Bianisotropic Media Research Articles

New spin-resolved thermal radiation laws for nonreciprocal bianisotropic media

A chiral absorber of light can emit spin-polarized (circularly polarized) thermal radiation based on Kirchhoff’s law which equates spin-resolved emissivity with spin-resolved absorptivity for reciprocal media at thermal equilibrium. No such law is known for nonreciprocal media. In this work, we discover three spin-resolved Kirchhoff’s laws of thermal radiation applicable for both reciprocal and nonreciprocal planar media. In particular, these laws are applicable to multi-layered or composite slabs of generic bianisotropic material classes which include (uniaxial or biaxial) birefringent crystals, (gyrotropic) Weyl semimetals, magnetized semiconductors, plasmas, ferromagnets and ferrites, (magnetoelectric) topological insulators, metamaterials and multiferroic media. We also propose an experiment to verify these laws using a single system of doped indium antimonide (InSb) thin film in an external magnetic field. Furthermore, we reveal a surprising result that the planar slabs of all these material classes can emit partially circularly polarized thermal light without requiring any surface patterning, and identify planar configurations which can experience nontrivial thermal optomechanical forces and torques upon thermal emission into the external environment at lower temperature (nonequilibrium). Our work also provides a new fundamental insight of detailed balance of angular momentum (in addition to energy) of equilibrium thermal radiation, and paves the way for practical functionalities based on thermal radiation using nonreciprocal bianisotropic materials.

Tutorial on Electromagnetic Nonreciprocity and its Origins

This tutorial provides an intuitive and concrete description of the phenomena of electromagnetic nonreciprocity that will be useful for readers with engineering or physics backgrounds. The notion of time reversal and its different definitions are discussed with special emphasis to its relationship with the reciprocity concept. Starting from the Onsager reciprocal relations generally applicable to many physical processes, we present the derivation of the Lorentz theorem and discuss other implications of reciprocity for electromagnetic systems. Next, we identify all possible routes towards engineering nonreciprocal devices and analyze in detail three of them: Based on external bias, based on nonlinear and time-variant systems. The principles of the operation of different nonreciprocal devices are explained. We address the similarity and fundamental difference between nonreciprocal effects and asymmetric transmission in reciprocal systems. In addition to the tutorial description of the topic, the manuscript also contains original findings. In particular, general classification of reciprocal and nonreciprocal phenomena in linear bianisotropic media based on the space- and time-reversal symmetries is presented. This classification serves as a powerful tool for drawing analogies between seemingly distinct effects having the same physical origin and can be used for predicting novel electromagnetic phenomena. Furthermore, electromagnetic reciprocity theorem for time-varying systems is derived and its applicability is discussed.

Tetra-hyperbolic and tri-hyperbolic optical phases in anisotropic metamaterials without magnetoelectric coupling due to hybridization of plasmonic and magnetic Bloch high-k polaritons

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. In hyperbolic metamaterials used for sensing, imaging, and other applications the high-k modes are purely magnetic or electric, which results in purely electric (magnetic) near-fields in response to electric (magnetic) sources. The hybridization predicted in this paper leads to the formation of high-k modes which feature both electric and magnetic fields. This can be used to induce magnetic near fields in response to electric dipole in realistic structures which opens novel avenues in the optical magnetism research. Our work 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, emission rate, directivity, and near-field control. To accomplish this, we develop a range of new techniques of theoretical optics for bianisotropic materials, including the quadratic index of refraction operator method, suitable to study the high-k polaritons with finite indices of refraction and the explicit expression for the characteristic matrix in generic bianisotropic media. We introduce the spatial stratification approach for the electric and magnetic responses of anisotropic homogeneous media to analyze the underlying Bloch waves. We believe that the formalisms developed here can be useful for the researchers in the field of theoretical optics of anisotropic and bianisotropic media in the future.

Spin-polarized unidirectional cylindrical waveguide in bianisotropic media.

