Lossless Medium Research Articles

Time domain analysis of impulse electromagnetic field at the interface of two media

Background. Ultrashort pulses of electromagnetic field are widely used in construction, archeology and demining, etc., by constructing effective georadars of the underlying surface, but theoretical study of physical processes of irradiation of medium is had a limit range of simplified model problems, usually in frequency domain. Therefore, the solutions of the problems of penetration of a pulsed wave with arbitrary time dependence into material medium are of special importance for understanding the possibilities and limitations of georadar’s study. Objectives. To obtain the analytical solution in time domain of the problems of reflection and propagation of a impulse electromagnetic wave through the interface of two media, which is the first model approximation to the description of physical processes that occur during operation of pulsed ultrawideband radar. Materials and methods. The problem of irradiation by nonstationary electric field of a lossless medium with a given permittivity is solved analytically by application of evolutionary approach. It consists in solving of Cauchy’s problem for the second-order partial differential equation Klein–Gordon type with respect to evolutionary coefficients. The components of the electromagnetic field in free space are found by integration by spectral parameters and summation by angular modes with appropriate combinations of basis functions. Results. Cauchy’s problems for differential equations that describe the behavior of reflected and refracted waves are solved. The electrical transverse components of the reflected and refracted waves as a function of time on the longitudinal axis were found for the case of irradiation with the step-like time dependence. Graphs of dependence of electric components on time and coordinates are plotted and analyzed. Conclusion. The phenomenon of an electromagnetic missiles in the medium that was irradiated by a pulsed electromagnetic wave of ultrashort duration was demonstrated for the first time. The obtained results can be generalized for the case of an arbitrary impulse by the Duhamel’s integral method. In addition, the electric field for observation point that do not lie on the longitudinal axis can be considered. An even more interesting continuation of the researches in terms of energy analysis is the study of the behavior of longitudinal electric and transverse magnetic components.

Broadband microwave absorber composed of sandwich structure with a lossless medium as the intermediate layer

A broadband microwave absorber with a sandwich structure has been designed, creatively taking lossless medium (paraffin or air) as the intermediate layer. The paraffin layer effectively adjusted the impedance of the absorber, especially at the high-frequency region, hence observably raising the upper limit of the effective absorption region from 14.5 GHz to 18 GHz. As a result, the effective absorption bandwidth (EAB, reflection loss less than −10 dB) is broadened to 10.1 GHz, covering the entire Ku band and the entire X band, with a total thickness of only 2.5 mm, among which the paraffin intermediate layer has a thickness of 0.8 mm. Based on Maxwell's equations, normalized Poynting vector and loss analysis are given, which reveals the paraffin layer can enhance the total loss, though paraffin is lossless. In addition, the intermediate paraffin layer can also be replaced with air or even vacuum, providing a new perspective for the design of a high-performance absorber with lighter weight.

Temporal Parity-Time Symmetry for Extreme Energy Transformations.

Temporal interfaces introduced by abrupt switching of the constitutive parameters of unbounded media enable unusual wave phenomena. So far, their explorations have been mostly limited to lossless media. Yet, non-Hermitian phenomena leveraging material loss and gain, and their balanced combination in parity-time (PT)-symmetric systems, have been opening new vistas in photonics. Here, we unveil the role that temporal interfaces offer in non-Hermitian physics, introducing the dual of PT symmetry for temporal boundaries. Our findings reveal unexplored interference mechanisms enabling extreme energy manipulation, and open new scenarios for time-switched metamaterials, connecting them with the broad opportunities offered by non-Hermitian phenomena.

Achieving geometrical enhancement of fields in chiral nanoplasmonics using fractional calculus

In this paper, an analytical approach has been developed for electromagnetic field enhancement in fractal nanostructure under the quasi-static limit. A metallic fractal embedded in an unbounded, isotropic, and lossless chiral medium has been treated under this approach. In addition, the field enhancement is also noted by imposing surface plasmon resonance condition. To achieve the desired objective, Maxwell divergence equations are considered and written in an appropriate form by mean of fractional calculus.

Optical theorems and symmetry relations in scattering problems.

