CiteULike: Tag metamaterial

Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap

M Notomi — 2006-08-07T21:49:58-00:00

Physical Review B, Vol. 62, No. 16. (15 October 2000), 10696.

Although light propagation in weakly modulated photonic crystals is basically similar to propagation in a diffraction grating in which conventional refractive index loses its meaning; we demonstrate that light propagation in strongly modulated two-dimensional (2D)/3D photonic crystals becomes refractionlike in the vicinity of the photonic bandgap. Such a crystal behaves as a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. By utilizing this phenomenon; negatively refractive material can be realized; which has interesting optical properties such as mirror-image refraction.

Experimental Verification of a Negative Index of Refraction

RA Shelby — 2006-08-07T22:09:33-00:00

Science, Vol. 292, No. 5514. (6 April 2001), pp. 77-79.

10.1126/science.1058847

Metamaterials and Negative Refractive Index

DR Smith — 2006-08-07T22:08:30-00:00

Science, Vol. 305, No. 5685. (6 August 2004), pp. 788-792.

Recently, artificially constructed metamaterials have become of considerable interest, because these materials can exhibit electromagnetic characteristics unlike those of any conventional materials. Artificial magnetism and negative refractive index are two specific types of behavior that have been demonstrated over the past few years, illustrating the new physics and new applications possible when we expand our view as to what constitutes a material. In this review, we describe recent advances in metamaterials research and discuss the potential that these materials may hold for realizing new and seemingly exotic electromagnetic phenomena. 10.1126/science.1096796

Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial

Gunnar Dolling — 2006-07-23T23:09:11-00:00

Science, Vol. 312, No. 5775. (12 May 2006), pp. 892-894.

We investigated the propagation of femtosecond laser pulses through a metamaterial that has a negative index of refraction for wavelengths around 1.5 micrometers. From the interference fringes of a Michelson interferometer with and without the sample, we directly inferred the phase time delay. From the pulse-envelope shift, we determined the group time delay. In a spectral region, phase and group velocity are negative simultaneously. This means that both the carrier wave and the pulse envelope peak of the output pulse appear at the rear side of the sample before their input pulse counterparts have entered the front side of the sample. 10.1126/science.1126021

New metamaterials with macroscopic behavior outside that of continuum elastodynamics

Graeme Milton — 2007-10-10T06:49:41-00:00

New J. Phys., Vol. 9, No. 10. (October 2007), 359.

Cloak for multilayered and gradually changing media

Jingjing Zhang — 2008-02-04T19:21:40-00:00

Physical Review B (Condensed Matter and Materials Physics), Vol. 77, No. 3. (2008)

Coordinate transformation approach has previously been used for designing a cloak which can shield an interior region in a homogeneous medium. In this paper, we consider the case where the background is no longer a homogeneous medium and determine the relative constitutive parameters of the cloak according to the multilayered and gradually changing background. We propose the parameters of cylindrical cloak structures working in multilayered and gradually changing media and the scheme of specifying these parameters could also be applied to the design of a cloak in an arbitrary isotropic background. The theoretical analysis based on coordinate transformation is given and numerical simulations are performed to illustrate these properties. The simulation results show that the cloaking with the proposed parameters performs well in these inhomogeneous background medium. Potential applications are also discussed.

Realizable response matrices of multiterminal electrical, acoustic, and elastodynamic networks at a given frequency

Graeme Milton — 2008-01-15T20:54:11-00:00

(7 Dec 2007)

We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in the three-dimensional case and in the two-dimensional case. Specifically we construct networks which realize any response matrix which is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Due to a mathematical equivalence we also obtain a characterization of the response matrices of discrete acoustic networks.

Cloaking via change of variables in electric impedance tomography

RV Kohn — 2008-02-09T17:39:24-00:00

Inverse Problems, Vol. 24, No. 1. (2008), 015016.

A recent paper by Pendry et al (2006 Science 312 1780-2) used the coordinate invariance of Maxwell's equations to show how a region of space can be 'cloaked'--in other words, made inaccessible to electromagnetic sensing--by surrounding it with a suitable (anisotropic and heterogenous) dielectric shield. Essentially the same observation was made several years earlier by Greenleaf et al (2003 Math. Res. Lett. 10 685-93, 2003 Physiol. Meas. 24 413-9) in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: (a) the cloaks they consider are rather singular; and (b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension n = 2. The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near-cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension n [?] 2.

Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid

Michael Schoenberg — 2008-02-08T17:49:03-00:00

The Journal of the Acoustical Society of America, Vol. 73, No. 1. (1983), pp. 61-67.

The problem of the reflection of acoustic waves from a periodically layered acoustic half-space is solved exactly at all frequencies. Pass and stop bands and the associated complex slowness surfaces of propagation through the periodic medium are found. In the low-frequency limit, when the wavelength normal to the layering is much greater than one period, it is shown that there always exists a homogeneous ideal fluid with the same reflection properties as the layered medium. However, the effective acoustic medium that models transmission as well as reflection at low frequencies has a bulk modulus Keff given by K–1–1 where the brackets denote a volume weighted average, and, for the inertial density appearing in the equations of motion, the effective medium has a transverse isotropic density tensor with , the density component parallel to the layering, given by 1/–1, and , the density component perpendicular to the layering given by . The range of wavespeeds speeds as a function of angle is shown to parallel the range of speeds in a Biot fluid as a function of the Biot coupling parameter. Normal propagation corresponds to full locking of the two phases in a Biot material and parallel propagation corresponds to the fully uncoupled case. The relation between the angle of propagation measured from the normal to the layering, and the corresponding Biot coupling parameter is that –1 is proportional to cot2 .

Modulation of negative index metamaterials in the near-IR range

Evgenia Kim — 2007-11-02T12:59:56-00:00

Applied Physics Letters, Vol. 91, No. 17. (2007)

Optical modulation of the effective refractive properties of a “fishnet” metamaterial with a Ag/Si/Ag heterostructure is demonstrated in the near-IR range and the associated fast dynamics of negative refractive index is studied by pump-probe method. Photoexcitation of the amorphous Si layer at visible wavelength and corresponding modification of its optical parameters is found to be responsible for the observed modulation of negative refractive index in near-IR. ©2007 American Institute of Physics

Elastic wave transparency of a solid sphere coated with metamaterials

Xiaoming Zhou — 2008-02-09T16:51:42-00:00

Physical Review B (Condensed Matter and Materials Physics), Vol. 77, No. 2. (2008)

The elastic wave transparency phenomenon of a solid sphere coated with metamaterials is investigated in a solid host medium having nonzero shear modulus. The first three scattering coefficients of the coated sphere are derived in the Rayleigh limit and expressed in terms of the effective parameters of the coated sphere assemblage. It is found that the effective bulk modulus, mass density, and shear modulus of the coated sphere system dominate the zeroth, first, and second order scattering effects, respectively. Quasistatic transparency conditions are obtained by setting these scattering coefficients to be zero. It is also shown that the obtained transparency conditions are the same as those derived from the neutral inclusion concept. Obtained results from full-wave analyses show that the given conditions can well predict the transparency induced by metamaterials even in the regime far beyond the Rayleigh limit.

Analysis of Cummer–Schurig acoustic cloaking

Liang-Wu Cai — 2007-12-20T10:56:27-00:00

New J. Phys., Vol. 9, No. 12. (December 2007), 450.

Which Elasticity Tensors are Realizable?

Graeme Milton — 2008-02-09T16:31:43-00:00

Journal of Engineering Materials and Technology, Vol. 117, No. 4. (1995), pp. 483-493.

It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.

Electromagnetic cloaking by layered structure ofhomogeneous isotropic materials

Ying Huang — 2008-01-25T17:54:58-00:00

Opt. Express, Vol. 15, No. 18. (2007), pp. 11133-11141.

Electromagnetic invisibility cloak requires material with anisotropic distribution of the constitutive parameters as first proposed by Pendry et al. [Science 312, 1780 (2006)]. In this paper, we proposed an electromagnetic cloak structure that does not require metamaterials with subwavelength structured inclusions to realize the anisotropy or inhomogeneity of the material parameters. We constructed a concentric layered structure of alternating homogeneous isotropic materials that can be treated as an effective medium with the required radius-dependent anisotropy. With proper design of the permittivity or the thickness ratio of the alternating layers, we demonstrated the low-reflection and power-flow bending properties of the proposed cloaking structure through rigorous analysis of the scattered electromagnetic fields. The proposed cloaking structure could be possibly realized by normal materials, therefore may lead to a practical path to an experimental demonstration of electromagnetic cloaking, especially in the optical range.

