includes operation 710 — deflecting an electromagnetic wave, whereby the electromagnetic wave converges towards a nominal focusing region having a nominal axial dimension.
- a focusing structure such as that depicted as element 110 in FIGS.
- Operation 710 optionally includes sub-operation 712 — deflecting a first component of the electromagnetic wave at a first frequency, whereby the first component converges toward a first nominal focusing subregion within the nominal focusing region, the first nominal focusing subregion having a first nominal axial subdimension — and sub-operation 714 — deflecting a second component of the electromagnetic wave at a second frequency, whereby the second electromagnetic wave converges toward a second nominal focusing subregion within the nominal focusing region, the second nominal focusing subregion having a second nominal axial subdimension.
- a focusing structure may provide a first nominal depth of focus for output electromagnetic energy at a first frequency and a second nominal depth of focus for output electromagnetic energy at a second frequency (e.g. where the focusing structure has a chromatic dispersion or aberration ).
- Flow 700 includes operation 720 — substantially-nonreflectively receiving the electromagnetic wave that converges towards the nominal focusing region.
- a focus- adjusting structure such as that depicted as element 120 in FIGS.5 and 6, may include an input surface region 510 that is substantially nonreflective of input electromagnetic energy incident upon the input surface region from an adjacent region (e.g. where the input surface region is substantially impedance-matched to the adjacent region).
- Flow 700 further includes operation 730 — spatially dilating the electromagnetic wave along a direction corresponding to the nominal axial dimension, thereby providing an actual focusing region having an actual axial dimension greater than the nominal axial dimension.
- a focus-adjusting structure such as that depicted as element 120 in FIGS. 1 and 3, may receive output electromagnetic energy 103 and influence the propagation thereof, whereby the output electromagnetic energy converges towards an actual focusing region 140 instead of a nominal focusing region 130; and the focus-adjusting structure may include a transformation medium corresponding to a coordinate transformation that includes a spatial dilation, e.g. as depicted in FIGS. 2 and 4.
- Operation 730 optionally includes sub-operation 732 — spatially dilating a first component of the electromagnetic wave at a first frequency, thereby providing a first actual focusing subregion within the actual focusing region, the first actual focusing subregion having a first actual axial subdimension greater than the nominal axial dimension — and sub- operation 734 — spatially dilating a second electromagnetic wave at a second frequency, thereby providing a second actual focusing subregion within the actual focusing region, the second actual focusing subregion having a second actual axial subdimension greater than the nominal axial dimension.
- a focus- adjusting structure may provide a first extended depth of focus for output electromagnetic energy at a first frequency and a second extended depth of focus for output electromagnetic energy at a second frequency, where the second extended depth of focus may be different than or substantially equal to the first extended depth of focus; and the focus- adjusting structure operable at first and second frequencies may include a transformation medium having an adjustable response to electromagnetic radiation, or a transformation medium having a frequency-dependent response to electromagnetic radiation.
- Flow 700 optionally further includes operation 740 — sensing the electromagnetic wave at one or more locations within the actual focusing region.
- one or more electromagnetic sensors such as those depicted as elements 150 in FIG. 1, may be positioned within an actual focusing region 140 to detect/receive/absorb the output electromagnetic energy 103.
- Flow 800 includes operation 810 — identifying a nominal focusing region for a focusing structure, the nominal focusing region having a nominal axial dimension.
- a nominal focusing region is depicted as region 130 in FIGS. 1 and 3.
- the nominal focusing region may correspond to a region centered on a nominal focal plane (or non-planar nominal focal surface) having a thickness corresponding to a nominal depth of focus.
- Operation 810 optionally includes sub-operation 812 — for electromagnetic waves at a first frequency, identifying a first nominal focusing subregion within the nominal focusing region for the focusing structure, the first nominal focusing subregion having a first nominal axial subdimension — and sub- operation 814 — for electromagnetic waves at a second frequency, identifying a second nominal focusing subregion within the nominal focusing region for the focusing structure, the second nominal focusing subregion having a second nominal axial subdimension.
- the focusing structure may have a chromatic dispersion or aberration, whereby the nominal focusing region depends upon the frequency of the input electromagnetic energy.
- Flow 800 further includes operation 820 — determining electromagnetic parameters for a spatial region containing the nominal focusing region, the electromagnetic parameters providing an actual focusing region having an actual axial dimension greater than the nominal axial dimension; where the electromagnetic parameters include (1) axial electromagnetic parameters and (2) transverse electromagnetic parameters that inversely correspond to the axial electromagnetic parameters.
- the spatial region can be a volume that encloses a focus-adjusting structure, such as that depicted as element 120 in FIGS. 1 and 3, and the determined electromagnetic parameters are the electromagnetic parameters of the focus-adjusting structure.
- the focus-adjusting structure may include a transformation medium, where the determined electromagnetic parameters satisfy or substantially satisfy equations (1) and (2), as described above; or, the determined electromagnetic parameters may be reduced parameters (as discussed earlier) where the corresponding non-reduced parameters satisfy equations (1) and (2).
- the determining of the electromagnetic parameters includes: determining a coordinate transformation (such as those depicted in FIGS. 2 and 4); then determining electromagnetic parameters for a co ⁇ esponding transformation medium (e.g. with equations (1) and (2)); then, optionally, reducing the electromagnetic parameters (e.g. to at least partially substitute a magnetic response for an electromagnetic response, or vice versa, as discussed above).
- Operation 820 optionally includes sub-operation 822 — for electromagnetic waves at a first frequency, determining a first subset of the electromagnetic parameters providing a first actual focusing subregion within the actual focusing region, the first actual focusing subregion having a first actual axial subdimension greater than the nominal axial dimension — and sub-operation 824 — for electromagnetic waves at a second frequency, determining a second subset of the electromagnetic parameters providing a second actual focusing subregion within the actual focusing region, the second actual focusing subregion having a second actual axial subdimension greater than the nominal axial dimension.
- the determined electromagnetic parameters may be the electromagnetic parameters of a focus-adjusting structure having a first extended depth of focus for output electromagnetic energy at a first frequency and a second extended depth of focus for output electromagnetic energy at a second frequency.
- the focus-adjusting structure may include a transformation medium having an adjustable response to electromagnetic radiation, e.g. adjustable between a first response, corresponding to the first subset of the electromagnetic parameters, and a second response, corresponding to the second subset of the electromagnetic parameters.
- the focus-adjusting structure may include a transformation medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters, so that the first and second subsets of the electromagnetic parameters are values of the frequency-dependent constitutive parameters at the first and second frequencies, respectively.