In this paper, we analyze a cylindrical waveguide consisting of two layers of bianisotropic material with anti-symmetric magnetoelectric coupling tensors. The analysis is carried out in terms of pseudo-electric and pseudo-magnetic fields which satisfy Maxwells' equations with gyrotropic permittivity and permeability tensors. We show that the rotationally symmetric modes of the waveguide are unidirectional with transverse pseudo-electric and transverse pseudo-magnetic modes propagating in opposite directions. These modes are surface waves whose electromagnetic field is concentrated near the interface between the two anisotropic materials. They follow the contour of the interface even in the case of sharp discontinuities and pass through an obstacle without backscattering if the obstacle does not change the polarization of the wave. Higher-order modes of the waveguide are also investigated. Although these modes are hybrid modes and not, strictly speaking, unidirectional, they practically behave as the rotationally symmetric mode.

Three-Dimensional Time-Harmonic Electromagnetic Scattering Problems from Bianisotropic Materials and Metamaterials: Reference Solutions Provided by Converging Finite Element Approximations

A recently developed theory is applied to deduce the well posedness and the finite element approximability of time-harmonic electromagnetic scattering problems involving bianisotropic media in free-space or inside waveguides. In particular, three example problems are considered of which one deals with scattering from plasmonic gratings that exhibit bianisotropy while the other two deal with bianisotropic obstacles inside waveguides. The hypotheses that guarantee the reliability of the numerical results are verified, and the ranges of the constitutive parameters of the media involved for which the finite element solutions are guaranteed to be reliable are deduced. It is shown that, within these ranges, there can be significant bianisotropic effects for the practical media considered as examples. The ensured reliability of the obtained results can make them useful as benchmarks for other numerical approaches. To the best of our knowledge, no other tool can guarantee reliable solutions.

Complex Bianisotropy Effect on the Propagation Constant of a Shielded Multilayered Coplanar Waveguide Using Improved Full Generalized Exponential Matrix Technique

A theoretical study of the electromagnetic propagation in a complex medium suspended multilayer coplanar waveguide (CPW) is presented. The study is based on the generalized exponential matrix technique (GEMT) combined with Galerkin’s spectral method of moments applied to a CPW printed on a bianisotropic medium. The analytical formulation is based on a Full-GEMT, a method that avoids usual procedures of heavy and tedious mathematical expressions in the development of calculations and uses matrix-based mathematical expressions instead. These particularities are exploited to develop a mathematical model for the characterization of wave propagation in a three-layer shielded suspended CPW structure. This study is based on the development of mathematical formulations in full compact matrix-based expressions resulting in Green’s functions in a matrix form. The implemented method incorporates a new accelerating procedure developed in the GEMT which provides an initial value used to speed up searching for the exact solution in the principal computation code. This helped us to obtain accurate solutions with tolerable computing time. Good agreements have been achieved with the literature in terms of accuracy and rapid convergence. The results for different cases of bianisotropy have been investigated, and particularly, the effect on the dispersion characteristics is presented and compared with the isotropic case.

Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Direct and inverse electromagnetic scattering problems for bi-anisotropic media**This paper is dedicated to the memory of Professor Armin Lechleiter.

This paper is concerned with the direct and inverse scattering of time-harmonic electromagnetic waves from bi-anisotropic media. For the direct problem, we establish an integro-differential equation formulation, its Fredholm property, and the uniqueness of a weak solution. Using this integro-differential formulation we study a fast spectral Galerkin method for the numerical solution to the direct problem. Numerical examples are presented and convergence of the spectral method is proved via Gårding estimates for (strongly singular) integro-differential equations. We solve the inverse problem of recovering bi-anisotropic scatterers from far-field data using orthogonality sampling methods. These methods aim to construct imaging functionals which are robust to noise, computationally cheap, and require data for only one or a few incident fields. We provide some theoretical analysis as well as numerical simulations for the proposed imaging functionals.

Transverse photon spin of bulk electromagnetic waves in bianisotropic media

Photons possess spin degree of freedom, which plays an important role in various applications such as optical communications, information processing and sensing. In isotropic media, photon spin is aligned with the propagation direction of light, obeying the principle of spin momentum locking. Interestingly, surface waves decaying away from an interface have a photon spin transverse to its propagation, opening exciting opportunities for the observation of spin-dependent excitation in confined systems. Here, we propose and realize transverse photon spin (T-spin) in a bulk medium, without relying on the presence of any interfaces. We show the mapping of the T-spin of surface modes to that of the bulk modes by introducing bianisotropy into the medium. We further discover that the interface between two bianisotropic media of opposite orientations supports edge-dependent propagating modes with tunable cutoff frequencies. Our results provide a new platform for manipulating the spin–orbit interaction of electromagnetic waves. A method to map the known tranverse photon spin of electromagnetic surface waves over to bulk modes is enabled thanks to bianisotropy.