A generalized form of the optical theorem (GOT), equivalent to the energy conservation law, is derived for an absorbing scatterer in a homogeneous lossless medium. The derivation is based on the symmetry of the scatterer's internal parameters, associated with the separation of the corresponding operators into conservative and dissipative components. It leads to the GOT as a constraint on the Green's function, while the conventional optical theorem follows as a specific case of the GOT.

Interaction of circularly polarized light with an absorptive electromagnetic conductor sphere – Radiation force and spin torque

The concept of a perfect electromagnetic conductor (PEMC) material, which is a class of a magneto-electric metamaterial, has been recently examined in the context of the optical radiation force theory [J. Quant. Spectr. Rad. Transfer, 233 (2019) 21–28; ibid 256 (2020) 107280], with particular emphasis on the rotary polarization effect and the contribution of the cross-polarized waves to the transfer of linear momentum, assuming an illumination of linearly-polarized plane progressive waves. The present investigation shows that additional cross-interference factors, which cannot be ignored, contribute to the time-averaged optical radiation force exerted on an absorptive electromagnetic conductor (AEMC) sphere when the incident field becomes circularly-polarized. Moreover, the analysis is extended to investigate the co-polarized, cross-polarized and cross-interference components of the time-averaged optical spin radiation torque. The multipole series expansion method in spherical coordinates is utilized to derive exact mathematical partial-wave series for the co-polarized, cross-polarized and cross-interference components of the radiation force and torque based on the integration of Maxwell’s radiation stress tensor and its moment over a spherical surface of large radius enclosing the sphere suspended in a lossless medium of wave propagation. Numerical results for the radiation force and spin torque efficiencies and their corresponding co-polarized, cross-polarized and cross-interference components illustrate the analysis with emphasis on the size parameter of the sphere ka, its electromagnetic admittance M as well as its imaginary part amounting to absorption. The computations are of importance from the standpoint of the fundamentals of the linear and angular momenta of circularly-polarized electromagnetic waves transferred to an AEMC and related applications in optical tweezers and particle manipulation of objects exhibiting circular dichroism.

Sophisticated Electromagnetic Scattering Solver Based on Deep Learning

In this paper, a deep learning (DL) framework is proposed to predict the scattering field, emerging superior efficiency without sacrificing accuracy. 2D and 3D scatterers in the scheme can be either lossless medium or metal. To achieve precise approximation, medium-scale data sets are sufficient in training the proposed model. As a result, the fully trained framework can realize three orders of magnitude faster than the conventional FDFD solver. Furthermore, our model also exhibits robust generalization ability in forecasting the field scattered by utterly distant from the training data set. We believe this work offers great potential for applications pertaining to EM forward problems.

Generalized Optical Theorem and Point Sources

A simple derivation of the general form of the optical theorem (GOT) is given for the case of a conservative scatterer in a homogeneous lossless medium, suitable for describing point sources and an observation region close to the scatterer. The presentation is based on the use of the operator approach and scalar wave equation in the limit of vanishingly small absorption. This approach does not require asymptotic estimates of rapidly oscillating integrals, does not use the integration of fluxes, which leads to the loss of information about the energy conservation law, and allows a natural generalization to the case of polarized radiation, as well as more complex multi-part fields. Such GOT generalizes the results known in the mathematical literature for models to the case of any conservative (real) scattering potential and arbitrary sources.

Natural Mode Series Expansion of Transient Transmission Field Through an N-Layer Structure

Time-domain (early- and late-time) transmission response of an $N$ -layer composite structure has been analytically investigated using contour integration for uniform plane waves with perpendicular and parallel polarizations. It has been shown that whereas the late-time transmission response of an $N$ -layer structure is a sum of damped sinusoids provided that it is terminated in a lossless medium (e.g., air medium), its early-time response can be represented as the summation of individual subregional responses, which can be expressed by natural series if any subregion is surrounded by lossless media (assuming that the last layer is lossless). Numerical examples are presented to investigate the early- and late-time transmission responses, and thus validate the results obtained from contour integration, of transparent $N$ -layer composite structures for perpendicular and parallel polarization cases.