- Flow 800 optionally further includes operation 830 — selecting one or more positions of one or more electromagnetic sensors within the Error! Reference source not found.
- electromagnetic sensors may be positioned in a phased array, a focal plane array, an axially-distributed arrangement, etc.
- Flow 800 optionally further includes operation 840 — configuring an artificially-structured material having an effective electromagnetic response that corresponds to the electromagnetic parameters in the spatial region.
- the configuring may include configuring the structure(s) and/or the materials that compose a photonic crystal or a metamaterial.
- Operation 840 optionally includes determining an arrangement of a plurality of electromagnetically responsive elements having a plurality of individual responses, the plurality of individual responses composing the effective electromagnetic response.
- the determining may include determining the positions, orientations, and individual response parameters (spatial dimensions, resonant frequencies, linewidths, etc.) of a plurality of metamaterial elements such as split-ring resonators, wire or nanowire pairs, etc.
- Operation 840 optionally includes configuring at least one electromagnetically-responsive structure to arrange a plurality of distributed electromagnetic responses, the plurality of distributed electromagnetic responses composing the effective electromagnetic response.
- the configuring may include configuring the distribution of loads and interconnections on a transmission line network, configuring an arrangement of layers in a layered metamaterial, configuring a pattern of etching or deposition (as with a nano-fishnet structure), etc.
- the system 900 includes a focusing unit 910 optionally coupled to a controller unit 940.
- the focusing unit 910 may include a focusing structure such as that depicted as element 110 in FIGS. 1 and 3.
- the focusing structure may be a variable or adaptive focusing structure, such as an electro-optic lens, a liquid or liquid-crystal lens, a mechanically-adjustable lens assembly, a variable metamaterial lens, or any other variable or adaptive focusing structure responsive to one or more control inputs to vary or adapt one or more focusing characteristics (focal length, aperture size, nominal depth of focus, operating frequency/frequency band, operating polarization, etc.) of the focusing structure; and the controller unit 940 may include control circuitry that provides one or more control inputs to the variable or adaptive focusing structure.
- the system 900 further includes a focus- adjusting unit 920 coupled to the controller unit 940.
- the focusing-adjusting unit 920 may include a focus-adjusting structure such as that depicted as element 120 in FIGS. 1 and 3.
- the focus-adjusting structure may be a variable focus-adjusting structure, such as a variable metamaterial responsive to one or more control inputs to vary one or more focus-adjusting characteristics (extended depth of focus, operating frequency/frequency band, operating polarization, effective coordinate transformation for a transformation medium, etc.); and the controller unit 940 may include control circuitry that provides one or more control inputs to the variable focus-adjusting structure.
- the controller unit 940 may include circuitry for coordinating or synchronizing the operation of the focusing unit 910 and the focus-adjusting unit 920; for example, the controller unit 940 may vary one or more focusing characteristics of a focusing structure (e.g.
- the system 900 optionally further includes a sensing unit 930 that may include one or more sensors, such as those depicted as elements 150 in FIG. 1, and associated circuitry such as receiver circuitry, detector circuitry, and/or signal processing circuitry.
- a sensing unit 930 may include one or more sensors, such as those depicted as elements 150 in FIG. 1, and associated circuitry such as receiver circuitry, detector circuitry, and/or signal processing circuitry.
- the sensing unit 930 is optionally coupled to the controller unit 940, and in some embodiments the controller unit 940 includes circuitry responsive to sensor data (from the sensor unit 930) to vary the focusing characteristics of a focusing structure and/or vary the focus-adjusting characteristics of a focus-adjusting structure.
- the controller unit 940 may include circuitry responsive to the sensor data to identify a frequency of received energy, adjust the focusing unit 910 to an operating frequency substantially equal to the frequency of received energy, and/or adjust the focus-adjusting unit 920 to an operating frequency substantially equal to the frequency of received energy.
- the controller unit may include circuitry responsive to the sensor data to identify an actual focusing region (e.g. depicted as region 140 in FIGS. 1 and 3) and vary the actual focusing region by varying the focusing characteristics of a focusing structure and/or varying the focus-adjusting characteristics of a focus-adjusting structure.
- FIG. 10 an illustrative embodiment is depicted that includes a negatively-refractive focusing structure 110.
- This and other drawings can represent a planar view of a three-dimensional embodiment, or a two-dimensional embodiment (e.g. in FIG. 10 where the structures are positioned inside a metallic or dielectric slab waveguide oriented normal to the page).
- the negatively-refractive focusing structure receives and negatively refracts electromagnetic energy, depicted as solid rays 102 (the use of a ray description, in FIG. 10 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.
- the negatively-refracted electromagnetic energy converges towards an interior focusing region 120 positioned inside the negatively-refractive focusing structure 110; in this example, the interior focusing region 120 is depicted as a slab having a thickness equal an axial extent 122 of the interior focusing region.
- the axial extent 122 corresponds to an axial direction indicated by the axial unit vector 160, with transverse unit vectors 161 and 162 defined perpendicular thereto, hi FIG. 10, the electromagnetic energy radiates from exemplary electromagnetic sources 101 in an exterior field region 130, the exterior field region being positioned outside the negatively-refractive focusing structure.
- the exterior field region 130 is depicted as a slab having a thickness equal to an axial extent 132 of the exterior field region.
- the electromagnetic sources 101 in the exterior field region correspond to electromagnetic images 103 in the interior focusing region.
- the axial extent 122 of the interior focusing region exceeds the axial extent 132 of the exterior field region (spanned, in this example, by the electromagnetic sources 101), thus demonstrating that the negatively- refractive focusing structure provides an axial magnification greater than one, and in this example the axial magnification corresponds to a ratio of the axial extent of the interior focusing region to the axial extent of the exterior field region.
- Embodiments optionally include one or more electromagnetic sensors (schematically depicted as ellipses 150) positioned within the interior focusing region (in the presented illustrative representation, sensors are linearly positioned along the axial extent 122 of the interior focusing region, but this is not intended to be limiting).
- embodiments provide a negatively-refractive focusing structure having an interior focusing region and an exterior field region; electromagnetic energy that radiates from the exterior field region, and couples to the negatively- refractive focusing structure, is subsequently substantially concentrated in the interior focusing region.
- each object point in the exterior field region defines a point spread function and a corresponding enclosed energy region (e.g.
- the interior focusing region is a union of the enclosed energy regions for the object points that compose the exterior field region.