Mueller matrix polarimetry of bianisotropic materials [Invited

Mueller matrix polarimetry is a powerful optical technique for characterization of both anisotropic and bianisotropic materials. This review emphasizes methods for the interpretation of measured Mueller matrices, from the meanings of matrix symmetries, to ab initio calculations of Mueller matrices that begin with Maxwell’s equations operating on materials with permittivity, permeability, and magnetoelectric constitutive tensors. We present an overview of polarimetry measurements in crystals as well as metamaterials that have optically responsive features on the order of the wavelength of visible light. Examples of the full measurement of the constitutive tensors of bianisotropic media from the analysis of their Mueller matrices, collected in either transmission or reflection, are illustrated for natural crystals, polycrystals, and nanofabricated metamaterials. Experimental and theoretical research into the complex optical responses of bianisotropic materials with polarized light is best expressed in terms of the Mueller matrix, as it offers an unambiguous and mathematically robust platform for analysis of light–matter interactions.

Nonlocal homogenization of PT -symmetric multilayered structures

Unique and highly tunable optical properties of PT-symmetric systems and metamaterials enable a plenty of entirely new linear and nonlinear optical phenomena with numerous applications, e.g., for designing subdiffraction lenses, nonreciprocal devices, etc. Therefore, the artificial media with the PT symmetry attract ever-increasing attention and are now a subject for intensive investigations. One of the commonly used methods providing information about the optical response of artificial nanostructural media is a so-called effective medium theory. Here we examine the possibility of utilizing the effective medium theory for a comprehensive analysis of PT-symmetric multilayered systems composed of alternating loss and gain slabs. We show that applicability of local effective material parameters (or Maxwell Garnett approximation) is very limited and cannot be exploited for a prediction of exceptional points marking a PT symmetry breaking. On the other hand, nonlocal bianisotropic effective medium parameters can be reliably used, if the thickness of a unit cell is much smaller than the radiation wavelength. In the case of obliquely incident plane waves, we reveal the limitation on the loss-gain coefficient, which should not be too large compared with the real part of the permittivity. We believe that our findings can improve the fundamental understanding of physics behind PT-symmetric systems and advance the development of auxiliary tools for analyzing their peculiar optical response.

The Application of Least-Squares Finite-Element Method to Simulate Wave Propagation in Bianisotropic Media

The finite-element method (FEM) has been one of the major numerical techniques for electromagnetics (EM) ever since the introduction of the spurious-free edge element. On the other hand, a so-called least-squares FEM(LSFEM) is becoming increasingly popular due to its unique properties. For instance, the generated stiffness matrix is positive definite. Effort has been made to apply this node-element-based LSFEM to model EM problems, mostly in the theoretical aspect. In this paper, we will use normalized Maxwell's equations incorporated with the constitutive relations of bianisotropic media, which represents the most general cases in the linear regime. Subsequently, the corresponding variational formulation is derived, followed by the generation of matrix systems. We then implement and validate various boundary conditions. Furthermore, we apply this scheme to simulate wave scattering in the presence of bianisotropic media that are categorized into three types. A good convergence rate and agreement between the LSFEM results and the referenced solutions has been achieved, which proves the Lagrange-element-based LSFEM as a feasible alternative to the edge-element-based FEM currently used in EM modeling.

Unidirectional Surface Waves in Bi-Anisotropic Media

We show theoretically that unidirectional surface waves can propagate on the surface of homogeneous bi-anisotropic layers with an anti-symmetric chirality tensor. These materials mimic the electromagnetic behavior of an anisotropic medium with gyrotropic permittivity and permeability tensors that operate on pseudo-electromagnetic fields. The unidirectional waves have transverse pseudo-electric or magnetic polarizations and pass through an obstacle without backscattering if the obstacle does not cause polarization change. The bi-anisotropic medium can be realized as a metamaterial comprising omega particles tailored to achieve the constitutive parameters desired.