Contraction operator transformation for the complex heterogeneous Helmholtz equation

An efficient solution of the three-dimensional Helmholtz equation is known to be crucial in many applications, especially geophysics. In this paper, we present and test two preconditioning approaches for the discrete problem resulting from the second order finite-difference discretization of this equation. The first approach combines shifted-Laplacian preconditioner with inversion of a separable matrix, corresponding to the horizontally-layered velocity model, using fast Fourier based transforms. The second approach is novel and involves a special transformation resulting in a preconditioner with a contraction operator (CO preconditioner). The two approaches have near the same arithmetical complexity; however, the second approach, developed in this paper, provides a faster convergence of an iterative solver as illustrated by numerical experiments and analysis of the spectral properties of the preconditioned matrices. Our numerical experiments involve parallel modeling of highly heterogeneous lossy and lossless media at different frequencies. We show that the CO-based solver can tackle problems with hundreds of millions of unknowns on a conventional cluster node. The CO preconditioned solver demonstrates a very moderate increase of iteration count with the frequency. We have conducted a comparison of the performance of the developed method versus open-source parallel sweeping preconditioner. The results indicate that, the CO solver is several times faster with respect to the wall-clock time and consumes substantially less memory than the code based on the sweeping preconditioner at least in the example we tested.

Surface beams resistant to diffraction and attenuation and structured at the millimeter scale

The construction of millimeter-structured surface beams by superimposing scalar Bessel beams has proven to be a powerful technique for creating visual two-dimensional (2D) images in lossless media. In the present paper, we show that surface frozen waves can indeed be designed even in media having non-zero extinction ratios. Examples are provided for specific surface intensity patterns, revealing that our proposed solutions are promising candidates for a wide range of applications encompassing optical trapping displays, 2D and three-dimensional (3D) imaging and printing, nanochannel ablation in glass, optical trapping and manipulation of micro-sized particles and atoms, and so on.

Study of polarizability of an electrically radially uni-axial chiral sphere with dispersive chiral coating in chiral medium

Study of the polarizability response of a nano-size spherical geometry is presented in this manuscript. The spherical geometry consists of an electrically radially uni-axial chiral sphere with dispersive chiral coating and is placed in an unbounded loss-less isotropic chiral medium. As the sphere is electrically radially anisotropic hence only permittivity is taken as a dyadic function and dispersion characteristics of the coating are incorporated through the Lorentz-Drude model. Field expressions and hence the polarizability response is studied under the quasi-static approximation. Limiting case and potential plot are also studied for the validation of the derived expressions and numerical results. To verify the impact of the host medium polarizability plots for chiral and free space host medium are also given whereas to study the impact of the material losses on polarizability, plots for the lossy and loss-less cases are also discussed.

The tailored saturated-unsaturateddefect modes obtained by nonlinear threshold light in graphene-based hyperbolicmetamaterial

The tailored saturated-unsaturated defect modes are realized in the proposed graphene-based hyperbolic metamaterials (HMs) in the mid-infrared and near-infrared bands by using the threshold light. In the case of saturated absorption, graphene is identified as a transparent and lossless medium. The effects of the incident angle, the number of periods, and the chemical potential of graphene are also taken into consideration. The computed results show that the greater saturated defect mode (SDM) can be observed at a smaller incident angle and a larger period. The unsaturated defect mode (USDM) cannot be affected by the incident angle while it can be controlled by the chemical potential. In addition, two novel threshold lights (0.2 MW/cm2 and 60 MW/cm2) producing bistable graphene absorption are analyzed by adopting nonlinear Kerr (NLK) materials. These results can be applied to nonlinear optical switches and logic devices.