- the negatively-refractive focusing structure provides an axial magnification, and in some applications the axial magnification corresponds to a ratio where the divisor is an axial separation between first and second object points and the dividend is an axial separation between centroids of first and second point spread functions corresponding to the first and second object points.
- the interior focusing region may be a planar or substantially planar slab (e.g. 120 in FIG. 10) having a slab thickness providing the axial extent of the interior focusing region (e.g.
- the interior focusing region may be a non-planar slab-like region, e.g. a cylindrically-, spherically-, ellipsoidally-, or otherwise-curved slab having a slab thickness providing the axial extent of the interior focusing region.
- the interior focusing region may be neither planar nor slab-like.
- the negatively-refractive focusing structure defines an optical axis as a symmetry or central axis of the negatively-refractive focusing structure, and the optical axis provides an axial direction, with transverse directions defined perpendicular thereto.
- the axial direction corresponds to a radius unit vector (and the transverse directions correspond to height/azimuth unit vectors or azimuth/zenith unit vectors, respectively); where the interior focusing region is an otherwise-curved slab, the axial direction corresponds to a vector locally normal to the slab surface (and the transverse directions correspond to orthogonal unit vectors locally tangent to the slab surface).
- a negatively-refractive focusing structure such as that depicted in FIG. 10, includes a transformation medium.
- the ray trajectories 102 in FIG. 10 correspond to a coordinate transformation that is multiple- valued and includes both a coordinate inversion and a uniform spatial dilation along the axial direction 160 (within the axial extent of the negatively-refractive focusing structure 110); this coordinate transformation can be used to identify constitutive parameters for a corresponding transformation medium (e.g. as provided in equations (1) and (2), or reduced parameters obtained therefrom) that responds to electromagnetic radiation as in FIG. 10.
- a corresponding transformation medium e.g. as provided in equations (1) and (2), or reduced parameters obtained therefrom
- the second branch 202 includes an axial coordinate inversion and a uniform axial coordinate dilation, and maps the untransformed coordinate region 220 to the interior focusing region 120.
- the figure also indicates the axial extent of the negatively-refractive focusing structure 110 on the z'-axis (coinciding, in this example, with the range of the second branch 202).
- a scale factor a scale factor
- FIGS. 10-11 presents a constant negative scale factor s ⁇ - ⁇ within the negatively-refractive focusing structure 110, corresponding to a coordinate inversion (whereby s ⁇ 0 ) and a uniform spatial dilation (whereby
- the uniform spatial dilation of FIGS. 10-11 corresponds to a transformation medium that is a uniform uniaxial medium.
- the scale factor is negative, so that the constitutive parameters in equation (12) are negative, and the transformation medium is a negatively-refractive medium defining a negative index of refraction.
- the negatively-refractive focusing structure includes a transformation medium that provides a non-uniform spatial dilation.
- a transformation medium that provides a non-uniform spatial dilation.
- FIG. 12 An example is depicted in FIG. 12 and the corresponding multiple-valued coordinate transformation is depicted in FIG. 13.
- a negatively-refractive focusing structure 110 provides an interior focusing region 120 for electromagnetic energy that radiates from an exterior field region 130.
- FIG. 10 the embodiment of FIG.
- embodiments of a negatively-refractive focusing structure operable to provide an interior focusing region for electromagnetic energy that radiates from an exterior field region, may comprise a transformation medium, the transformation medium corresponding to a multiple- valued coordinate transformation that maps an untransformed region to the exterior field region, and further maps the untransformed region to the interior focusing region; and the constitutive relations of this transformation medium may be implemented with an artificially-structured material (such as a metamaterial), as described previously.
- an artificially-structured material such as a metamaterial
- the coordinate transformation includes a coordinate inversion and spatial dilation along an axial direction of the interior focusing region, and a scale factor of the spatial dilation (within the interior focusing region) may correspond to a ratio of an axial extent of the interior focusing region to an axial extent of the exterior field region.
- a scale factor of the spatial dilation may correspond to a ratio of an axial extent of the interior focusing region to an axial extent of the exterior field region.
- a substantially cylindrically- or spherically-curved interior focusing region may correspond to a (uniform or nonuniform) inversion/dilation of a cylindrical or spherical radius coordinate;
- a substantially ellipsoidally-curved interior focusing region may correspond to a (uniform or non-uniform) inversion/dilation of a confocal ellipsoidal coordinate; etc.
- the negatively-refractive focusing structure 110 is depicted in FIGS. 10 and 12 as a planar slab, but this is a schematic illustration and is not intended to be limiting.
- the negatively-refractive focusing structure can be a cylindrically-, spherically-, or ellipsoidally-curved slab, or any other slab- or non- slab-like structure configured to provide an interior focusing region for negatively- refracted electromagnetic energy with an axial magnification substantially greater than one.
- equations (1) and (2) generally provide a medium that is substantially nonreflective.
- the input surface region may be substantially nonreflective by virtue of a substantial impedance- matching to the adjacent region.
- a wave impedance of the input surface region is substantially equal to a wave impedance of the adjacent region.
- the wave impedance of an isotropic medium is while the wave impedance of a generally anisotropic medium is a tensor quantity, e.g. as defined in L. M. Barkovskii and G. N. Borzdov, "The impedance tensor for electromagnetic waves in anisotropic media," J. Appl. Spect. 20, 836 (1974) (herein incorporated by reference).
- an impedance-matching is a substantial matching of every matrix element of the wave impedance tensor (i.e. to provide a substantially nonrefiective interface for all incident polarizations); in other embodiments an impedance-matching is a substantial matching of only selected matrix elements of the wave impedance tensor (e.g.
- the adjacent region defines a permittivity ⁇ ⁇ and a permeability ⁇ x , where either or both parameters may be substantially unity or substantially non-unity;
- the input surface region defines a permittivity ⁇ 2 and a permeability ⁇ 2 , where either or both parameters may be substantially unity or substantially non-unity; and the impedance- matching condition implies
- the surface normal direction and the surface parallel direction can vary with position along the input surface region.
- Some embodiments provide one or more electromagnetic sensors positioned within the interior focusing region of the negatively-refractive focusing structure.
- electromagnetic sensors such as those depicted FIG. 10 and in other embodiments, are electromagnetic devices having a detectable response to received or absorbed electromagnetic energy.
- Electromagnetic sensors can include antennas (such as wire/loop antennas, horn antennas, reflector antennas, patch antennas, phased array antennas, etc.), solid-state photodetectors (such as photodiodes, CCDs, and photoresistors), vacuum photodetectors (such as phototubes and photomultipliers) chemical photodetectors (such as photographic emulsions), cryogenic photodetectors (such as bolometers), photoluminescent detectors (such as phosphor powders or fluorescent dyes/markers), MEMS detectors (such as microcantilever arrays with electromagnetically responsive materials or elements) or any other devices operable to detect and/or transduce electromagnetic energy.
