Integral Equation Method for Electromagnetic Wave Propagation inStratified Anisotropic Dielectric-Magnetic Materials

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmissioncoefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics, which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.     

Electromagnetic Reflection from Conductive Plate Coated with Nonuniform Plasma

Based on the theories of electromagnetic (EM) field and generalized reflection coefficient, a simple method is put forward to deal with the EM reflection coefficient of conductive plate coated with nonuniform plasma. The plasma slab is modeled by a series of subslabs, in which the electron-number density is assumed to be constant. The overall number density profile across the whole slab follows any practical distribution function. The reflection coefficient is then deduced and its functional dependence on the number density, incident wave frequency, collision frequency, and background magnetic field is discussed.     

Self-collimating photonic crystal polarization beam splitter

We present theoretical and experimental results of a polarization splitter device that consists of a photonic crystal (PhC) slab, which exhibits a large reflection coefficient for TE and a high transmission coefficient for TM polarization. The slab is embedded in a PhC tile operating in the self-collimation mode. Embedding the polarization-discriminating slab in a PhC with identical lattice symmetry suppresses the in-plane diffraction losses at the PhC-non-PhC interface. The optimization of the PhC-non-PhC interface is thereby decoupled from the optimization of the polarizing function. Transmissions as high as 35% for TM- and 30% for TE-polarized light are reported.     

Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry

We study adiabatic transformation in optical waveguides with discrete translational symmetry. We calculate the reflection and transmission coefficient for a structure consisting of a slab waveguide that is adiabatically transformed into a photonic crystal waveguide and then back into a slab waveguide. The calculation yields high transmission over a wide frequency range of the photonic crystal waveguide band and indicates efficient coupling between the slab waveguide and the photonic crystal waveguide. Other applications of adiabatic mode transformation in photonic crystal waveguides and the coupled-resonator optical waveguides are also discussed.     

On Reflection and Transmission of Electromagnetic Waves Obliquely Incident on Relativistically Moving Uniaxial and Isotropic Plasma Slabs

The oscillations in the power reflection coefficient as a function of the normalized slab velocity are shown for electromagnetic waves obliquely incident on a relativistically moving uniaxial plasma slab with an infinitely strong magneto-static field parallel to the slab boundaries. This paper also summarizes and concludes the sequence on the reflection and transmission of electromagnetic waves obliquely incident on relativistically moving uniaxial and isotropic plasma slabs.     

Resonance reflection by the one-dimensional Rosen-Morse potential well in the Gross-Pitaevskii problem

We consider the quantum above-barrier reflection of a particle by the one-dimensional Rosen-Morse potential well, for the nonlinear Schrödinger equation (the Gross-Pitaevskii equation) with a small nonlinearity. The most interesting case is realized in resonances when the reflection coefficient is exactly equal to zero for the linear Schrödinger equation. Then the reflection is determined by only a small nonlinear term in the Gross-Pitaevskii equation. The simple analytic expression is obtained for the reflection coefficient produced only by the nonlinearity. The analytic condition is found for the common action of the potential well and the nonlinearity to produce the zero reflection coefficient. The reflection coefficient is also derived analytically in the vicinity of a resonance shifted by the nonlinearity.     

Effects of metal irises on the guided-mode properties in asymmetrical slab waveguides

The diffraction phenomenon caused by metal transverse irises placed into an asymmetrical slab waveguide is examined by using the integral equation method. We concentrate on the possibility of controlling the radiation characteristics of the structure by changing the irises positions and the slab waveguide asymmetry. The aperture electric-field distribution is expressed in terms of a finite series of Chebyshev polynomials. The dominant TE guided-mode reflection and transmission coefficients, the near-field distribution and the far-field radiation pattern are calculated, while numerical results are presented for several cases of asymmetrical slab waveguides and different irises’ positions.     

On an integral equation arising in the transport of radiation through a slab involving internal reflection

In an earlier contribution to this journal [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)], we derived an integral equation for the transmission of radiation through a slab of finite thickness which incorporated internal reflection at the surfaces. Here we generalise the problem to the case when there is a source on each face and the reflection coefficients are different at each face. We also discuss numerical and analytic solutions of the equation discussed in [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)] when the reflection is governed by the Fresnel conditions. We obtain numerical and graphical results for the reflection and transmission coefficients, the scalar intensity and current and the emergent angular distributions at each face. The incident source is either a mono-directional beam or a smoothly varying distribution which goes from isotropic to a normal beam. Of particular interest is the philosophy of the numerical solution and whether a direct numerical approach is more effective than one involving a more elegant analytical solution using replication and the Hilbert problem. We also develop the solution of this problem using diffusion theory and compare the results with the exact transport solution. An erratum to this article is available at .     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.     

Plasmons and polaritons in a semi-infinite plasma and a plasma slab

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.     

