This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane electromagnetic waves in ordinary dielectrics, the kinematical and dynamical aspects of these phenomena are studied, such as the intensity of the various wave components and the change in the polarization of the wave as it crosses the boundary. As a prerequisite of this, we show that the plane wave solution must be written as a suitable superposition of the circularly amplitudes on both sides of the interface, we elucidate which is the appropriate set of conditions that the solution must satisfy at the boundary, and we set down the minimal, and complete, set of equations that must be solved for the coefficient amplitudes in order to satisfy the boundary conditions. The equations are solved explicitly for some particular cases and configurations (e.g., normal incidence), the salient features of those solutions are analyzed in some detail, and the general solution to the equations is given as well.
Negative reflection and negative refraction are exotic phenomena that can be achieved by platforms such as double-negative metamaterial, hyperbolic metamaterial, and phase-discontinuity metasurface. Recently, natural biaxial van der Waals (vdW) materials, which support extremely anisotropic, low-loss, and highly confined polaritons from infrared to visible regime, are emerging as promising candidates for planar reflective and refractive optics. Here, we introduce three degrees of freedom, namely interface, crystal direction, and electric tunability to manipulate the reflection and refraction o…
The general reflection and refraction laws at the metasurface with the abrupt phase shift were derived by two different methods of Fermat's principle and the boundary conditions respectively. It is found that one or two critical angles for total internal reflection exist when a light hits on the optical sparse material from the optical denser material, and one such a critical angle exists when light spreads from the optical sparse material to the optical denser material. Anomalous reflection and refraction, such as, negative reflection and negative refraction may occur when a light passes thro…
By generalizing the well known results for reflection and refraction of plane waves at the vacuum-medium interface to Gaussian light beams, we obtain analytic formulas for reflection and refraction of the TM and TE laser light pulses. This enables us to give a possible explanation why no reflection was observed in light pulse photographs in some vicinity of the air-resin interface, given in L. Gao, J. Liang, C. Li, and L. V. Wang, Nature 516 (2014) 74-77. We suggest how to modify the experimental setup so as to observe the reflected pulse.
We show that nanosphere dispersed liquid crystal (NDLC) metamaterial can be characterized in near IR spectral region as an indefinite medium whose real parts of effective ordinary and extraordinary permittivities are opposite in signs. Based on this fact we design a novel electrooptic effect: external electric field driven switch between normal refraction, negative refraction and reflection of TM incident electromagnetic wave from the boundary vacuum/NDLC. A detailed analysis of its functionality is given based on effective medium theory combined with a study of negative refraction in anisotro…
Partially coherent light beams are encountered both in classical and in quantum optics. Their coherence properties generally depend on the correlation properties of their sources. In this paper, we propose a technique for controlling the coherence properties of optical beams in laboratory environment. The technique is based on the fact that coherence properties of partially coherent electromagnetic beams can be changed on refraction and on reflection, and that the changes can be controlled by varying the angle of incidence.
We report the design, fabrication, and characterization of bianisotropic Huygens' metasurfaces (BHMSs) for refraction of normally incident beams towards 71.8 degrees. As previously shown, all three BHMS degrees of freedom, namely, electric polarizability, magnetic polarizability and omega-type magnetoelectric coupling, are required to ensure no reflections occur for such wide-angle impedance mismatch. The unit cells are composed of three metallic layers, yielding a printed-circuit-board (PCB) structure. The fabricated BHMS is characterized in a quasi-optical setup, used to accurately assess sp…
We derive the paraxial meridional ray tracing equations from the unified reflection-refraction law using geometric algebra. This unified law states that the normal vector to the interface is a rotation of the incident ray or of the refracted ray or of the reflected ray by an angle equal to the angle of incidence or of refraction. We obtain the finite meridional ray tracing equations by simply equating the arguments of the exponential rotation operators. We then derive the paraxial limits of these equations with the help of sign function identities. We show that by embedding the sign functions …
We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations of the electric and magnetic fields on both sides of the boundary. It is shown that the polarization-dependent distortions of the beam trajectory (in particular, the "longitudinal" Goos-Hänchen shift and the "lateral" Imbert-Fedorov shift of the beam center of gravity) are directly connected to the incident beam longitudinal component and appear due to its …
Non-uniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected plane waves and show that perfect performance can be realized. The method is based on the use of an equivalent i…
Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing anomalous reflection and refraction for all polarizations of incident light.