- antennas such as wire/loop antennas, horn antennas, reflector antennas, patch antennas, phased array antennas, etc.
- solid-state photodetectors such as photodiodes, CCDs, and photoresistors
- vacuum photodetectors such as phototubes and photomultipliers
- Some embodiments include a plurality of electromagnetic sensors positioned within the interior focusing region.
- a first example is a multiplet of sensors operable at a corresponding multiplet of wavelengths or wavelength bands, i.e. a first sensor operable at a first wavelength/wavelength band, a second sensor operable at a second wavelength/wavelength band, etc.
- a second example is a focal plane array of sensors or sensor multiplets (e.g. a Bayer or Foveon sensor).
- a third example is a phased array of antennas.
- the plurality of sensors can be axially distributed (as in FIG. 10); for example, the axial extent of the interior focusing region may admit a plurality of parallel focal plane sensor arrays.
- the negatively-refractive focusing structure provides an interior focusing region with an axial magnification substantially greater than one for electromagnetic energy 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 particular TE polarization (e.g.
- TM polarization e.g. where the magnetic field is in a particular direction transverse to the axial direction, as with p-polarized electromagnetic energy
- circular polarization etc.
- other embodiments provide an interior focusing region with an axial magnification substantially greater than one that is substantially the same interior focusing region with substantially the same axial magnification for any polarization of electromagnetic energy, e.g. for unpolarized electromagnetic energy).
- the negatively-refractive focusing structure provides a first interior focusing region with a first axial magnification substantially greater than one for electromagnetic energy at a first frequency, and a second interior focusing region with a second axial magnification substantially greater than one for electromagnetic energy at a second frequency.
- the first axial magnification may be different than or substantially equal to the first axial magnification
- the first and second interior focusing regions may be substantially (or completely) non- overlapping, partially overlapping or substantially (or completely) overlapping.
- 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 providing a negatively- refractive focusing structure operable at first and second frequencies may include a transformation medium having an adjustable response to electromagnetic radiation.
- the transformation medium may have a response to electromagnetic radiation that is adjustable (e.g. in response to an external input or control signal) between a first response and a second response, the first response providing the first interior focusing region for electromagnetic energy at the first frequency, and the second response providing the second interior focusing region for electromagnetic energy at the second frequency.
- a transformation medium with an adjustable electromagnetic response may be implemented with variable metamaterials, e.g. as described in R. A.
- a negatively-refractive focusing structure operable at first and second frequencies may include transformation medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters.
- the frequency-dependent response at a first frequency may provide a first interior focusing region for electromagnetic energy at the first frequency
- the frequency-dependent response at a second frequency may provide second interior focusing region for electromagnetic energy at the second frequency.
- a transformation 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 600 includes operation 610 — negatively refracting an electromagnetic wave at a surface region, the surface region defining a surface normal direction.
- a negatively-refractive focusing structure such as that depicted as element 110 in FIG. 14, may include an input surface region 510 that negatively refracts electromagnetic energy incident upon the input surface region from an adjacent region, and the negatively-refractive focusing structure may include a transformation medium that provides a coordinate inversion (for a coordinate corresponding to a direction normal to the surface, e.g. the direction 521 in FIG. 14), the coordinate inversion corresponding to a negatively- refractive response of the transformation medium.
- Flow 600 further includes operation 620 — spatially dilating the refracted electromagnetic wave along a dilation direction, the dilation direction corresponding to the surface normal direction.
- a negatively-refractive focusing structure such as that depicted as element 110 in FIGS. 10 and 12, may spatially dilate refracted electromagnetic energy 102 along an axial direction (e.g. the direction 160 in FIGS.
- Operation 620 optionally includes sub-operation 622 — spatially dilating a first component of the refracted electromagnetic wave at a first frequency along the dilation direction — and sub-operation 624 — spatially dilating a second component of the refracted electromagnetic wave at a second frequency along the dilation direction.
- a negatively-refractive focusing structure may provide a first interior focusing region with a first axial magnification for electromagnetic energy at a first frequency and a second interior focusing region with a second axial magnification for electromagnetic energy at a second frequency, where the second axial magnification may be different than or substantially equal to the first axial magnification; and this negatively-refractive focusing structure operable at first and second frequencies may include a transformation medium having an adjustable response to electromagnetic radiation, or a transformation medium having a frequency-dependent response to electromagnetic radiation.
- Flow 600 optionally includes operation 630 — sensing the electromagnetic wave at one or more locations within a focusing region that is provided by the negatively refracting and the spatially dilating.
- a negatively-refractive focusing structure 110 such as that depicted in FIGS. 10 and 12, may provide an interior focusing region 120, and one or more electromagnetic sensors, such as those depicted as elements 150 in FIG. 10, may be positioned within the interior focusing region to detect/receive/absorb the electromagnetic energy 102.
- Flow 700 includes operation 710 — determining electromagnetic parameters that define a negative refractive index in a spatial region, the electromagnetic parameters providing an axial magnification substantially greater than one for an interior focusing region within the spatial region.
- the spatial region may be a volume that encloses a negatively-refractive focusing structure, such as that depicted as element 110 in FIGS. 10 and 12, and the determined electromagnetic parameters may be the electromagnetic parameters of the negatively-refractive focusing structure.
- the negatively-refractive focusing structure may include a transformation medium, where the determined electromagnetic parameters satisfy or substantially satisfy equations (1) and (2), as described above; or, the determined electromagnetic parameters may be reduced parameters (as discussed earlier) where the corresponding non-reduced parameters satisfy equations (1) and (2).
- the determining of the electromagnetic parameters includes: determining a coordinate transformation (such as those depicted in FIGS. 11 and 13); then determining electromagnetic parameters for a corresponding transformation medium (e.g. with equations (1) and (2)); then, optionally, reducing the electromagnetic parameters (e.g. to at least partially substitute a magnetic response for an electromagnetic response, or vice versa, as discussed above).
- Operation 710 optionally includes sub-operation 712 — for electromagnetic waves at a first frequency, determining a first subset of the electromagnetic parameters providing a first axial magnification substantially greater than one for a first interior focusing subregion within the interior focusing region — and sub-operation 714 — for electromagnetic waves at a second frequency, determining a second subset of the electromagnetic parameters providing a second axial magnification substantially greater than one for a second interior focusing subregion within the interior focusing region.