One path to acoustic cloaking

Steven Cummer — 2007-03-03T21:40:34-00:00

New J. Phys., Vol. 9, No. 3. (March 2007), 45.

On perfect cloaking

David Miller — 2008-01-30T18:51:18-00:00

Opt. Express, Vol. 14, No. 25. (11 December 2006), pp. 12457-12466.

We show in principle how to cloak a region of space to make its contents classically invisible or transparent to waves. The method uses sensors and active sources near the surface of the region, and could operate over broad bandwidths. A general expression is given for calculating the necessary sources, and explicit, fully causal simulations are shown for scalar waves. Vulnerability to broad-band probing is discussed, and any active scheme should detectable by a quantum probe, regardless of bandwidth.

Optical conformal mapping.

U Leonhardt — 2006-08-11T08:50:15-00:00

Science, Vol. 312, No. 5781. (23 June 2006), pp. 1777-1780.

An invisibility device should guide light around an object as if nothing were there, regardless of where the light comes from. Ideal invisibility devices are impossible, owing to the wave nature of light. This study develops a general recipe for the design of media that create perfect invisibility within the accuracy of geometrical optics. The imperfections of invisibility can be made arbitrarily small to hide objects that are much larger than the wavelength. With the use of modern metamaterials, practical demonstrations of such devices may be possible. The method developed here can also be applied to escape detection by other electromagnetic waves or sound.

Acoustic cloaking in three dimensions using acoustic metamaterials

Huanyang Chen — 2008-01-23T22:50:04-00:00

Applied Physics Letters, Vol. 91, No. 18. (2007)

On modifications of Newton's second law and linear continuum elastodynamics

Graeme Milton — 2008-01-25T17:45:07-00:00

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, No. 2079. (March 2007), pp. 855-880.

In this paper, we suggest a new perspective, where Newton's second law of motion is replaced by a more general law which is a better approximation for describing the motion of seemingly rigid macroscopic bodies. We confirm a finding of Willis that the density of a body at a given frequency of oscillation can be anisotropic. The relation between the force and the acceleration is non-local (but causal) in time. Conversely, for every response function satisfying these properties, and having the appropriate high-frequency limit, there is a model which realizes that response function. In many circumstances, the differences between Newton's second law and the new law are small, but there are circumstances, such as in specially designed composite materials, where the difference is enormous. For bodies which are not seemingly rigid, the continuum equations of elastodynamics govern behaviour and also need to be modified. The modified versions of these equations presented here are a generalization of the equations proposed by Willis to describe elastodynamics in composite materials. It is argued that these new sets of equations may apply to all physical materials, not just composites. The Willis equations govern the behaviour of the average displacement field whereas one set of new equations governs the behaviour of the average-weighted displacement field, where the weighted displacement field may attach zero weight to ‘hidden’ areas in the material where the displacement may be unobservable or not defined. From knowledge of the average-weighted displacement field, one obtains an approximate formula for the ensemble averaged energy density. Two other sets of new equations govern the behaviour when the microstructure has microinertia, i.e. where there are internal spinning masses below the chosen scale of continuum modelling. In the first set, the average displacement field is assumed to be observable, while in the second set an average-weighted displacement field is assumed to be observable.

Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell's Equations

Marco Rahm — 2008-01-25T17:03:57-00:00

(17 Jun 2007)

The technique of applying form-invariant, spatial coordinate transformations of Maxwell's equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.

Nonmagnetic cloak with minimized scattering

Wenshan Cai — 2008-02-04T13:30:26-00:00

Applied Physics Letters, Vol. 91, No. 11. (2007)

High refractive-index sonic material based on periodic subwavelength structure

Feiyan Cai — 2008-03-24T21:18:59-00:00

Applied Physics Letters, Vol. 91, No. 20. (2007)

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Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density

Yiqun Ding — 2008-03-24T21:17:37-00:00

Physical Review Letters, Vol. 99, No. 9. (2007)

We report a metamaterial which simultaneously possesses a negative bulk modulus and mass density. This metamaterial is a zinc blende structure consisting of one fcc array of bubble-contained-water spheres (BWSs) and another relatively shifted fcc array of rubber-coated-gold spheres (RGSs) in epoxy matrix. The negative bulk modulus and mass density are simultaneously derived from the coexistent monopolar resonances from the embedded BWSs and dipolar resonances from the embedded RGSs. The Poisson ratio of the metamaterial also turns negative near the resonance frequency.

