We present a new, fully analytical point scattering model which can be applied to arbitrary anisotropic magneto-electric dipole scatterers, including split ring resonators (SRRs), chiral and anisotropic plasmonic scatterers. We have taken proper account of reciprocity and radiation damping for electric and magnetic scatterers with any general polarizability tensor. Specifically, we show how reciprocity and energy balance puts constraints on the electrodynamic responses arbitrary scatterers can have to light. Our theory sheds new light on the magnitude of cross sections for scattering and extinction, and for instance on the emergence of structural chirality in the optical response of geometrically non-chiral scatterers like SRRs. We apply the model to SRRs and discuss how to extract individual components of the polarizability matrix and extinction cross sections. Finally, we show that our model describes well the extinction of stereo-dimers of split rings, while providing new insights in the underlying coupling mechanisms.
Recently it was discovered that periodic lattices of metamaterial scatterers show optical activity, even if the scatterers or lattice show no 2D or 3D chirality, if the illumination breaks symmetry. In this Letter we demonstrate that such `pseudo-chirality' is intrinsic to any single planar metamaterial scatterer and in fact has a well-defined value at a universal bound. We argue that in any circuit model, a nonzero electric and magnetic polarizability derived from a single resonance automatically imply strong bianisotropy, i.e., magneto-electric cross polarizability at the universal bound set…
Analogous to electromagnetic bianisotropy, engineered piezoelectric metamaterials can possess electro-momentum coupling between the macroscopic momentum and electric stimuli. This indicates the applicability of piezoelectric metamaterials for wave scattering with an extra design degree of freedom, in the same way as acoustic materials with Willis coupling between the macroscopic momentum and strain. To fully utilize this novel bianisotropy, we derive for the first time tight theoretical bounds on the effect of electro-momentum coupling on scatterers based on energy conservation and combining t…
In a scattering experiment, the induced dipole moments of a magnetoelectric point scatterer in response to driving fields are given by its polarizability tensor α. Its linewidth will be dictated by the local density of optical states (LDOS) at the scatterer's position. To retrieve the magnetoelectric cross coupling components of αfor an archetypical magnetoelectric scatterer - a split ring resonator - we study the frequency dependent extinction cross section as a function of distance to an interface. Rather than following a purely electric or purely magnetic LDOS, we find a dependence which re…
The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and optimization are used. Detailed numerical results are given and the connections between the different approaches are enlightened.
We show that it is possible to design an invisible wavelength-sized metal-dielectric metamaterial object without evoking cloaking. Our approach is an extension of the neutral inclusion concept by Zhou and Hu [Phys.Rev.E 74, 026607 (2006)] to Mie scatterers. We demonstrate that an increase of metal fraction in the metamaterial leads to a transition from dielectric-like to metal-like scattering, which proceeds through invisibility or optical neutrality of the scatterer. Formally this is due to cancellation of multiple scattering orders, similarly to plasmonic cloaking introduced by Alu and Enghe…
Resonant scattering of electromagnetic (EM) waves by small particles is considered as one of the basic problem in metamaterial science. At present, special subwavelength resonators are considered as structural elements in chiral and bianisotropic metamaterials. There is a general consensus that these small scatterers behave like "artificial atoms", meta-atoms, with strong electrical and magnetic responses and an interconnection between these responses. However, the observed effect of magnetoelectric (ME) coupling in these meta-atoms is not associated with the near-field manipulation properties…
We propose a new class of metamaterials called magneto-optical metamaterials that offer enhanced angle of rotation in polarization compared to bulk magneto-optical materials. In the proposed approach, the permittivity tensor of a magneto-optical material is tailored by embedded wire meshes behaving as artificial plasma. We have shown that the angle of rotation in the magneto-optical metamaterial can be enhanced up to 9 times compared to bulk magneto-optical material alone while the polarization extinction ratio remains below -20dB and insertion loss is less than 1.5dB.