- the determined electromagnetic parameters may be the electromagnetic parameters of a negatively-refractive focusing structure providing a first interior focusing region with a first axial magnification for electromagnetic energy at a first frequency and a second interior focusing region with a second axial magnification for electromagnetic energy at a second frequency.
- the negatively- refractive focusing structure may include a transformation medium having an adjustable response to electromagnetic radiation, e.g. adjustable between a first response, corresponding to the first subset of the electromagnetic parameters, and a second response, corresponding to the second subset of the electromagnetic parameters.
- the negatively-refractive focusing structure may include a transformation medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters, so that the first and second subsets of the electromagnetic parameters are values of the frequency-dependent constitutive parameters at the first and second frequencies, respectively.
- Flow 700 optionally further includes operation 720 — selecting one or more positions of one or more electromagnetic sensors within the spatial region.
- electromagnetic sensors may be positioned in a phased array, an focal plane array, an axially-distributed arrangement, etc.
- Flow 700 optionally further includes operation 730 — configuring an artificially-structured material having an effective electromagnetic response that corresponds to the electromagnetic parameters in the spatial region.
- the configuring may include configuring the structure(s) and/or the materials that compose a photonic crystal or a metamaterial.
- Operation 730 optionally includes determining an arrangement of a plurality of electromagnetically responsive elements having a plurality of individual responses, the plurality of individual responses composing the effective electromagnetic response.
- the determining may include determining the positions, orientations, and individual response parameters (spatial dimensions, resonant frequencies, linewidths, etc.) of a plurality of metamaterial elements such as split-ring resonators, wire or nanowire pairs, etc.
- Operation 730 optionally includes configuring at least one electromagnetically-responsive structure to arrange a plurality of distributed electromagnetic responses, the plurality of distributed electromagnetic responses composing the effective electromagnetic response.
- the configuring may include configuring the distribution of loads and interconnections on a transmission line network, configuring an arrangement of layers in a layered metamaterial, configuring a pattern of etching or deposition (as with a nano-fishnet structure), etc.
- the system 800 includes a focusing unit 810 optionally coupled to a controller unit 830.
- the focusing unit 810 may include a negatively- refractive focusing structure such as that depicted as element 110 in FIGS. 10 and 12.
- the negatively-refractive focusing structure may be a variable negatively-refractive focusing structure, such as a variable metamaterial responsive to one or more control inputs to vary one or more focusing characteristics (axial magnification, operating frequency/frequency band, operating polarization, effective coordinate transformation for a transformation medium, etc.); and the controller unit 830 may include control circuitry that provides one or more control inputs to the variable negatively-refractive focusing structure.
- the system 800 optionally further includes a sensing unit 820 that may include one or more sensors, such as those depicted as elements 150 in FIG. 10, and associated circuitry such as receiver circuitry, detector circuitry, and/or signal processing circuitry.
- the sensing unit 820 is optionally coupled to the controller unit 830, and in some embodiments the controller unit 830 includes circuitry for coordinating or synchronizing the operation of the focusing unit 810 and the sensing unit 820.
- the controller unit 830 may include circuitry responsive to sensor data (from the sensor unit 820) to vary the focusing characteristics of the focusing structure.
- the controller unit may include circuitry responsive to the sensor data to identify a frequency/polarization of received energy, and adjust the focusing unit to an operating frequency/polarization substantially equal to the frequency/polarization of the received energy.
- the controller unit may include circuitry responsive to the sensor data to identify a target interior focusing region (and/or a target axial magnification), and corresponding adjust the focusing system whereby a negatively-refractive focusing structure provides an interior focusing region substantially equal to the target interior focusing region (and/or an axial magnification substantially equal to the target axial magnification).
- FIG. 18 an illustrative embodiment is depicted that includes a negatively-refractive focusing structure 110.
- FIG. 18 can represent a planar view of a three-dimensional embodiment, or a two-dimensional embodiment (e.g. in FIG. 18 where the structures are positioned inside a metallic or dielectric slab waveguide oriented normal to the page).
- the negatively-refractive focusing structure receives and negatively refracts electromagnetic energy, depicted as solid rays 102 (the use of a ray description, in FIG. 18 and elsewhere, is a heuristic convenience for purposes of visual illustration, and is not intended to connote any limitations or assumptions of geometrical optics; farther, the elements depicted in FIG. 18 can have spatial dimensions that are variously less than, greater than, or comparable to a wavelength of interest).
- the negatively-refracted electromagnetic energy converges towards an interior focusing region 120 positioned inside the negatively-refractive focusing structure 110; in this example, the interior focusing region 120 is depicted as a slab having a thickness equal an axial extent 122 of the interior focusing region.
- the axial extent 122 corresponds to an axial direction indicated by the axial unit vector 160, with transverse unit vectors 161 and 162 defined perpendicular thereto, hi FIG. 18, the electromagnetic energy radiates from exemplary electromagnetic sources 101 in an exterior field region 130, the exterior field region being positioned outside the negatively-refractive focusing structure.
- the exterior field region 130 is depicted as a slab having a thickness equal to an axial extent 132 of the exterior field region.
- the electromagnetic sources 101 in the exterior field region correspond to electromagnetic images 103 in the interior focusing region.
- the axial extent 132 of the exterior field region exceeds the axial extent 122 of the interior focusing region (spanned, in this example, by the electromagnetic images 103), thus demonstrating that the negatively- refractive focusing structure provides an axial magnification less than one, and in this example the axial magnification corresponds to a ratio of the axial extent of the interior focusing region to the axial extent of the exterior field region.
- Embodiments optionally include one or more electromagnetic sensors (schematically depicted as ellipses 150) positioned within the interior focusing region (in the presented illustrative representation, sensors are linearly positioned along the axial extent 122 of the interior focusing region, but this is not intended to be limiting).
- embodiments provide a negatively-refractive focusing structure having an interior focusing region and an exterior field region; electromagnetic energy that radiates from the exterior field region, and couples to the negatively- refractive focusing structure, is subsequently substantially concentrated in the interior focusing region.
- each object point in the exterior field region defines a point spread function and a corresponding enclosed energy region (e.g.
- the interior focusing region is a union of the enclosed energy regions for the object points that compose the exterior field region.
- the negatively-refractive focusing structure provides an axial magnification, and in some applications the axial magnification corresponds to a ratio where the divisor is an axial separation between first and second object points and the dividend is an axial separation between centroids of first and second point spread functions corresponding to the first and second object points, hi some embodiments, the interior focusing region may be a planar or substantially planar slab (e.g. 120 in FIG. 18) having a slab thickness providing the axial extent of the interior focusing region (e.g.