FDTD analysis on the effect of plasma parameters on the reflection coefficient of the electromagnetic wave

In this paper, the dielectric constant of dispersive medium is written as rational polynomial function, and the relationship between D and E is derived in time-domain. It is named shift operator FDTD (SO-FDTD) method. Compared to the analytical solution, the high accuracy and efficiency of this method is verified by calculating the reflection coefficient of the electromagnetic wave through a cold plasma slab. The effect on reflection coefficient is calculated by using the SO-FDTD method. The result shows that some factors effect on reflection coefficient. They are as follows: plasma thickness, electron density, electron distribution and incident frequency. And on most conditions, parabola distribution helps reduce reflection coefficient more effectively than homogeneous distribution.     

The generalization of Fresnel formulae in the soft x-ray region. S polarization

The formula for the S-polarized reflection coefficient of a dielectric slab valid in the soft X-ray region following from the Ewald microscopical model of a dielectric is presented. Further the comparison with the classical Fresnel coefficient is performed and the results of model calculations are demonstrated.     

Zakharov-Shabat inverse problem with meromorphic reflection coefficient

We analyze the Zakharov-Shabat-type inverse problem when the reflection coefficient contains poles in the eigenvalue plane, as an extension of the earlier work by Atkinson in the case of the Schrödinger problem. It is demonstrated that due to the mutual influence of such a pole and the usual bound-state pole, a discontinuous solitary wave profile is generated. Furthermore, we also examine the form of the nonlinear field only due to the pole of the reflection coefficient. A different approach is necessary to convert the GLM equation into a purely differential one for its solution.     

Numerical calculation of the reflection, absorption, andtransmission of microwaves by a nonuniform plasma slab

The reflection, absorption, and transmission of microwaves by a magnetized, steady-state, two-dimensional, nonuniform plasma slab is studied. A discussion on the effect of various plasma parameters on the reflected power, absorbed power, and transmitted power is presented. The nonuniform plasma slab is modeled by a series of subslabs. Even though it is assumed that the number density is constant in each subslab, the overall number density profile across the whole slab follows a parabolic function. The partial reflection coefficient at each subslab boundary is computed along with the absorption at each subslab. The total reflected, absorbed, and transmitted powers are then deduced and their functional dependence on the number density, collision frequency, and angle of propagation is studied     

Effect of reflecting modes on combined heat transfer within an anisotropic scattering slab

Under various interface reflecting modes, different transient thermal responses will occur in the media. Combined radiative-conductive heat transfer is investigated within a participating, anisotropic scattering gray planar slab. The two interfaces of the slab are considered to be diffuse and semitransparent. Using the ray tracing method, an anisotropic scattering radiative transfer model for diffuse reflection at boundaries is set up, and with the help of direct radiative transfer coefficients, corresponding radiative transfer coefficients (RTCs) are deduced. RTCs are used to calculate the radiative source term in energy equation. Transient energy equation is solved by the full implicit control-volume method under the external radiative-convective boundary conditions. The influences of two reflecting modes including both specular reflection and diffuse reflection on transient temperature fields and steady heat flux are examined. According to numerical results obtained in this paper, it is found that there exits great difference in thermal behavior between slabs with diffuse interfaces and that with specular interfaces for slabs with big refractive index.     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.     

垂直入射电磁波在大气压非平衡等离子体层中的传播特性

用数值模拟的方法对大气压非平衡等离子体薄层中，不同的电子密度分布对微波反射、吸收和透射的影响进行了研究。所采用的理论分析方法是分层模型和镶嵌不变原理。计算中考虑了微波在子层间的多次反射和吸收。数值结果表明，对于电磁波的吸收来说，等离子体中具有二次分布的电子密度，其效果要高于线性分布10%左右；而对于反射来说，线性分布效率更高。功率反射系数随波长的增大而增大，功率吸收系数A也不是单调的，当电子密度不变时，A存在一个峰值，随着电磁波波长的增加而增加，达到最大值后，缓慢降低。     

On the dielectric theory of a crystalline slab of point molecules

We discuss the dielectric response of a crystalline slab of point molecules to an incident plane electromagnetic wave. The slab is assumed to be made up of non-polar, polarizable molecules (a) lying at points of a simple cubic lattice and (b) interacting only via the electromagnetic field. Expressions for the dispersion relations, polarisation and electric fields and the transmission coefficient are derived. Conditions under which a point dielectric equation of state holds are obtained. This simple system exhibits three resonances near the transverse optic frequency.     

One-Dimensional Inverse Scattering Problem in Acoustics

We are concerned with the inverse scattering problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteristics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrödinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scattering scheme to construct profiles with certain predetermined reflection and transmission characteristics.     

Boundary problems for polariton propagation in thin layers and quantum wells

Summary We show how to compute the optical functions (reflection and transmission) of a semiconductor thin slab, in the vicinity of nearly degenerate exciton states. Additional boundary conditions are not required in the coherentwave-function approach and multiple-polariton effects are included since Maxwell equations are satisfied. When the slab thickness is comparable to the exciton Bohr radius, centre of mass quantization results. When the slab thickness is smaller than the Bohr radius, we obtain, quantum well polaritons. Numerical examples appropriate to GaAs are given.