Electromagnetic Waves In Dielectric Media Research Articles

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations---usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. The resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

An efficient matrix approach for the numerical solutions of electromagnetic wave model based on fractional partial derivative

In this article, we construct an efficient numerical method by combining the matrix and Kronecker multiplication to solve a fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM). We adopted the operational matrix method (OMM) based on Bernoulli and Hermite wavelets for approximating the space and time derivatives. The proposed method transform FPDE into a system of an algebraic equation. For a better understanding of the method, numerical algorithms are also provided for the considered problems. Furthermore, the convergence of approximation and theoretical unconditional stability have been proved with respect to squire integrable norm. Finally, two numerical experiments with different fractional-order derivatives have been performed and compared with the analytical solutions to illustrate the accuracy and efficiency of the method. It is observed that the OMM is simple, easy to implement, yields highly accurate results at a small number of basis functions.

Generation and detection of high-frequency gravitational waves in dielectrics, excited by the intense ultrashort laser pulse

The generation and detection of scalar or pseudoscalar high-frequency gravitational waves in some dielectrics, excited by ultrashort intense laser pulses are proposed. Hidden photons and axion particles are elemental excitations of such gravitational waves. The properties of longitudinal electromagnetic waves in dielectric media have been described from the point of view of photon-hidden photon conversion processes in these crystals. Scalar bound photonic states in dielectric media are analyzed. The experimental schemes for photon-hidden photon conversion with taking part in longitudinal electromagnetic excitations in media have been proposed. Hertz gravitational laboratory experiments with the illumination of the dielectric media by intense ultrashort laser pulses and the “Light Sching Trough Wall” scheme using are analyzed.

Two‐dimensional shifted Legendre polynomial collocation method for electromagnetic waves in dielectric media via almost operational matrices

In this paper, a numerical solution of fractional partial differential equations (FPDEs) for electromagnetic waves in dielectric media will be discussed. For the solution of FPDEs, we developed a numerical collocation method using an algorithm based on two‐dimensional shifted Legendre polynomials approximation, which is proposed for electromagnetic waves in dielectric media. By implementing the partial Riemann–Liouville fractional derivative operators, two‐dimensional shifted Legendre polynomials approximation and its operational matrix along with collocation method are used to convert FPDEs first into weakly singular fractional partial integro‐differential equations and then converted weakly singular fractional partial integro‐differential equations into system of algebraic equation. Some results concerning the convergence analysis and error analysis are obtained. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2017 John Wiley & Sons, Ltd.

Two-dimensional wavelets collocation method for electromagnetic waves in dielectric media

In this article, we deal with a numerical wavelet collocation method (NWCM) using a technique based on two-dimensional wavelets (TDWs) approximation proposed for the fractional partial differential equations (FPDEs) for electromagnetic waves in dielectric media (EWDM). By implementing the Riemann–Liouville fractional derivative, TDWs approximation and its operational matrix along with collocation method are utilized to reduce FPDEs firstly into weakly singular fractional partial integro-differential equations (FPIDEs) and then reduced weakly singular FPIDEs into system of algebraic equation. Using Legendre wavelet approximation (LWA) and Chebyshev wavelet approximation (CWA), we investigated the convergence analysis and error analysis of the proposed problem. Finally, some examples are included for demonstrating the efficiency of the proposed method via LWA and CWA respectively.

Atangana-Baleanu fractional derivative applied to electromagnetic waves in dielectric media

This work presents alternative solutions of the fractional waves in dielectric media using the Atangana–Baleanu fractional operator in Liouville-Caputo and Riemann–Liouville sense, the order considered is for the space-time domain. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. New results are presented and the analytical solutions are given in terms of the multivariate Mittag-Leffler functions preserving the physical units of the system studied. Numerical simulations were performed for different values of fractional order.

Integral equations for the electromagnetic field in dielectrics

We study static the electric field and electromagnetic waves in dielectric media. In contrast to the standard approach, we use, formulate and solve integral equations for the field. We discuss the case of an electrostatic field of a point charge placed inside a dielectric; the integral equation approach allows us to find and interpret the dielectric constant in terms of molecular polarizability. Next we discuss propagation of electromagnetic waves using the same integral equation approach. We derive the dispersion relation and find the reflection and transmission coefficients at the boundary between the vacuum and the dielectric. The present approach supplements the standard approach based on macroscopic Maxwell equations and contributes to better a understanding of some electromagnetic effects.

Universal character of the fractional space-time electromagnetic waves in dielectric media

This work presents an alternative solution for the mathematical analysis of the fractional waves in dielectric media. For the fractional wave equation, the Caputo fractional derivative was considered, the order of the spatial and temporal fractional derivatives are , respectively. In this analysis, we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space and time derivatives into the fractional wave equation. We will consider source free Maxwell equations in isotropic and homogeneous dielectric medium. The general solutions obtained in our research have been expressed in terms of the multivariate Mittag–Leffler functions, these functions depend only on the parameters and preserving the appropriated physical units according to the system studied.