Maximal transmission of acoustic energy flux in inhomogeneous waveguides and robustness analyses

Inhomogeneity in a medium will cause wave scattering, influencing the transfer of energy or information. However, it is possible to prepare a prescribed wavefront which propagates through an inhomogeneous medium with unity flux-transmittance. This phenomenon is first predicted in the context of mesoscopic electron transport. Another remarkable phenomenon is the bimodal distribution of the transmission singular values, which implies that in a lossless medium the full solution space in the scattering region can be spanned only by open channels, which are completely transmitted, and closed channels, which are completely reflected. In mesoscopic physics, random-matrix theory is usually utilized to deal with the statistical properties of matrices with randomly distributed entries since the medium is assumed to be randomly fluctuating. In this paper, we propose a method of systematically studying the maximal flux transmission through an inhomogeneous acoustic waveguide. The model is chosen to be a waveguide with varying cross-sections and a penetrable scatterer, and the method is based on the coupled mode theory. This method can be used to analyze the frequency of nearly complete transmission for an arbitrary incident wave, and to analyze the incident wave that is able to generate the maximal flux-transmittance for any given frequency. We construct the transmission matrix and the horizontal wavenumber matrix by using orthonormal basis functions, and give the expression of flux-transmittance. Then the optimal incident wave which brings the maximal transmittance through the scattering region is derived based on singular value decomposition. The optimal incident waves are independent of the evanescent modes since evanescent modes do not transfer any energy. But the evanescent modes can give rise to the multivaluedness of wave solutions with complete flux transmission. Considering the fact that acoustic waveguides can naturally resist the influence of highly oscillating perturbations since most of them correspond to evanescent modes), the maximal flux transmission in waveguide is thus found to be highly robust. Especially at a specific frequency, the complete wave transmission has perfect robustness. This proposed method can be generalized to any other frequency, to other types of scatterers, or to other kinds of boundary conditions, and can provide guidance in designing acoustic metamaterials and in highly efficient communication.

Discrete spectrum radiation from a charged particle moving in a medium with Maxwell's fish-eye refraction-index profile

Radiation from a charged particle moving in a medium with Maxwell fish eye refraction index profile is considered. It is shown that the radiation spectrum has a discrete character. The main emitted wavelength is proportional to the refractive profiles radius and has a dipole character in a regular medium. Cherenkov like threshold velocity is established. A cardinal rearrangement of angular distribution in a lossless medium is predicted. This behavior is caused by the total internal reflection in a lossless medium as opposed to photons attenuated total reflection in the regular medium. Lossless medium ensures that both directed and monochromatic emission can serve as a light source in the corresponding regions.

Broadband Electromagnetic Wave Tunneling with Transmuted Material Singularity.

Subwavelength channels filled with near-zero-index (NZI) media can realize extraordinary optical functionalities, for example, tunneling electromagnetic wave without reflections, but usually confined in a narrow wavelength band due to the material singularity (refractive index n≈0), which seriously limits the practical potentials. In this Letter, we show this limit can be fundamentally overcome by an alternative, named near-zero-index-featured (NZIF) structure, with the singularity transmuted via a controlled optical conformal mapping, enabling the device implementation with nonmagnetic normal dielectrics (i.e., relative permittivity >1). Their equivalence is strictly examined through a subwavelength tunneling waveguide. Classic wave tunneling features in a broad frequency range are revealed in various confined geometries. These properties are robust against the disturbance of several kinds of structural defects benefited from the infinite effective local wavelength. The broadband and lossless NZIF medium proposed here provides a promising way to pursue the fascinating light controlling functionalities as initially enabled by singular NZI materials.

Numerical evaluation of a fractional calculus model for the spatial impulse response of a circular piston

In lossless media, exact analytical expressions for the spatial impulse response describe the effect of diffraction in the time domain for several specific transducer shapes. At present, no exact analytical expressions are available for lossy media, so numerical evaluation of the spatial impulse response is required. For attenuation that follows a power law, the spatial impulse response is numerically evaluated by superposing contributions from time-domain Green's functions for the Power Law Wave Equation, which is a fractional calculus model for power law attenuation. To demonstrate examples of lossy spatial impulse responses obtained with these time-domain Green's functions, which are expressed in terms of maximally skewed stable densities, numerical results are computed for a circular transducer using different attenuation values and compared with the analytical result for a lossless medium. The results show that the numerically computed spatial impulse response for a lossy medium converges to the analytical result evaluated in a lossless medium as the value of the attenuation constant decreases. As the attenuation constant grows larger, the temporal extent increases, and the sharp edges are replaced by increasingly smooth curves, as observed in numerical evaluations of the lossy spatial impulse response evaluated in multiple locations.