- the interior focusing region may be a non-planar slab-like region, e.g. a cylindrically-, spherically-, ellipsoidally-, or otherwise-curved slab having a slab thickness providing the axial extent of the interior focusing region, hi other embodiments, the interior focusing region may be neither planar nor slab-like.
- the negatively-refractive focusing structure defines an optical axis as a symmetry or central axis of the negatively-refractive focusing structure, and the optical axis provides an axial direction, with transverse directions defined perpendicular thereto.
- the axial direction corresponds to a radius unit vector (and the transverse directions correspond to height/azimuth unit vectors or azimuth/zenith unit vectors, respectively); where the interior focusing region is an otherwise-curved slab, the axial direction corresponds to a vector locally normal to the slab surface (and the transverse directions correspond to orthogonal unit vectors locally tangent to the slab surface).
- a negatively-refractive focusing structure such as that depicted in FIG. 18, includes a transformation medium.
- this coordinate transformation corresponds to a coordinate transformation that is multiple- valued and includes both a coordinate inversion and a uniform spatial contraction along the axial direction 160 (within the axial extent of the negatively-refractive focusing structure 110); this coordinate transformation can be used to identify constitutive parameters for a corresponding transformation medium (e.g. as provided in equations (1) and (2), or reduced parameters obtained therefrom) that responds to electromagnetic radiation as in FIG. 18.
- a corresponding transformation medium e.g. as provided in equations (1) and (2), or reduced parameters obtained therefrom
- the second branch 202 includes an axial coordinate inversion and a uniform axial coordinate contraction, and maps the untransformed coordinate region 220 to the interior focusing region 120.
- the figure also indicates the axial extent of the negatively-refractive focusing structure 110 on the z'-axis (coinciding, in this example, with the range of the second branch 202).
- a scale factor the example of FIGS. 18-19 presents a constant negative scale factor -1 ⁇ s ⁇ 0 within the negatively-refractive focusing structure 110, corresponding to a coordinate inversion (whereby s ⁇ 0 ) and a uniform spatial contraction (whereby ⁇ s ⁇ ⁇ 1 ; in some instances within this document, as shall be apparent to one of skill in the art, the use of the term "scale factor," when used in the context of a spatial contraction, may refer to the absolute value of a negative scale factor such as described here).
- the uniform spatial dilation of FIGS. 18-19 corresponds to a transformation medium that is a uniform uniaxial medium.
- the scale factor is negative, so that the constitutive parameters in equation (17) are negative, and the transformation medium is a negatively-refractive medium defining a negative index of refraction.
- the negatively-refractive focusing structure includes a transformation medium that provides a non-uniform spatial dilation.
- FIG.20 An example is depicted in FIG.20 and the corresponding multiple- valued coordinate transformation is depicted in FIG. 21.
- a negatively-refractive focusing structure 110 provides an interior focusing region 120 for electromagnetic energy that radiates from an exterior field region 130.
- FIG. 18 the embodiment of FIG.
- the scale factor in this relation satisfies, in some interval(s), the relation -1 ⁇ s ⁇ 0 (corresponding to a local spatial contraction and coordinate inversion), and in other interval(s), the relation s ⁇ — 1 (corresponding to a local spatial dilation and coordinate inversion).
- the constitutive relations are again given by equations (17), where s is variable in the axial direction, and the transformation medium is a non-uniform uniaxial medium (again with negative constitutive parameters and defining a negative index of refraction).
- embodiments of a negatively-refractive focusing structure operable to provide an interior focusing region for electromagnetic energy that radiates from an exterior field region, may comprise a transformation medium, the transformation medium corresponding to a multiple-valued coordinate transformation that maps an untransformed region to the exterior field region, and further maps the untransformed region to the interior focusing region; and the constitutive relations of this transformation medium may be implemented with an artificially-structured material (such as a metamaterial), as described previously.
- an artificially-structured material such as a metamaterial
- the coordinate transformation includes a coordinate inversion and spatial contraction along an axial direction of the interior focusing region
- a scale factor of the spatial contraction may correspond to a ratio of an axial extent of the interior focusing region to an axial extent of the exterior field region.
- a substantially cylindrically- or spherically-curved interior focusing region may correspond to a (uniform or non-uniform) inversion/contraction of a cylindrical or spherical radius coordinate;
- a substantially ellipsoidally-curved interior focusing region may correspond to a (uniform or non-uniform) inversion/contraction of a confocal ellipsoidal coordinate; etc.
- the negatively-refractive focusing structure 110 is depicted in FIGS. 18 and 20 as a planar slab, but this is a schematic illustration and is not intended to be limiting.
- the negatively-refractive focusing structure can be a cylindrically-, spherically-, or ellipsoidally-curved slab, or any other slab- or non- slab-like structure configured to provide an interior focusing region for negatively- refracted electromagnetic energy with an axial magnification substantially less than one.
- equations (1) and (2) generally provide a medium that is substantially nonreflective. More generally, the input surface region may be substantially nonreflective by virtue of a substantial impedance-matching to the adjacent region. With impedance-matching, a wave impedance of the input surface region is substantially equal to a wave impedance of the adjacent region.
- the wave impedance of an isotropic medium is
- an impedance-matching is a substantial matching of every matrix element of the wave impedance tensor (i.e. to provide a substantially nonreflective interface for all incident polarizations); in other embodiments an impedance-matching is a substantial matching of only selected matrix elements of the wave impedance tensor (e.g.
- the adjacent region defines a permittivity ⁇ ⁇ and a permeability ⁇ x , where either or both parameters may be substantially unity or substantially non-unity;
- the input surface region defines a permittivity ⁇ 2 and a permeability ⁇ 2 , where either or both parameters may be substantially unity or substantially non-unity; and the impedance- matching condition implies ⁇ s ⁇ (19)
- ⁇ 2 and ⁇ 2 may be tensor quantities.
- a surface normal direction and a surface parallel direction e.g. depicted as elements 521 and 522, respectively, in FIG. 22
- some embodiments provide a input surface region that defines: a surface normal permittivity ⁇ 2 corresponding to the surface normal direction and a surface parallel permittivity corresponding to the surface parallel direction; and/or a surface normal permeability ⁇ 2 corresponding to the surface normal direction and a surface parallel permeability corresponding to the surface parallel direction; and the impedance-matching condition may imply (in addition to equation (19)) one or both of the following conditions:
- the surface normal direction and the surface parallel direction can vary with position along the input surface region.