We demonstrate resonant Faraday polarization rotation in plasmonic arrays of bimetallic nano-ring resonators consisting of Au and Ni sections. This metamaterial design allows to optimize the trade-off between the enhancement of magneto-optical effects and plasmonic dissipation. Although Ni sections correspond to as little as ~6% of the total surface of the metamaterial, the resulting magneto-optically induced polarization rotation is equal to that of a continuous film. Such bimetallic metamaterials can be used in compact magnetic sensors, active plasmonic components and integrated photonic cir…
We demonstrate experimentally and theoretically that a local excitation of a single scatterer of relative dielectric permittivity ε = 6 permits to excite broad dipolar and quadrupolar electric and magnetic resonances that shape the emission pattern in an un- precedented way. By suitably positioning the feed with respect to the sphere at a ?=3 distance, this compact antenna is able to spectrally sort the electromagnetic emission ei- ther in the forward or in the backward direction, together with a high gain in directivity. Materials with ε = 6 can be found in the whole spectrum of frequencies p…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propag…
In this paper we explored the scattering behavior of thin cylinders made of LHM and coated by a monoatomic graphene layer. A spectral tunability of the resonance peaks is evidenced by altering the chemical potential of the graphene coating, a fact that occurs at any state of polarization of the incident plane wave in opposition to the case of scatterers of dielectric core. On the contrary, no invisibility condition can be satisfied for dielectric environments. A singular performance is also found for cylinders with permittivity and permeability near zero. Practical implementations of our resul…
Metamaterials with artificial optical properties have attracted significant research interest. In particular, artificial magnetic resonances in non-unity permeability tensor at optical frequencies in metamaterials have been reported. However, only non-unity diagonal elements of the permeability tensor have been demonstrated to date. A gyromagnetic permeability tensor with non-zero off-diagonal elements has not been observed at the optical frequencies. Here we report the observation of gyromagnetic properties in the near-infrared wavelength range in a magneto-plasmonic metamaterial. The non-zer…
Using a multiple scattering technique, we derived closed-form expressions for effective constitutive parameters and electro/magneto-strictive tensor components for 2D bi-anisotropic metamaterials. Using the principle of virtual work, we obtained the electromagnetic stress tensor that can be used to calculate the optical force density inside such media. The analytic expressions are tested against full wave numerical simulations. Our effective medium theory is essential for providing a complete macroscopic description of the optical and opto-mechanical properties of bi-anisotropic composites.
We studied a metasurface constituted as a periodic array of semiconductor split-ring resonators. The resonance frequencies of the metasurface excited by normally incident light were found to be continuously tunable in the terahertz regime through an external magnetostatic field of suitable orientation. As such metasurfaces can be assembled into 3D metamaterials, the foregoing conclusion also applies to metamaterials comprising semiconductor split-ring resonators.
Manipulation of radiation is required for enabling a span of electromagnetic applications. Since properties of antennas and scatterers are very sensitive to a surrounding environment, macroscopic artificially created materials are good candidates for shaping their characteristics. In particular, metamaterials enable controlling both dispersion and density of electromagnetic states, available for scattering from an object. As the result, properly designed electromagnetic environment could govern waves' phenomena. Here electromagnetic properties of scattering dipoles, situated inside a wire medi…
In this paper we reveal the physics behind the formation of tri- and tetra-hyperbolic phases in anisotropic metamaterials without magnetoelectric coupling and describe the anti-crossing splitting phenomenon in the hyperbolic dispersion which arises due to the hybridization of the plasmonic and magnetic Bloch high-k polaritons. This considerably deepens the understanding of the high-k polaritons and the topology of the optical iso-frequency surfaces in k-space and will find applications in optical nano-resolution imaging and emission rate and directivity control. To accomplish this, we develop …
Using the multiple-scale homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metafilm. The scatterers that compose the metafilm are of arbitrary shape and are embedded between two different magneto-dielectric media. The parameters in these boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the metafilm.
We develop a theoretical formalism for collectively responding point scatterers where the radiating electromagnetic fields from each emitter are considered in the electric dipole, magnetic dipole, and electric quadrupole approximation. The contributions of the electric quadrupole moment to electromagnetically-mediated interactions between the scatterers are derived in detail for a system where each scatterer represents a linear $RLC$ circuit resonator, representing common metamaterial resonators in radiofrequency, microwave, and optical regimes. The resulting theory includes a closed set of eq…
Scatterings and transport in Weyl semimetals have caught growing attention in condensed matter physics, with observables including chiral zero modes and the associated magnetoresistance and chiral magnetic effects. Measurement of electrical conductance is usually performed in these studies, which, however, cannot resolve the momentum of electrons, preventing direct observation of the phase singularities in scattering matrix associated with Weyl point. Here we experimentally demonstrate a helical phase distribution in the angle (momentum) resolved scattering matrix of electromagnetic waves in a…
The optical properties of some nanomaterials can be controlled by an external magnetic field, providing active functionalities for a wide range of applications, from single-molecule sensing to nanoscale nonreciprocal optical isolation. Materials with broadband tunable magneto-optical response are therefore highly desired for various components in next-generation integrated photonic nanodevices. Concurrently, hyperbolic metamaterials received a lot of attention in the past decade since they exhibit unusual properties that are rarely observed in nature and provide an ideal platform to control th…
We examine the effect of inhomogeneous broadening on the collective response of a planar metamaterial consisting of asymmetric split ring resonators. We show that such a response leads to a transmission resonance that can persist when the broadening of individual meta-atom resonance frequencies is roughly one half the frequency characterizing the split ring asymmetry. We also find that larger degrees of inhomogeneous broadening can drastically alter the cooperative response, destroying this resonance. The reduced effect of cooperative response due to inhomogeneous broadening may find applicati…
