Incident Plane Electromagnetic Wave Research Articles

Transmission of a plane electromagnetic wave obliquely incident on a one-dimensional isotropic dielectric medium with an arbitrary refractive index

A new method is suggested for finding the reflection and transmission amplitudes of an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional finite size dielectric medium. Within the transfer matrix method it is shown that the problem reduces to a set of first-order differential equations with the scattering amplitudes being functions of the size of the medium. We also show that when the unknown functions are chosen as a suitable combination of a scattering amplitudes, the problem reduces to a Cauchy problem for the wave equations describing the s- and p-polarized waves.

An integral equation method for the electromagnetic scattering from a scatterer on an absorbing plane

Consider a time-harmonic electromagnetic plane wave incident on a scatterer on a grounded absorbing plane modelized as an infinite impedance plane. In this paper, a new integral representation formula is rigorously derived. Existence and uniqueness of weak solutions for the model problem are also established. The proof of existence is based on an extension of the Hodge decomposition technique to open boundaries. The results reported in this paper form a basis for numerical solutions of the electromagnetic scattering problem from a scatterer on an absorbing plane.

Reflection of a plane electromagnetic wave obliquely incident on a one-dimensional isotropic dielectric medium with an arbitrary refractive index

A new method is suggested for finding the reflection and transmission amplitudes of an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional finite size dielectric medium. Within the transfer matrix method it is shown that the problem reduces to a set of first-order differential equations with the scattering amplitudes being functions of the size of the medium. We also show that when the unknown functions are chosen as a suitable combination of a scattering amplitudes, the problem reduces to a Cauchy problem for the wave equations describing the s- and p-polarized waves.

Scattering of an electromagnetic wave in a one-dimensional medium with an arbitrary index of refraction

A new method of determining the amplitudes of scattering of a plane electromagnetic wave incident at an angle a onto an arbitrary, isotropic, one-dimensionally inhomogeneous medium of finite thickness is developed. It is shown that this problem reduces to a Cauchy problem for a system of two first-order, linear differential equations.

Scattering by a nonhomogeneous object embedded in a periodic structure

Abstract Consider a time-harmonic electromagnetic plane wave incident on a periodic (grating) structure. A nonhomogeneous object is placed inside the periodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has many recent physical and biological applications. In this Note, an integral representation approach is presented to solve the problem. In particular, it is shown that the perturbation due to the object decays exponentially along the direction of periodicity of the structure provided that no surface waves occur. Based on the approach, a general solution method is also discussed.

An integral equation method for the electromagnetic scattering from cavities

Consider a time-harmonic electromagnetic plane wave incident on a cavity in a ground plane. The physical process is modelled by Maxwell's equations. In this paper, integral representations of the solutions to the model problem in both fundamental polarizations are derived and studied. Existence and uniqueness of the solutions for the integral equations are established. The integral equations approach forms a basis for numerical solution of the model problem. In particular, for each fundamental polarization, an integral formulation with Gårding-type estimates is derived. These formulations provide a basis for variational boundary element methods for solving the cavity problem. The Gårding-type estimates imply convergence results for conforming boundary element methods. Copyright © 2000 John Wiley & Sons, Ltd

Influence of the magnetic field on the angular power spectrum of an electromagnetic wave multiply scattered in a turbulent collisional magnetized plasma

We consider a small-amplitude plane electromagnetic wave incident on a semi-infinite layer of a collisional turbulent magnetized plasma. The system of differential equations for the statistical moments of the angular power spectrum of the normal wave is derived in the narrow-angle approximation of radiation transfer theory. The dependence of the center of mass, variance, and asymmetry of the normal-wave spectrum on the distance from the plasma boundary is studied numerically. The results for different refraction angles of the illuminating wave and magnitudes and directions of the external magnetic field are presented. The nonmonotonic dependences of the variance and the third central moment on the distance from the plasma boundary are revealed. These dependences are shown to become more nonmonotonic if the absorption of the scattered waves becomes more isotropic, in particular, if the strength of the external magnetic field increases.

THE GENERAL SOLUTION FOR THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE REFLECTED AND TRANSMITTED FROM THE INTERFACE BETWEEN A STATIONARY DIELECTRIC MEDIUM AND A DIELECTRIC MEDIUM MOVING IN AN ARBITRARY DIRECTION

The problem of reflection and transmission of an electromagnetic plane wave incident from a dielectric medium, reflected and transmitted by another dielectric medium which moving in an arbitrary direction is analyzed in detail. The field vectors of the reflected and transmitted waves, and the reflection and transmission coefficients as well as the energy relations are deduced for the reflected, transmitted and incident waves. In particular, the properties of the force exerted on the moving medium by a plane wave are discussed in comparison with the case in which the incident space is free space and some new phenomenon are suggested for notice.

Analysis of the diffraction from periodic chiral structures

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R 3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed by Maxwell's equations together with the Drude-Born-Fedorov (constitutive) equations. In this Note, it is shown that for all but possibly a discrete set of parameters, there is a unique quasiperiodic weak solution to the diffraction problem. Our proof is based on a Hodge decomposition, a compact imbedding result, as well as the Lax-Milgram Lemma.