We demonstrate bending of light on the same side of the normal in a free standing corrugated metal film under bi-directional illumination. Coherent perfect absorption (CPA) is exploited to suppress the specular zeroth order leading to effective back-bending of light into the `-1' order, while the `+1' order is resonant with the surface mode. The effect is shown to be phase sensitive yielding CPA and superscattering in the same geometry.
In this talk we present and discuss a new general approach to the synthesis of metasurfaces for full control of transmitted and reflected fields. The method is based on the use of an equivalent impedance matrix which connects the tangential field components at the two sides on the metasurface. Finding the impedance matrix components, we are able to synthesize metasurfaces which perfectly realize the desired response. We will explain possible alternative physical realizations and reveal the crucial role of bianisotropic coupling to achieve full control of transmission through perfectly matched …
It is found that the amphoteric refraction, i.e. the refraction can be either positive or negative depending on the incident angles, could occur at a planar interface associated with a uniaxially anisotropic positive index media (PIM) or an anisotropic negative index media (NIM). Particularly, the anomalous negative refraction can occur at a planar interface from an isotropic PIM to an anisotropic PIM, whereas the anomalous positive refraction occurs at the interface from an isotropic PIM to an anisotropic NIM. The optimal conditions to yield the two unusual refractions are obtained. The diffe…
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisfy, they are Monge-Ampère partial differential equations, and we prove existence of solutions.
We theoretically study negative refraction of inhomogeneous waves at the interface of lossy isotropic media. We obtain explicit (up to the sign) expressions for the parameters of a wave transmitted through the interface between two lossy media characterized by complex permittivity and permeability. We show that the criterion of negative refraction that requires negative permittivity and permeability can be used only in the case of a homogeneous incident wave at the interface between a lossless and lossy media. In a more general situation, when the incident wave is inhomogeneous, or both media …
We simulate and discuss novel spatio-temporal propagation effects that relate specifically to pulsed, phase-mismatched second harmonic generation in a negative index material having finite length. Using a generic Drude model for the dielectric permittivity and magnetic permeability, the fundamental and second harmonic frequencies are tuned so that the respective indices of refraction are negative for the pump and positive for the second harmonic signal. A phase-locking mechanism causes part of the second harmonic signal generated at the entry surface to become trapped and dragged along by the …
There are three widely-used conditions for characterizing negative refraction in isotropic dielectric-magnetic materials. Here we demonstrate that whilst all the different conditions are equivalent for purely passive media, they are distinct if active media are considered. Further, these criteria can also be applied to negative refraction in acoustic materials, where we might replace the dielectric permittivity $ε$ with a bulk modulus $κ$, and the magnetic permeability $μ$ with the mass density $ρ$.
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov--Imbert transverse shift of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in general case from ones derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by Onoda et al. [Phys. Rev. Lett. 93, 083901 (2004)]. We a…
Artificial gauge fields enable extending the control over dynamics of uncharged particles, by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed a growing interest in artificial gauge fields that are generated either by geometry or by time-dependent modulation, as they have been the enablers for topological phenomena and synthetic dimensions in many physical settings, e.g., photonics, cold atoms and acoustic waves. Here, we formulate and experimentally demonstrate the generalized laws of refraction …
Spatiotemporal Co-reflection with Spacetime Discontinuities at Moving Interfaces
School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology（黑龙江省等离子体物理及应用技术重点实验室）
A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change direction, but will actually split into two separate beams with a small difference in the respective angles of refraction. Here we report the observation of this phenomenon. We also demonstrate that the angle of reflection does not equal the angle of incidence in a chiral medium. Unlike conventional optical rotation, which depends on the path-length through…
Light refraction, i.e. the bending of the path of a light wave at the interface between two different dielectric media, is ubiquitous in optics. Refraction arises from the different speed of light and is unavoidable in continuous media according to Snell's Law. Here we show rather counterintuitively that omnidirectional refractionless propagation can be observed for discretized light crossing a tilted interface separating two homogeneous waveguide lattices.