Electromagnetic metamaterials offer a great avenue to engineer and amplify the nonlinear response of materials. Their electric, magnetic, and magneto-electric linear and nonlinear response are related to their structure, providing unprecedented liberty to control those properties. Both the linear and the nonlinear properties of metamaterials are typically anisotropic. While the methods to retrieve the effective linear properties are well established, existing nonlinear retrieval methods have serious limitations. In the present work, we generalize a nonlinear transfer matrix approach to account…
While metamaterials are often desirable for near-field functions, such as perfect lensing, or cloaking, they are often quantified by their response to plane waves from the far field. Here, we present a theoretical analysis of the local density of states near lattices of discrete magnetic scatterers, i.e., the response to near field excitation by a point source. Based on a point-dipole theory using Ewald summation and an array scanning method, we can swiftly and semi-analytically evaluate the local density of states (LDOS) for magnetoelectric point sources in front of an infinite two-dimensiona…
Antireflection or impedance matching is a topic that has been extensively researched by the optical and microwave communities over the past century and until today. However, due to the diverging wave impedances of TE (s) and TM (p) polarizations with increasing incident angle, it is impossible to achieve perfect matching simultaneously for both polarizations at an oblique incident angle with a single conventional matching layer. In this paper, we show that simultaneous perfecting matching of an arbitrary substrate at an arbitrary incident angle from air is possible with a single uniaxial metam…
We present a semi-analytical point-dipole method that uses Ewald lattice summation to find the dispersion relation of guided plasmonic and bianisotropic modes in metasurfaces composed of 2D periodic lattices of arbitrarily strongly scattering magneto-electric dipole scatterers. This method takes into account all retarded electrodynamic interactions as well as radiation damping selfconsistently. As illustration we analyze the dispersion of plasmon nanorod lattices, and of 2D split ring resonator lattices. Plasmon nanorod lattices support transverse and longitudinal in-plane electric modes. Scat…
We study the scattering of magnetoinductive plane waves by internal (external) capacitive (inductive) defects coupled to a one-dimensional split-ring resonator array. We examine a number of simple defect configurations where Fano resonances occur and study the behavior of the transmission coefficient as a function of the controllable external parameters. We find that for embedded capacitive defects, the addition of a small amount of coupling to second neighbors is necessary for the occurrence of Fano resonance. For external inductive defects, Fano resonances are commonplace, and they can be tu…
Electromagnetic scattering from moving bodies, being inherently time-dependent phenomenon, gives rise to a generation of new frequencies, which could characterize the motion. While a standard linear path leads to a constant Doppler shift, accelerating scatterers could generate a micro-Doppler frequency comb. Here, a spectra produced by rotating objects, was studied and observed in a bi-static lock in detection scheme. Internal geometry of a scatterer was shown to determine the spectra, while the degree of structural asymmetry was suggested to be identified via signatures in the micro-Doppler c…
We explore the electrodynamic coupling between a plane wave and an infinite two-dimensional periodic lattice of magneto-electric point scatterers, deriving a semi-analytical theory with consistent treatment of radiation damping, retardation, and energy conservation. We apply the theory to arrays of split ring resonators and provide a quantitive comparison of measured and calculated transmission spectra at normal incidence as a function of lattice density, showing excellent agreement. We further show angle-dependent transmission calculations for circularly polarized light and compare with the a…
Some novel quasi-planar chiral inclusions, feasible from standard photo-etching techniques, are proposed. It is shown that such inclusions can be designed in order to present balanced electric, magnetic and magneto-electric polarizabilities. Using these inclusions, random and periodic bi-isotropic artificial metamaterials exhibiting a balanced positive/negative refractive index can be build up. These metamaterials would exhibit reasonable bandwidths and excellent matching to free space.
Most applications of memory effects in disordered optical media, such as the tilt-tilt and shift-shift spatial correlations, have focused on imaging through and inside biological tissues. Here we put forward a metamaterial platform not only to enhance but also to tune memory effects in random media. Specifically, we investigate the shift-shift and tilt-tilt spatial correlations in metamaterials composed of coated spheres and cylinders by means of the radiative transfer equation. Based on the single-scattering phase function, we calculate the translation correlations in anisotropically scatteri…
Engineered core-shell cylinders are good candidates for applications in invisibility and cloaking.In particular, hyperbolic nanotubes demonstrate tunable ultra-low scattering cross section in the visible spectral range. In this work we investigate the limits of validity of the condition for invisibility, which was shown to rely on reaching an epsilon near zero in one of the components of the effective permittivity tensor of the anisotropic metamaterial cavity. For incident light polarized perpendicularly to the scatterer axis, critical deviations are found in low-birefringent arrangements and …
We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field opera…
In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwell's equations in a space-time dependent magneto-electric medium with direct application to the simulation of the recently proposed spacetime cloak. We utilize a dual grid FDTD method overlapped to the time domain to provide a stable approach for the simulation of magneto-electric medium with time and space varying permittivity, permeability and coupling coefficient. The developed method can be applied to explore other new physical possibilities offered by spacetime cl…
We investigate electromagnetic scattering of normally irradiated gyrotropic, magneto-optical core-shell cylinders using Lorenz-Mie theory. A general expression for time-averaged electromagnetic energy inside a coated gyroelectric and gyromagnetic scatterer is derived. Using realistic material parameters for a silica core and InSb shell, we calculate the stored electromagnetic energy and the scattering anisotropy. We show that the application of an external magnetic field along the cylinder axis induces a drastic decrease in electromagnetic absorption in a frequency range in the terahertz, wher…