Homogenization of the dielectric and magnetic permeability tensors for anisotropic and bianisotropic layered media

The paper deals with the problem of calculating the effective properties of a multilayer system consisting of layers of anisotropic or bianisotropic media. It is assumed that the electromagnetic field is described by the Maxwell equations, and the layers are coordinate surfaces in some orthogonal coordinate system. No assumptions are made in advance about the properties of the dielectric and magnetic permeability tensors. The thickness of the layers is considered to be small in comparison with the wavelengths of all waves that can propagate in the system (long-wave approximation) and in comparison with the curvature radii of the layers as well as with the characteristic size of inhomogeneity in the layers. To construct an approximate solution, it is proposed to use a generalization of the matrix homogenization method. For the applicability of the method, it is necessary to rewrite the system of initial equations for a layered medium in a special form. The main advantage of the proposed approach, to find the parameters of an effective medium, is the absence of the need to solve complex partial differential equations. It is enough only to operate with matrices. The matrix homogenization method also makes it possible to obtain effective characteristics of a periodic structure with each period consisting of a set of thin layers. The study is illustrated by examples of finding effective tensors of dielectric and magnetic permeabilities for a system of planar, cylindrical, and spherical layers. In addition, the dependence of the magnetoelectric coefficient on the layer thicknesses for the cases listed above are compared.

Elliptic Operators with Honeycomb Symmetry: Dirac Points, Edge States and Applications to Photonic Graphene

Consider electromagnetic waves in two-dimensional {\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator $\LA=-\nabla_\bx\cdot A(\bx) \nabla_\bx$, where $A(\bx)$ is $\Lambda_h-$ periodic ($\Lambda_h$ denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, $A(\bx)$ is $\mathcal{P}\mathcal{C}-$ invariant ($A(\bx)=\overline{A(-\bx)}$) and $120^\circ$ rotationally invariant ($A(R^*\bx)=R^*A(\bx)R$, where $R$ is a $120^\circ$ rotation in the plane). We first obtain results on the existence, stability and instability of Dirac points, conical intersections between two adjacent Floquet-Bloch dispersion surfaces. We then show that the introduction through small and slow variations of a {\it domain wall} across a line-defect gives rise to the bifurcation from Dirac points of highly robust (topologically protected) {\it edge states}. These are time-harmonic solutions of Maxwell's equations which are propagating parallel to the line-defect and spatially localized transverse to it. The transverse localization and strong robustness to perturbation of these edge states is rooted in the protected zero mode of a one-dimensional effective Dirac operator with spatially varying mass term. These results imply the existence of {\it uni-directional} propagating edge states for two classes of time-reversal invariant media in which $\mathcal{C}$ symmetry is broken: magneto-optic media and bi-anisotropic media. Our analysis applies and extends the tools previously developed in the context of honeycomb Schr\"odinger operators.

Complete 72-parametric classification of surface plasmon polaritons in quartic metamaterials

We propose a general and complete classification of all possible new and old kinds of surface plasmon polaritons (SPPs) that can propagate at boundaries of arbitrary linear, local bi-anisotropic media, including the quartic metamaterials. In particular, we introduce a new kind of generic bi-exponential SPPs with arbitrary frequency, wavelength, propagation direction, and penetration depths and fields. We show that any such an SPP is supported by a broad 72-parametric invariance class of pairs of interfacing media. A member of each invariance class is a pair of anisotropic materials without magnetoelectric couplings.