We extend designs of perfect lenses to the focussing of surface plasmon polaritons (SPPs) propagating at the interface between two anisotropic media of opposite permittivity sign. We identify the role played by the components of anisotropic and heterogeneous tensors of permittivity and permeability, deduced from a coordinate transformation, in the dispersion relation governing propagation of SPPs. We illustrate our theory with three-dimensional finite element computations for focussing of SPPs by perfect flat and cylindrical lenses.
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian light beams. These formulas show the presence of anomalous refraction phenomena at any slab thickness, including negative refraction and flat lensing effects, induced by the reflection on the rear face.
Reflection and Refraction at Nonlinear Temporal Boundaries in Synthetic Lattices
Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（安徽量子网络重点实验室，中国科学技术大学）；CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学院量子信息与量子物理学卓越创新中心，中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）；Anhui Center for Fundamental Sciences in Theoretical Physics, University of Science and Technology of China（安徽理论物理基础科学中心，中国科学技术大学）
Theoretical and computational study of reflection and refraction of electromagnetic waves with $p$-polarized and normal incidence electric wave amplitude vector on anisotropic, inhomogeneous and linear medium has been done. The medium used in this study is a model of susceptibility in the form of rank-2 tensor which its value depends on the frequency, position and time. Theoretical and computational formulation of transmittance and reflectance are then tested using vacuum and FeF$_2$ magnetic material.
The duality of space and time in Maxwell's equations has prompted interest in time boundaries and the accompanying temporal analog of spatial reflection and refraction. However, achieving observable time boundary effects at optical frequencies in real materials is challenging. In this work, we demonstrate that time reflection and refraction can be observed in a two-band model centered around a non-zero reference energy. Our model can be physically implemented in the synthetic frequency dimension as a system of two coupled dynamically-modulated ring resonators. We find that modulation at microw…
This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to the generalized Snell-Descartes laws. Our main finding is that the generalized laws of refrac-tion and reflection as previously stated have to be modified in order to describe the propagation of light through metasurfaces made of diffractive elements. We provide the appropriate laws that take a different form depending on the properties of the metasurface. Ou…
One of the striking properties of artificially structured materials is the negative refraction, an optical feature that known natural materials do not exhibit. Here, we propose a simple design, composed of two parallel layers of materials with different refraction indices $n_1=-n_2$, that constructs perfect reflection-less devices. The electromagnetic waves can tunnel from one layer to the other, a feature that resembles a truncation of the physical space leading to an electromagnetic warp drive. Since the refractive indices do not require any large values, this method demonstrates for the fir…
We reveal an enhanced and switchable spin Hall effect (SHE) of light near Brewster angle on reflection both theoretically and experimentally. The obtained spin-dependent splitting reaches 3200nm near Brewster angle, 50 times larger than the previous reported values in refraction. We find that the amplifying factor in week measurement is not a constant which is significantly different from that in refraction. As an analogy of SHE in electronic system, a switchable spin accumulation in SHE of light is detected. We were able to switch the direction of the spin accumulations by slightly adjusting …
The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present significantly different characteristics which depend on the polarization. The omnidirectional total reflection and oblique total transmission can occur in the interface associated with the AMM. If appropriate conditions are satisfied, one polarized wave exhibits the total refraction, while the other presents the total reflection. We find that the opposite amph…
I compute from first principles the local heating rate $q$ (the amount of electromagnetic energy converted to heat per unit time per unit volume) for electromagnetic waves propagating in magnetically and electrically polarizable media. I find that, in magnetic media, this rate has two separate contributions, $q^{(V)}$ and $q^{(S)}$, the first coming from the volume of the medium and the second from its surface. I argue that the second law of thermodynamics requires that the volume contribution be positive and that this requirement, in turn, prohibits negative refraction. This result holds for …