Scattering characteristics of simplified cylindrical invisibility cloaks

Min Yan — 2008-02-04T13:23:34-00:00

Opt. Express, Vol. 15, No. 26. (24 December 2007), pp. 17772-17782.

The previously reported simplified cylindrical linear cloak is improved so that the cloak’s outer surface is impedance-matched to free space. The scattering characteristics of the improved linear cloak is compared to the previous counterpart as well as the recently proposed simplified quadratic cloak derived from quadratic coordinate transformation. Significant improvement in invisibility performance is noticed for the improved linear cloak with respect to the previously proposed linear one. The improved linear cloak and the simplified quadratic cloak have comparable invisibility performances, except that the latter however has to fulfill a minimum shell thickness requirement (i.e. outer radius must be larger than twice of inner radius). When a thin cloak shell is desired, the improved linear cloak is much more superior than the other two versions of simplified cloaks.

A Dynamical Effective Medium Theory for Elastic Metamaterials

Ying Wu — 2008-03-10T12:35:06-00:00

(8 Jul 2007)

We develop a dynamical effective medium theory to accurately predict the unusual properties of elastic metamaterials in two dimensions near the resonant frequencies. The theory shows that the effective bulk modulus, shear modulus, and mass density can be made negative by choosing proper resonant scatterers, leading to 8 possible types of wave propagation. The theory not only provides a convenient tool to search for various metamaterials with desired properties, but also gives a unified physical picture of these properties. Here we demonstrate two examples. One possesses large band gaps at low frequencies. The other exhibits two regions of negative refraction: one for both longitudinal and transverse waves and the other for longitudinal waves only.

Effective dynamic mass density of composites

Jun Mei — 2007-12-01T16:32:44-00:00

Physical Review B (Condensed Matter and Materials Physics), Vol. 76, No. 13. (2007)

The static mass density of a composite is simply the volume average of its constituents' densities. The dynamic density of a composite is defined to be the quantity that enters in evaluating the elastic wave velocity at the low-frequency limit. We show through a rigorous derivation that the effective dynamic mass density of an inhomogeneous mixture can differ from its static counterpart when the composite matrix is a fluid or, more generally, when there are relative motions between the matrix and inclusions. Derivation of the dynamic mass density expressions, involving taking the long wavelength limit of the rigorous multiple scattering theory, is detailed for the two-dimensional case. We also extend the effective dynamic mass density expression to finite frequencies where there can be low-frequency resonances. By combining both analytical and numerical approaches, negative or complex dynamic mass density is obtained for composites that contain a sufficient fraction of locally resonant inclusions. Thus, the dynamic mass density of a composite can differ from the static (volume-averaged) value even in the zero frequency limit, although both must be positive in that limit. Negative or complex dynamic mass density can occur at finite frequencies. These two results are shown to be consistent with each other, as well as related by the same underlying physics. As by-products of our rigorous derivation, we also verify some prior known results on the effective elastic moduli of composites.

Improvement of cylindrical cloaking with the SHS lining

A Greenleaf — 2008-02-11T17:27:28-00:00

Opt. Express, Vol. 15, No. 20. (1 October 2007), pp. 12717-12734.

We analyze the effectiveness of cloaking an infinite cylinder from observations by electromagnetic waves in three dimensions. We show that, as truncated approximations of the ideal permittivity and permeability material parameters tend towards the singular ideal cloaking values, the D and B fields blow up near the cloaking surface. Since the metamaterials used to implement cloaking are based on effective medium theory, the resulting large variation in D and B poses a challenge to the suitability of the field-averaged characterization of ε and μ. We also consider cloaking with and without the SHS (soft-and-hard surface) lining. We demonstrate numerically that cloaking is significantly improved by the SHS lining, with both the far field of the scattered wave significantly reduced and the blow up of D and B prevented.

Controlling electromagnetic fields.

JB Pendry — 2006-08-11T08:48:28-00:00

Science, Vol. 312, No. 5781. (23 June 2006), pp. 1780-1782.

Using the freedom of design that metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields-electric displacement field D, magnetic induction field B, and Poynting vector B-are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.

Geometric picture of optical complementary media

Monzon — 2008-03-10T14:11:22-00:00

European Journal of Physics, Vol. 29, No. 3. (May 2008), pp. 431-437.