- electromagnetic sensors positioned within the interior focusing region of the negatively-refractive focusing structure.
- electromagnetic sensors such as those depicted FIG. 18 and in other embodiments, are electromagnetic devices having a detectable response to received or absorbed electromagnetic energy.
- Electromagnetic sensors can include antennas (such as wire/loop antennas, horn antennas, reflector antennas, patch antennas, phased array antennas, etc.), solid-state photodetectors (such as photodiodes, CCDs, and photoresistors), vacuum photodetectors (such as phototubes and photomultipliers) chemical photodetectors (such as photographic emulsions), cryogenic photodetectors (such as bolometers), photoluminescent detectors (such as phosphor powders or fluorescent dyes/markers), MEMS detectors (such as microcantilever arrays with electromagnetically responsive materials or elements) or any other devices operable to detect and/or transduce electromagnetic energy.
- antennas such as wire/loop antennas, horn antennas, reflector antennas, patch antennas, phased array antennas, etc.
- solid-state photodetectors such as photodiodes, CCDs, and photoresistors
- vacuum photodetectors such as phototubes and photomultipliers
- the electromagnetic sensors include devices or materials that may undergo a change in state (such as a phase change or chemical reaction) in response to absorbed or received electromagnetic energy, e.g. a photoresist, a light-sensitive polymer, etc.
- the electromagnetic sensors include devices or materials having a nonlinear response to absorbed or received electromagnetic radiation, e.g. a nonlinear optical material.
- Some embodiments include a plurality of electromagnetic sensors positioned within the interior focusing region.
- a first example is a multiplet of sensors operable at a corresponding multiplet of wavelengths or wavelength bands, i.e. a first sensor operable at a first wavelength/wavelength band, a second sensor operable at a second wavelength/wavelength band, etc.
- a second example is a focal plane array of sensors or sensor multiplets (e.g. a Bayer or Foveon sensor).
- a third example is a phased array of antennas.
- the plurality of sensors can be axially distributed (as in FIG. 18); for example, the axial extent of the interior focusing region may admit a plurality of parallel focal plane sensor arrays.
- the negatively-refractive focusing structure provides an interior focusing region with an axial magnification substantially less than one for electromagnetic energy 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 particular TE polarization (e.g.
- TM polarization e.g. where the magnetic field is in a particular direction transverse to the axial direction, as with p-polarized electromagnetic energy
- circular polarization etc.
- other embodiments provide an interior focusing region with an axial magnification substantially less than one that is substantially the same interior focusing region with substantially the same axial magnification for any polarization of electromagnetic energy, e.g. for unpolarized electromagnetic energy).
- the negatively-refractive focusing structure provides a first interior focusing region with a first axial magnification substantially less than one for electromagnetic energy at a first frequency, and a second interior focusing region with a second axial magnification substantially less than one for electromagnetic energy at a second frequency.
- the first axial magnification may be different than or substantially equal to the first axial magnification
- the first and second interior focusing regions may be substantially (or completely) non- overlapping, partially overlapping or substantially (or completely) overlapping.
- 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 providing a negatively- refractive focusing structure operable at first and second frequencies may include a transformation medium having an adjustable response to electromagnetic radiation.
- the transformation medium may have a response to electromagnetic radiation that is adjustable (e.g. in response to an external input or control signal) between a first response and a second response, the first response providing the first interior focusing region for electromagnetic energy at the first frequency, and the second response providing the second interior focusing region for electromagnetic energy at the second frequency.
- a transformation medium with an adjustable electromagnetic response may be implemented with variable metamaterials, e.g. as described in R. A.
- a negatively-refractive focusing structure operable at first and second frequencies may include transformation medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters.
- the frequency-dependent response at a first frequency may provide a first interior focusing region for electromagnetic energy at the first frequency
- the frequency-dependent response at a second frequency may provide second interior focusing region for electromagnetic energy at the second frequency.
- a transformation 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 600 includes operation 610 — negatively refracting an electromagnetic wave at a surface region, the surface region defining a surface normal direction.
- a negatively-refractive focusing structure such as that depicted as element 110 in FIG. 22, may include an input surface region 510 that negatively refracts electromagnetic energy incident upon the input surface region from an adjacent region, and the negatively-refractive focusing structure may include a transformation medium that provides a coordinate inversion (for a coordinate corresponding to a direction normal to the surface, e.g. the direction 521 in FIG. 22), the coordinate inversion corresponding to a negatively-refractive response of the transformation medium.
- Flow 600 further includes operation 620 — spatially contracting the refracted electromagnetic wave along a contraction direction, the contraction direction corresponding to the surface normal direction.
- a negatively-refractive focusing structure such as that depicted as element 110 in FIGS. 18 and 20, may spatially contract refracted electromagnetic energy 102 along an axial direction (e.g. the direction 160 in FIGS.
- Operation 620 optionally includes sub-operation 622 — spatially contracting a first component of the refracted electromagnetic wave at a first frequency along the contraction direction — and sub-operation 624 — spatially contracting a second component of the refracted electromagnetic wave at a second frequency along the contraction direction.
- a negatively-refractive focusing structure may provide a first interior focusing region with a first axial magnification for electromagnetic energy at a first frequency and a second interior focusing region with a second axial magnification for electromagnetic energy at a second frequency, where the second axial magnification may be different than or substantially equal to the first axial magnification; and this negatively-refractive focusing structure operable at first and second frequencies may include a transformation medium having an adjustable response to electromagnetic radiation, or a transformation medium having a frequency-dependent response to electromagnetic radiation.
- Flow 600 optionally includes operation 630 — sensing the electromagnetic wave at one or more locations within a focusing region that is provided by the negatively refracting and the spatially contracting.
- a negatively- refractive focusing structure 110 such as that depicted in FIGS. 18 and 20, may provide an interior focusing region 120, and one or more electromagnetic sensors, such as those depicted as elements 150 in FIG. 18, may be positioned within the interior focusing region to detect/receive/absorb the electromagnetic energy 102.
- Flow 700 includes operation 710 — determining electromagnetic parameters that define a negative refractive index in a spatial region, the electromagnetic parameters providing an axial magnification substantially less than one for an interior focusing region within the spatial region.
- the spatial region may be a volume that encloses a negatively-refractive focusing structure, such as that depicted as element 110 in FIGS. 18 and 20, and the determined electromagnetic parameters may be the electromagnetic parameters of the negatively-refractive focusing structure.