Acoustic bianisotropic metasurfaces for broadband non-reciprocal sound transport

Acoustic bianisotropic materials are media in which the unconventional momentum—strain and stress—particle velocity couplings offer rich mechanical wave dynamics. For instance, transformation elastodynamics have revealed that bianisotropic media could enable extraordinary control over the propagation of elastic waves including the ability to cloak regions of space from detection with mechanical waves. The development of metamaterials have provided the tools to implement these unconventional materials and the first experimental acoustic bianisotropic materials have featured interesting properties such as independent engineering of transmission and reflection. However, despite recent work in this area, the wave dynamics enabled by mechanical bianisotropy have not been fully uncovered and explored. In this presentation we demonstrate experimentally the power of active bianisotropic metasurfaces to produce highly non-reciprocal sound transport in free space in a remarkably broadband fashion and in very compact materials. In addition, we show that this unusual mechanism for non-reciprocal sound propagation is truly linear and does not rely on any type of frequency conversion or other non-linear processes.Acoustic bianisotropic materials are media in which the unconventional momentum—strain and stress—particle velocity couplings offer rich mechanical wave dynamics. For instance, transformation elastodynamics have revealed that bianisotropic media could enable extraordinary control over the propagation of elastic waves including the ability to cloak regions of space from detection with mechanical waves. The development of metamaterials have provided the tools to implement these unconventional materials and the first experimental acoustic bianisotropic materials have featured interesting properties such as independent engineering of transmission and reflection. However, despite recent work in this area, the wave dynamics enabled by mechanical bianisotropy have not been fully uncovered and explored. In this presentation we demonstrate experimentally the power of active bianisotropic metasurfaces to produce highly non-reciprocal sound transport in free space in a remarkably broadband fashion and in very compac...

Guided waves at bianisotropic fluid interfaces

Willis fluids are characterized by constitutive relations that couple the pressure and momentum density to both the particle velocity and the volume strain. This effective dynamic response coupling may arise due to microstructural asymmetry, long range order, or time-varying material properties and has been shown to be analogous to electromagnetic bianisotropic media [Phys. Rev. B 96, 104303 (2017)]. In this study, we report on the existence of guided waves at the interface between two fluids when at least one displays Willis coupling. Criteria for the existence of these waves are discussed in terms of the material properties, frequency, and wave number, and expressions for the dispersion relation and rate of spatial decay away from the interface are obtained analytically. We demonstrate that interface waves are supported when one of the fluids possesses Willis coupling, in contrast to an interface between two classical isotropic fluids, which cannot support interface waves. Special cases are highlighted via numerical examples. [Work supported by ONR, NSF, the Applied Research Laboratories at The University of Texas at Austin, and the NRC Research Associateship Program.]

Acoustic focusing via guided waves in bianisotropic fluid layers

Willis fluids display a complex, effective dynamic response stemming from microstructural asymmetry, long range order, and/or time-varying material properties. These materials are characterized by constitutive relations that couple the pressure and momentum density to both the particle velocity and the volume strain. This coupling has been shown to be analogous to electromagnetic bianisotropic media, which exhibit coupled electric and magnetic fields [Phys. Rev. B 96, 104303 (2017)]. In a recent study, an acoustic lens composed of an array of Willis fluid layers was demonstrated, where the pressure phase imparted by each array element was tuned by varying the direction of Willis polarization and was determined using finite element analysis. In this work, we report on analytical solutions for guided waves in layers of fluid displaying Willis coupling and derive dispersion relations for layers with rigid and pressure-release boundary conditions. Special cases highlighting the effect of Willis polarization direction are presented via numerical examples. The acoustic lens is revisited with array phases obtained from analytical solutions, eliminating the need for finite element methods. Lenses designed for focusing and steering incident pressure waves are demonstrated using fully analytical models. [Work supported by NSF, ONR, and ARL:UT.]

Analysis and synthesis of bianisotropic metasurfaces by using analytical approach based on equivalent parameters

An analytical method is presented to analyze and synthesize bianisotropic metasurfaces. The equivalent parameters of metasurfaces in terms of meta-atom properties and other specifications of metasurfaces are derived. These parameters are related to electric, magnetic, and electromagnetic/magnetoelectric dipole moments of the bianisotropic media, and they can simplify the analysis of complicated and multilayer structures. A metasurface of split ring resonators is studied as an example demonstrating the proposed method. The optical properties of the meta-atom are explored, and the calculated polarizabilities are applied to find the reflection coefficient and the equivalent parameters of the metasurface. Finally, a structure consisting of two metasurfaces of the split ring resonators is provided, and the proposed analytical method is applied to derive the reflection coefficient. The validity of this analytical approach is verified by full-wave simulations which demonstrate good accuracy of the equivalent parameter method. This method can be used in the analysis and synthesis of bianisotropic metasurfaces with different materials and in different frequency ranges by considering electric, magnetic, and electromagnetic/magnetoelectric dipole moments.