Controlling the Emission of Electromagnetic Sources by Coordinate transformation

Yu Luo — 2008-03-10T12:31:21-00:00

(21 Dec 2007)

The coordinate transformation on the space that contains electromagnetic sources is studied. We find that, not only the permittivity and permeability tensors of the media, but also the sources inside the media will take another form in order to behave equivalently as the original case. It is demonstrated that, a source of arbitrary shape and position in the free space can be replaced by an appropriately designed metamaterial coating with current distributed on the inner surface and would not be detected by outer observers, because the emission of the source can be controlled at will in this way. As examples, we show how to design conformal antennas by covering the sources with transformation media. The method proposed in this letter provides a completely new approach to develop novel active EM devices.

Ultrasonic metamaterials with negative modulus.

N Fang — 2008-02-04T13:15:02-00:00

Nat Mater, Vol. 5, No. 6. (June 2006), pp. 452-456.

The emergence of artificially designed subwavelength electromagnetic materials, denoted metamaterials, has significantly broadened the range of material responses found in nature. However, the acoustic analogue to electromagnetic metamaterials has, so far, not been investigated. We report a new class of ultrasonic metamaterials consisting of an array of subwavelength Helmholtz resonators with designed acoustic inductance and capacitance. These materials have an effective dynamic modulus with negative values near the resonance frequency. As a result, these ultrasonic metamaterials can convey acoustic waves with a group velocity antiparallel to phase velocity, as observed experimentally. On the basis of homogenized-media theory, we calculated the dispersion and transmission, which agrees well with experiments near 30 kHz. As the negative dynamic modulus leads to a richness of surface states with very large wavevectors, this new class of acoustic metamaterials may offer interesting applications, such as acoustic negative refraction and superlensing below the diffraction limit.

Double-negative acoustic metamaterial

Jensen Li — 2008-02-04T13:10:30-00:00

Physical Review E, Vol. 70, No. 5. (18 November 2004), 055602.

We show here the existence of acoustic metamaterial; in which both the effective density and bulk modulus are simultaneously negative; in the true and strict sense of an effective medium. Our double-negative acoustic system is an acoustic analogue of Veselago’s medium in electromagnetism; and shares many unique consequences; such as negative refractive index. The double negativity in acoustics is derived from low-frequency resonances; as in the case of electromagnetism; but the negative density and modulus are derived from a single resonance structure as distinct from electromagnetism in which the negative permeability and negative permittivity originates from different resonance mechanisms.

Metamaterial Electromagnetic Cloak at Microwave Frequencies

D Schurig — 2007-11-02T17:43:11-00:00

Science, Vol. 314, No. 5801. (10 November 2006), pp. 977-980.

A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was "hidden" inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space. 10.1126/science.1133628

Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect

Frédéric Zolla — 2008-02-11T16:16:10-00:00

Opt. Lett., Vol. 32, No. 9. (1 May 2007), pp. 1069-1071.

We present a finite-element analysis of a diffraction problem involving a coated cylinder enabling the electromagnetic cloaking of a lossy object with sharp wedges located within its core. The coating consists of a heterogeneous anisotropic material deduced from a geometrical transformation as first proposed by Pendry [Science 312, 1780 (2006)]. We analyze the electromagnetic response of the cloak in the presence of an electric line source in p polarization and a loop of magnetic current in s polarization. We find that the electromagnetic field radiated by such a source located a fraction of a wavelength from the cloak is perturbed by less than 1%. When the source lies in the coating, it seems to radiate from a shifted location.

Experimental study on negative effective mass in a 1D mass–spring system

Shanshan Yao — 2008-04-15T18:11:53-00:00

New J. Phys., Vol. 10, No. 4. (April 2008), 043020.

Acoustic metamaterials for sound focusing and confinement

Sébastien Guenneau — 2007-11-07T20:44:54-00:00

New J. Phys., Vol. 9, No. 11. (November 2007), 399.

Calculation of material properties and ray tracing in transformation media

D Schurig — 2008-01-25T02:47:14-00:00

Opt. Express, Vol. 14, No. 21. (16 October 2006), pp. 9794-9804.

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability.

General relativity in electrical engineering

Ulf Leonhardt — 2006-10-23T23:32:22-00:00

New J. Phys., Vol. 8, No. 10. (October 2006), 247.