- the negatively-refractive focusing structure may include a transformation medium, where the determined electromagnetic parameters satisfy or substantially satisfy equations (1) and (2), as described above; or, the determined electromagnetic parameters may be reduced parameters (as discussed earlier) where the corresponding non-reduced parameters satisfy equations (1) and (2).
- the determining of the electromagnetic parameters includes: determining a coordinate transformation (such as those depicted in FIGS. 19 and 21); then determining electromagnetic parameters for a corresponding transformation medium (e.g.
- Operation 710 optionally includes sub-operation 712 — for electromagnetic waves at a first frequency, determining a first subset of the electromagnetic parameters providing a first axial magnification substantially less than one for a first interior focusing subregion within the interior focusing region — and sub-operation 714 — for electromagnetic waves at a second frequency, determining a second subset of the electromagnetic parameters providing a second axial magnification substantially less than one for a second interior focusing subregion within the interior focusing region.
- the determined electromagnetic parameters may be the electromagnetic parameters of a negatively- refractive focusing structure providing a first interior focusing region with a first axial magnification for electromagnetic energy at a first frequency and a second interior focusing region with a second axial magnification for electromagnetic energy at a second frequency.
- the negatively-refractive focusing structure may include a transformation medium having an adjustable response to electromagnetic radiation, e.g. adjustable between a first response, corresponding to the first subset of the electromagnetic parameters, and a second response, corresponding to the second subset of the electromagnetic parameters.
- the negatively-refractive focusing structure may include a transformation medium having a frequency-dependent response to electromagnetic radiation, corresponding to frequency-dependent constitutive parameters, so that the first and second subsets of the electromagnetic parameters are values of the frequency-dependent constitutive parameters at the first and second frequencies, respectively.
- Flow 700 optionally further includes operation 720 — selecting one or more positions of one or more electromagnetic sensors within the spatial region.
- electromagnetic sensors may be positioned in a phased array, an focal plane array, an axially-distributed arrangement, etc.
- Flow 700 optionally further includes operation 730 — configuring an artificially-structured material having an effective electromagnetic response that corresponds to the electromagnetic parameters in the spatial region.
- the configuring may include configuring the structure(s) and/or the materials that compose a photonic crystal or a metamaterial.
- Operation 730 optionally includes determining an arrangement of a plurality of electromagnetically responsive elements having a plurality of individual responses, the plurality of individual responses composing the effective electromagnetic response.
- the determining may include determining the positions, orientations, and individual response parameters (spatial dimensions, resonant frequencies, linewidths, etc.) of a plurality of metamaterial elements such as split-ring resonators, wire or nanowire pairs, etc.
- Operation 730 optionally includes configuring at least one electromagnetically-responsive structure to arrange a plurality of distributed electromagnetic responses, the plurality of distributed electromagnetic responses composing the effective electromagnetic response.
- the configuring may include configuring the distribution of loads and interconnections on a transmission line network, configuring an arrangement of layers in a layered metamaterial, configuring a pattern of etching or deposition (as with a nano-fishnet structure), etc.
- the system 800 includes a focusing unit 810 optionally coupled to a controller unit 830.
- the focusing unit 810 may include a negatively- refractive focusing structure such as that depicted as element 110 in FIGS. 18 and 20.
- the negatively-refractive focusing structure may be a variable negatively-refractive focusing structure, such as a variable metamaterial responsive to one or more control inputs to vary one or more focusing characteristics (axial magnification, operating frequency/frequency band, operating polarization, effective coordinate transformation for a transformation medium, etc.); and the controller unit 830 may include control circuitry that provides one or more control inputs to the variable negatively-refractive focusing structure.
- the system 800 optionally further includes a sensing unit 820 that may include one or more sensors, such as those depicted as elements 150 in FIG. 18, and associated circuitry such as receiver circuitry, detector circuitry, and/or signal processing circuitry.
- the sensing unit 820 is optionally coupled to the controller unit 830, and in some embodiments the controller unit 830 includes circuitry for coordinating or synchronizing the operation of the focusing unit 810 and the sensing unit 820.
- the controller unit 830 may include circuitry responsive to sensor data (from the sensor unit 820) to vary the focusing characteristics of the focusing structure.
- the controller unit may include circuitry responsive to the sensor data to identify a frequency/polarization of received energy, and adjust the focusing unit to an operating frequency/polarization substantially equal to the frequency/polarization of the received energy.
- the controller unit may include circuitry responsive to the sensor data to identify a target interior focusing region (and/or a target axial magnification), and corresponding adjust the focusing system whereby a negatively-refractive focusing structure provides an interior focusing region substantially equal to the target interior focusing region (and/or an axial magnification substantially equal to the target axial magnification).
- a signal bearing medium examples include, but are not limited to, the following: a recordable type medium such as a floppy disk, a hard disk drive, a Compact Disc (CD), a Digital Video Disk (DVD), a digital tape, a computer memory, etc.; and a transmission type medium such as a digital and/or an analog communication medium (e.g., a fiber optic cable, a waveguide, a wired communications link, a wireless communication link, etc.).
- electrical circuitry includes, but is not limited to, electrical circuitry having at least one discrete electrical circuit, electrical circuitry having at least one integrated circuit, electrical circuitry having at least one application specific integrated circuit, electrical circuitry forming a general purpose computing device configured by a computer program (e.g., a general purpose computer configured by a computer program which at least partially carries out processes and/or devices described herein, or a microprocessor configured by a computer program which at least partially carries out processes and/or devices described herein), electrical circuitry forming a memory device (e.g., forms of random access memory), and/or electrical circuitry forming a communications device (e.g., a modem, communications switch, or optical-electrical equipment).
- a computer program e.g., a general purpose computer configured by a computer program which at least partially carries out processes and/or devices described herein, or a microprocessor configured by a computer program which at least partially carries out processes and/or devices described herein
- electrical circuitry forming a memory device
Abstract
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US12/220,705 US9019632B2 (en) | 2008-05-30 | 2008-07-25 | Negatively-refractive focusing and sensing apparatus, methods, and systems |
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US12/228,140 US7830618B1 (en) | 2008-05-30 | 2008-08-07 | Negatively-refractive focusing and sensing apparatus, methods, and systems |
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Also Published As
Publication number | Publication date |
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WO2009148542A1 (en) | 2009-12-10 |
WO2009148548A1 (en) | 2009-12-10 |
CN102112919B (en) | 2015-09-30 |
CN102112919A (en) | 2011-06-29 |
EP2294482A4 (en) | 2012-02-08 |
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