Nonlinear ultrasound simulation in an axisymmetric coordinate system using a k-space pseudospectral method.

A full-wave model for nonlinear ultrasound propagation through a heterogeneous and absorbing medium in an axisymmetric coordinate system is developed. The model equations are solved using a nonstandard or k-space pseudospectral time domain method. Spatial gradients in the axial direction are calculated using the Fourier collocation spectral method, and spatial gradients in the radial direction are calculated using discrete trigonometric transforms. Time integration is performed using a k-space corrected finite difference scheme. This scheme is exact for plane waves propagating linearly in the axial direction in a homogeneous and lossless medium and significantly reduces numerical dispersion in the more general case. The implementation of the model is described, and performance benchmarks are given for a range of grid sizes. The model is validated by comparison with several analytical solutions. This includes one-dimensional absorption and nonlinearity, the pressure field generated by plane-piston and bowl transducers, and the scattering of a plane wave by a sphere. The general utility of the model is then demonstrated by simulating nonlinear transcranial ultrasound using a simplified head model.

An extremely ultrathin flexible Huygens’s transformer

The current study aims to present the physical perception of a meta-surface energy harvester’s (MEH’s) design based on space-time physics of a traveling wave. Regarding the relation between the wave-velocity and field-impedance, the balance condition in Huygens’s meta-atoms is provided. Accordingly, it was demonstrated that MEH behaves as a transformer at far-field. It was observed that the location of the metallic-via is mimicked by the number of loop coils in the secondary of the transformer in the unit-cell. In addition, the impedance matching between the wave impedance in a lossless medium and MEH’s load was to be tuned by adjusting the size parameters of the unit-cell at a desired resonance frequency. For this purpose, the present study developed a simple design framework to achieve the resonance frequency at a more optimum pace based on surrogate modeling. The theoretical analyses are validated by the results of full-wave and circuit simulations. Finally, a recently developed flexible MEH was further extended to a multi-polarization structure using more compact cells. The fabricated flexible MEH has 10 × 10 number of deep subwavelength thick cells (≈0.004λ0), while traditional MEH was basically designed only to fit on the planar surface. The new design paves the way for the multi-polarized MEH to wrap around the cylindrical surface as a 2D-isotropic MEH. The results of the data analyses show that the simulation and experimental results enjoy an acceptable agreement.

Effective Electrodynamics Theory for the Hyperbolic Metamaterial Consisting of Metal–Dielectric Layers

In this work, we study the dynamical behaviors of the electromagnetic fields and material responses in the hyperbolic metamaterial consisting of periodically arranged metallic and dielectric layers. The thickness of each unit cell is assumed to be much smaller than the wavelength of the electromagnetic waves, so the effective medium concept can be applied. When electromagnetic (EM) fields are present, the responses of the medium in the directions parallel to and perpendicular to the layers are similar to those of Drude and Lorentz media, respectively. We derive the time-dependent energy density of the EM fields and the power loss in the effective medium based on Poynting theorem and the dynamical equations of the polarization field. The time-averaged energy density for harmonic fields was obtained by averaging the energy density in one period, and it reduces to the standard result for the lossless dispersive medium when we turn off the loss. A numerical example is given to reveal the general characteristics of the direction-dependent energy storage capacity of the medium. We also show that the Lagrangian density of the system can be constructed. The Euler–Lagrange equations yield the correct dynamical equations of the electromagnetic fields and the polarization field in the medium. The canonical momentum conjugates to every dynamical field can be derived from the Lagrangian density via differentiation or variation with respect to that field. We apply Legendre transformation to this system and find that the resultant Hamiltonian density is identical to the energy density up to an irrelevant divergence term. This coincidence implies the correctness of the energy density formula we obtained before. We also give a brief discussion about the Hamiltonian dynamics description of the system. The Lagrangian description and Hamiltonian formulation presented in this paper can be further developed for studying the elementary excitations or quasiparticles in other hyperbolic metamaterials.