Transformation media that rotate electromagnetic fields

Huanyang Chen — 2008-01-25T17:10:44-00:00

Applied Physics Letters, Vol. 90, No. 24. (2007)

On the cloaking effects associated with anomalous localized resonance

Graeme Milton — 2008-02-04T23:29:57-00:00

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 462, No. 2074. (October 2006), pp. 3027-3059.

Regions of anomalous localized resonance, such as occurring near superlenses, are shown to lead to cloaking effects. This occurs when the resonant field generated by a polarizable line or point dipole acts back on the polarizable line or point dipole and effectively cancels the field acting on it from outside sources. Cloaking is proved in the quasistatic limit for finite collections of polarizable line dipoles that all lie within a specific distance from a coated cylinder having a shell permittivity ϵs≈−ϵm≈−ϵc where ϵm is the permittivity of the surrounding matrix, and ϵc is the core permittivity. Cloaking is also shown to extend to the Veselago superlens outside the quasistatic regime: a polarizable line dipole located less than a distance d/2 from the lens, where d is the thickness of the lens, will be cloaked due to the presence of a resonant field in front of the lens. Also a polarizable point dipole near a slab lens will be cloaked in the quasistatic limit.

Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations

Zhichao Ruan — 2008-01-01T16:44:37-00:00

Physical Review Letters, Vol. 99, No. 11. (2007)

A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner boundary of the cloak shell. We confirm that a cloak with the ideal material parameters is a perfect invisibility cloak by systematically studying the change of the scattering coefficients from the near-ideal case to the ideal one. However, because of the slow convergence of the zeroth-order scattering coefficients, a tiny perturbation on the cloak would induce a noticeable field scattering and penetration.

Full-Wave Invisibility of Active Devices at All Frequencies

Allan Greenleaf — 2008-02-11T16:09:58-00:00

Communications in Mathematical Physics, Vol. 275, No. 3. (4 November 2007), pp. 749-789.

Abstract There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or “cloaking”) from observation by electromagnetic (EM) waves. Here, we prove invisibility with respect to solutions of the Helmholtz and Maxwell’s equations, for several constructions of cloaking devices. The basic idea, as in the papers [GLU2, GLU3, Le, PSS1], is to use a singular transformation that pushes isotropic electromagnetic parameters forward into singular, anisotropic ones. We define the notion of finite energy solutions of the Helmholtz and Maxwell’s equations for such singular electromagnetic parameters, and study the behavior of the solutions on the entire domain, including the cloaked region and its boundary. We show that, neglecting dispersion, the construction of [GLU3, PSS1] cloaks passive objects, i.e., those without internal currents, at all frequencies k. Due to the singularity of the metric, one needs to work with weak solutions. Analyzing the behavior of such solutions inside the cloaked region, we show that, depending on the chosen construction, there appear new “hidden” boundary conditions at the surface separating the cloaked and uncloaked regions. We also consider the effect on invisibility of active devices inside the cloaked region, interpreted as collections of sources and sinks or internal currents. When these conditions are overdetermined, as happens for Maxwell’s equations, generic internal currents prevent the existence of finite energy solutions and invisibility is compromised. We give two basic constructions for cloaking a region D contained in a domain $$Ω⊂\mathbb R^n, n≥ 3$$ , from detection by measurements made at $$∂Ω$$ of Cauchy data of waves on Ω. These constructions, the single and double coatings, correspond to surrounding either just the outer boundary $$∂ D^+$$ of the cloaked region, or both $$∂ D^+$$ and $$∂ D^-$$ , with metamaterials whose EM material parameters (index of refraction or electric permittivity and magnetic permeability) are conformal to a singular Riemannian metric on Ω. For the single coating construction, invisibility holds for the Helmholtz equation, but fails for Maxwell’s equations with generic internal currents. However, invisibility can be restored by modifying the single coating construction, by either inserting a physical surface at $$∂ D^-$$ or using the double coating. When cloaking an infinite cylinder, invisibility results for Maxwell’s equations are valid if the coating material is lined on $$∂ D^-$$ with a surface satisfying the soft and hard surface (SHS) boundary condition, but in general not without such a lining, even for passive objects.

The group and energy transport velocity distributions for ideal invisibility cloaks

Huanyang Chen — 2008-01-25T02:30:52-00:00

(24 Dec 2007)

We obtained the group velocity expressions for both two dimensional and three dimensional cloaks from the dispersion relations. The group velocity and energy transport velocity distributions for a 3D ideal cloak are shown explicitly. Near the operation frequency, its magnitude is always smaller than the velocity of light. The group and energy transport velocities have rather peculiar distributions. The velocity along a line joining the origin of the cloak is a constant, while the velocities approach zero at the inner boundary of the cloak. A ray pointing right into the origin of the cloak will experience abrupt changes of velocities when it impinges on the inner surface of the cloak.