As one of the most fundamental optical phenomena, refraction between isotropic media is characterized by light bending towards the normal to the boundary when passing from a low- to a high-refractive-index medium. However, in anisotropic media, refraction is a much more exotic phenomenon. The most general case of refraction between two anisotropic media remains unexplored, particularly in natural media and at the nanoscale. Here, we visualize and comprehensively study refraction of electromagnetic waves between two strongly anisotropic (hyperbolic) media, and, importantly, we do it with the us…
We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, however, in general, do not satisfy the conservation laws for individual photons in consequence of the lack of the ``which path'' information in a two-channel wave scattering. The field structure for the reflected/refracted beam is analyzed. In the scattering of a linearly-polarized beam, photons of opposite helic…
It has been shown that for left-handed metamaterials and generally for negative refraction media the refraction index cannot be entered unequivocally and cannot be considered as real, and especially as negative. This index for above referred media is not expedient
We theoretically propose that Weyl semimetals may exhibit negative refraction at some frequencies close to the plasmon frequency, allowing transverse magnetic (TM) electromagnetic waves with frequencies smaller than the plasmon frequency to propagate in the Weyl semimetals. The idea is justified by the calculation of reflection spectra, in which \textit{negative} refractive index at such frequencies gives physically correct spectra. In this case, a TM electromagnetic wave incident to the surface of the Weyl semimetal will be bent with a negative angle of refraction. We argue that the negative …
We design three-dimensional (3D) metallic nanowire media with different structures and numerically demonstrate that they can be homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain the dispersion relations from which we retrieve the effective permittivities. The pseudo focusing for the real 3D wire medium agrees very well with the homogeneous medium having the effective permittivity tensor of the wire medium. Studies also show that in the long-wavelength limit, the hyperb…
When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell's law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.
By introducing a new mechanism based on purely imaginary conjugate metamaterials (PICMs), we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PICMs, which is a breakthrough to the unidirectional limit in parity time (PT) symmetric systems. Compared with PT symmetric systems that require two different kinds of materials, the proposed negative refraction can be realized with only two identical media. In addition, asymmetric excitation with bidirectional total transmission is observed in our PICM system. Therefore, a new way to realize negative ref…
We develop an approach to use nanostructured plasmonic materials as a non-magnetic negative-refractive index system at optical and near-infrared frequencies. In contrast to conventional negative refraction materials, our design does not require periodicity and thus is highly tolerant to fabrication defects. Moreover, since the proposed materials are intrinsically non-magnetic, their performance is not limited to proximity of a resonance so that the resulting structure has relatively low loss. We develop the analytical description of the relevant electromagnetic phenomena and justify our analyt…
In this work is elaborated the wording of Fermat`s principle for electromagnetic waves spreading in materials with negative index of refractions (MNR). The recent experiments with such material has confirmed their main characteristics, predicted earlier. It is shown that for MNR not applicable wording of Fermat`s principle through minimum (or extremum) of time of spreading the wave between two points. The correct wording for this case is a wording through extremum of total optical length for way between two points moreover optical length at passing of wave through MNR is taken negative. In pap…
This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, $ω(θ_\mathbf{k})$ ($θ_\mathbf{k}$: phase velocity direction, associated with the wave vector, $\mathbf{k}$), with the equally important impedance relation, $η(θ_\mathbf{S})$ ($θ_\mathbf{S}$: group velocity direction, associated with the Poynting vector, $\mathbf{S}$). Second, it explains the interluminal-regime phenomenon of double-downstream wave transmission across a stationary interface between a regular me…