Mass change of dielectric media induced by propagation of electromagnetic waves

It has been experimentally confirmed that an electromagnetic wave carries momentum and thus exerts forces on dielectrics. Combining wave-particle duality with the theory of relativity, it was shown in the present work that the electromagnetic wave also increases the mass of the dielectric medium through which the incident wave propagates. The change in the mass density of the medium, or the mass density of the electromagnetic wave in the medium, was found to be proportional to the energy density of the incident wave. At an absolute temperature T, the mass density of the black body radiation was shown to be proportional to T4. “Weighing” the light wave in a glass fiber provides a novel technique to study the particle nature of electromagnetic waves in dielectric media.

Comment on “Scattering-theory analysis of waveguide-resonator coupling”

We show that the Hermitian Hamiltonian formalism in the paper "Scattering-theory analysis of waveguide-resonator coupling" by Xu [Phys. Rev. E 62, 7389 (2000)] is incompatible with the standard perturbation analysis in a strict sense and hence needs to be used with caution. To improve, a perturbation analysis strictly compatible Hermitian Hamiltonian formalism for modeling the adiabatic time evolution of electromagnetic wave in dielectric medium is outlined. Using a quantum T -matrix based approach, we demonstrate the validity of our Hermitian Hamiltonian formalism and more importantly the effectiveness of the application of quantum formal scattering theory in electromagnetics by exactly rederiving the Rayleigh formula for the total cross section of a nonmagnetic dielectric sphere at the long-wavelength limit.

Local nonlinear electrodynamics

The propagation of electromagnetic waves in dielectric media characterized by the coefficients ε α β = ε α β ( E μ , B μ , ∂ ν E μ , ∂ ν B μ ) and μ α β = μ α β ( E μ , B μ , ∂ ν E μ , ∂ ν B μ ) is examined in the eikonal approximation of electrodynamics. Employing the techniques Hadamard–Papapetrou (HPD) and Spacetime Integration (STI), we derive the dispersion relation, the polarization modes and effective geometry associated to the model.

Fractional integro-differential equations for electromagnetic waves in dielectric media

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We obtain fractional integro-differential equations for electromagnetic waves in a dielectric. The electromagnetic fields in dielectrics demonstrate a fractional power-law relaxation. The fractional integro-differential equations for electromagnetic waves are common to a wide class of dielectric media regardless of the type of physical structure, the chemical composition, or the nature of the polarizing species (dipoles, electrons, or ions).

The discrete spectrum of the periodic Maxwell operator perturbed by a decreasing potential

The propagation of electromagnetic waves in dielectric medium with decreasing perturbations (defects) is studied. We use the Maxwell operator M=∇×p(x)∇× and the perturbed operator Mλ=∇×(p(x)+λq(x))∇× to describe the “background” medium and perturbed medium, respectively, where λ>0 is the coupling constant. Under the assumption that M has a spectral gap G, we prove that a defect can create an eigenvalue of any given fixed value τ∊G for some λ>0, provided that the support of the defect is large enough. We also consider the asymptotic distribution of eigenvalues in the gap and bounds on the number of eigenvalue branches.

Self-consistent schemes in the problem of electromagnetic wave propagation through dielectric media with isolated inhomogeneities

Two main self-consistent schemes (the effective field and effective medium methods) are applied for the calculation of phase velocities and attenuation factors of plane monochromatic electromagnetic waves in dielectric media with random sets of spherical inclusions. The results of the calculations obtained in the frameworks of the methods are investigated and compared in a wide region of volume concentrations of inclusions and frequencies of exciting fields. This analysis together with experimental data given in literature allows to evaluate the region of application of the methods for the solution of the considered problem.

Computer simulation of the linear and nonlinear propagation of electromagnetic waves in dielectric media

We present a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. We construct the model by combining a microscopic model used in the semiclassical approximation for the dielectric media and the particle model developed for the plasma simulations. The model is then used for studying linear and nonlinear wave propagation in a dielectric medium such as an optical fiber. It is shown that the model may be useful for the study of nonlinear wave propagation and harmonic generation in nonlinear dielectric media.

Solitons in a Dielectric Medium under an External Magnetic Field

It is known that the behaviour of electromagnetic waves in dielectric media is affected by the presence of an external magnetic field. The Faraday effect may be a typical example of the influences of the external magnetic field on the electromagnetic waves in dielectric ~edia.l) In the absence of the external magnetic field, nonlinear electromagnetic waves in dielectric media have been extensively investigated so far. In this case, a nonlinear Schrodinger equation for the complex amplitude of the wave has been derived and the propagation of envelope soliton has been shown. 2 ) It seems, however, that in the presence of an external magnetic field the behaviour of nonlinear electromagnetic waves in dielectric media has not been investigated. The purpose of the present paper is to investigate the propagation of nonlinear electromagnetic waves of long wavelength in a dielectric medium along an external magnetic field by means of the reductive perturbation method. 3