Acoustic metamaterials for new two-dimensional sonic devices

Daniel Torrent — 2007-09-12T01:00:26-00:00

New J. Phys., Vol. 9, No. 9. (September 2007), 323.

Anisotropic conductivities that cannot be detected by EIT

A Greenleaf — 2008-01-25T02:27:39-00:00

Physiological Measurement, Vol. 24, No. 2. (2003), pp. 413-419.

We construct anisotropic conductivities in dimension 3 that give rise to the same voltage and current measurements at the boundary of a body as a homogeneous isotropic conductivity. These conductivities are non-zero, but degenerate close to a surface inside the body.

Full-wave simulations of electromagnetic cloaking structures

Steven Cummer — 2008-01-25T02:26:11-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 74, No. 3. (2006)

Pendry et al. have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. Neither the coordinate transformation-based analytical formulation nor the supporting ray-tracing simulation indicate how material perturbations and full-wave effects might affect the solution. We report fully electromagnetic simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaking structure are not especially sensitive to modest permittivity and permeability variations. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight– (homogeneous) layer approximation of the ideal continuous medium. An imperfect but simpler version of the cloaking material is derived and is shown to reproduce the ray bending of the ideal material in a manner that may be easier to experimentally realize.

Negative Refraction Makes a Perfect Lens

JB Pendry — 2006-08-11T09:29:01-00:00

Physical Review Letters, Vol. 85, No. 18. (30 October 2000), 3966.

With a conventional lens sharpness of the image is always limited by the wavelength of light. An unconventional alternative to a lens; a slab of negative refractive index material; has the power to focus all Fourier components of a 2D image; even those that do not propagate in a radiative manner. Such âsuperlensesâ can be realized in the microwave band with current technology. Our simulations show that a version of the lens operating at the frequency of visible light can be realized in the form of a thin slab of silver. This optical version resolves objects only a few nanometers across.

Comment on "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell"

Allan Greenleaf — 2008-02-11T16:04:03-00:00

(21 Jan 2008)

In a recent Letter, Cummer et al. give a description of material parameters for acoustic wave propagation giving rise to a 3D spherical cloak, and verify the cloaking phenomenon on the level of scattering coefficients. A similar configuration has been given by Chen and Chan. In this Comment, we show that these theoretical constructions follow directly from our earlier work <a href="http://arxiv.org/abs/math/0611185">this http URL</a> on full wave analysis of cloaking for the Helmholtz equation with respect to Riemannian metrics. Furthermore, the analysis there covers the case of acoustically radiating objects being enclosed in the cloaked region.

Electromagnetic Wave Interactions with a Metamaterial Cloak

Hongsheng Chen — 2008-01-30T19:04:03-00:00

Physical Review Letters, Vol. 99, No. 6. (2007)

We establish analytically the interactions of electromagnetic wave with a general class of spherical cloaks based on a full wave Mie scattering model. We show that for an ideal cloak the total scattering cross section is absolutely zero, but for a cloak with a specific type of loss, only the backscattering is exactly zero, which indicates the cloak can still be rendered invisible with a monostatic (transmitter and receiver in the same location) detection. Furthermore, we show that for a cloak with imperfect parameters the bistatic (transmitter and receiver in different locations) scattering performance is more sensitive to t= than nt=.

Scattering Theory Derivation of a 3D Acoustic Cloaking Shell

Steven Cummer — 2008-01-18T10:17:28-00:00

Physical Review Letters, Vol. 100, No. 2. (2008)

Through acoustic scattering theory we derive the mass density and bulk modulus of a spherical shell that can eliminate scattering from an arbitrary object in the interior of the shell—in other words, a 3D acoustic cloaking shell. Calculations confirm that the pressure and velocity fields are smoothly bent and excluded from the central region as for previously reported electromagnetic cloaking shells. The shell requires an anisotropic mass density with principal axes in the spherical coordinate directions and a radially dependent bulk modulus. The existence of this 3D cloaking shell indicates that such reflectionless solutions may also exist for other wave systems that are not isomorphic with electromagnetics.