Peculiarities of the defect modes of cholesteric liquid crystals (CLCs) with an isotropic/anisotropic defect inside are investigated. The influence of the defect layer thickness and its anisotropy of refraction, the influence of the system thickness and of the defect layer position in the system, as well as the influence of the dielectric borders on the defect modes is investigated. It is shown that it is possible to change reflection at the defect modes in wide intervals and change the defect mode wavelength, by tuning the defect location and its thickness. Such a system possesses transmissio…
The widely-accepted theoretical treatment of the electromagnetic boundary problem of evanescent wave transfer at an interface between a normal medium of n=1 and an ideal negative index medium of n=-1 neglects the non-zero induced surface current and charge densities at the interface and is self-inconsistent. We re-solve the electromagnetic boundary problem by taking into account the non-zero induced surface current and charge densities that have been neglected so far by others. We give the exact induced surface current and charge distributions for this special case and solve the refracted and …
Crystal quartz is a well-known anisotropic medium with optically active phonons in the THz region where hyperbolic phonon-polaritons can be excited. Here, we use this material to illustrate how the behavior of bulk and surface hyperbolic polaritons can be drastically modified by changing the orientation of the crystal's anisotropy axis with respect to its surface. We demonstrate, both theoretically and experimentally, phenomena associated with the orientation of hyperbolic media. We show the consequences of slight changes in the crystal's orientation in various ways, from the creation of hyper…
The concept of negative refraction is attracting a lot of attention. The initial ideas and the misconceptions that have arisen are discussed in sufficient detail to understand the conceptual structure that binds negative refraction to the existence of backward wave and forward wave phenomena. A presentation of the properties of isotropic media supporting backward waves is followed by a discussion of negative phase velocity media, causality, anisotropic crystals and some connections to photonic crystals. The historical background is always coupled to a detailed presentation of all the issues. T…
The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size, with an enhanced rate $ξ_γ(W)^{-1}=ξ_0(W)^{-1}+ξ_γ (0)^{-1}$, where $ξ_0(W)$ is the localization length of the equivalent passive random medium and $ξ_γ(0)$ is the attenuation/amplification length of the corresponding perfect system with a ${\cal PT}$-symmetric refraction index profile. While transmitance processes are reciprocal to left and right incident wav…
Space-time (ST) wave packets are a class of pulsed optical beams whose spatio-temporal spectral structure results in propagation invariance, tunable group velocity, and fascinating refractive phenomena. Here, we investigate the refraction of ST wave packets at a planar interface between two dispersive, homogeneous, isotropic media. We formulate a new refractive invariant for ST wave packets in this configuration, from which we obtain a law of refraction that determines the change in their group velocity across the interface. We verify this new refraction law in ZnSe and CdSe, both of which man…
This is the second of a series of papers devoted to develop a microscopical approach to the dipole emission process and its relation to coherent transport in random media. In this Letter, we deduce a relation between the transverse decay rate of an emitter in a virtual cavity and the complex refraction index of the host medium. We argue on the possibility of a criterion for inhibition/enhancement of spontaneous emission in function of the transition frequency and the correlation length of the host scatterers. In addition, we study the radiative/non-radiative nature of the net power emission th…
We investigate the reflection and refraction behaviors of electromagnetic waves at the interface between an isotropic material and the anisotropic medium with a unique dispersion relation. We show that the refraction angle of whether phase or energy flow for $E$-polarized waves is opposite to that for $H$-polarized waves, though the dispersion relations for $E$- and $H$-polarized waves are the same in such anisotropic media. For a certain polarized wave the refraction behaviors of wave vector and energy flow are also significantly different. It is found that waves exhibit different propagation…
The four wavenumbers associated with planewave propagation in a Faraday chiral medium (FCM) with relatively huge magnetoelectric coupling give rise to enhanced possibilities for negative-phase-velocity propagation and therefore negative refraction. They can also give rise to the phenomenon of negative reflection. In particular, for a nondissipative example, we deduced that an incident plane wave with positive/negative phase velocity can result in a negatively reflected plane wave with negative/positive phase velocity, as well as a positively reflected plane wave with positive/negative phase ve…