Scattering From a Buried Insulated Loop Excited By an Incident Electromagnetic Plane Wave

Rigorous analysis for the electromagnetic fields scattered by a buried insulated loop in a homogeneous earth is presented. The loop is excited by a plane wave incident on the air-earth plane interface. The Fourier components of the circulating current in the loop are expressed in terms of internal and external impedances. The latter are given in integral forms that can be evaluated semi-analytically. It is shown that peaks of induced current in the loop occur at a set of frequencies which depend on the permittivity of the earth's medium. The scattered fields in the air are found to have both co-polar and cross-polar components of comparable magnitudes.

Speckle correlations in the light scattered from weakly rough random metal surfaces

Diagrammatic perturbation theory and computer simulation methods are used to compute the angular intensity correlation function C(q, k|q′,k′)=([I(q|k) - (I(q|k))] × [I(q′|k′) - (I(q′|k′))]) for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. I(q|k) is the squared modulus of the scattering matrix for the system, and q, q′ and k, k′ are the projections on the mean scattering surface of the wavevectors of the scattered and incident light, respectively. Contributions to C include: (a) short-range memory effect and time-reversed memory effect terms, C (1); (b) an additional short-range term of comparable magnitude C (10); (c) a long-range term C (2); (d) an infinite-range term C (3); and (e) a term C (1.5) that along with C (2) displays peaks associated with the excitation of surface plasmon polaritons. The diagrammatic methods are also extended to treat the angular intensity correlation function for the scattering of p to p, p to s, s to p, and s to s polarizations of light from a two-dimensional randomly rough surface. These correlations are again described in terms of C (1), C (10), C (1.5), C (2), and C (3) contributions to C for the two-dimensional surfaces. Short-range memory and time-reversed memory effects are observed in the two-dimensional C (1) correlations, and peaks associated with the excitation of surface polaritons are observed in the two-dimensional C (1.5) and C (2) correlations. Most of the results for the one- and two-dimensional systems are presented for incident electromagnetic plane waves. In addition, results for one-dimensional systems are presented for incident electromagnetic beams of finite width. Some of the results for one-dimensional surfaces are corroborated by means of computer simulation techniques.

Sur un problème inverse pour les équations de Maxwell dans un réseau doublement périodique

Consider an electromagnetic plane wave incident on a doubly periodic structure in ø 3. We prove that the knowledge of the tangential component of the electric field on an elementary section determines the electric permittivity of the grating.

Scattering-matrix propagation algorithm in full-vectorial optics of multilayer grating structures

The scattering of an electromagnetic plane wave incident upon an inhomogeneous multilayer structure is considered in symbolic form. In this framework a scattering-matrix propagation algorithm that decouples recurrences for backward- and forward-scattered wave amplitudes is developed. By construction the scattering-matrix solution procedure is stable against increase of truncation order and depths and number of layers, irrespective of numerical implementation. For grating structures a numerical study using Fouriertransform discretization is performed. In this implementation the convergence issue for TM polarization is recapitulated.

Zero infrared reflectance anomaly in doped silicon lamellar gratings. II. Electric field amplitude distributions across the grating profile

Spatial (in-depth by lateral) electric field amplitude distributions in zero-reflectance binary lamellar gratings in increasingly doped n-Si irradiated by a normally incident TE-polarized plane electromagnetic wave of wavelength 10.6 μm are studied. It is shown that the maximum of electric field amplitude in these gratings is enhanced over the incident field value both for dielectric- and metallic-like cases. For zero-reflectance the maximum of the electric field amplitude is located deep inside the grating line for dielectric-like Si, and deep inside the grating groove for metallic-like Si. In the latter case for non-zero reflectance the maximum of the electric field amplitude is located at the top surface of the grating.

Uniqueness theorems for an inverse problem in a doubly periodic structure

Consider an electromagnetic plane wave incident on a doubly periodic structure in R3. The inverse problem is to determine the shape of the structure from the scattered field. Uniqueness theorems are proved by applying the uniqueness theorem of Cauchy-Kowalewska, by extending Isakov's approach and using a result on local injectivity of maps between finite-dimensional spaces.

DISTRIBUTION OF HEATING POTENTIAL IN AN ECCENTRIC SPHERES MODEL OF A CRANIAL STRUCTURE

We determine the electromagnetic (EM) field in a layered eccentric spheres model of the human head. The model allows for eccentricity between the inner and the outer sets of the concentric spherical layers that simulate brain and skull. Excitation is provided by an incident plane EM wave or by a nearby dipole. The induced EM field is determined through a compact formulation based on indirect mode matching. Numerical results are presented for models adapted to adult and infant heads. Interest is in the RF/microwave absorption characteristics of the head. Conditions for hot spot occurence are investigated too. Applications include EM hyperthermia and cellular phone side‐effects.

Dependent Scattering Properties of Woven Fibrous Insulations for Normal Incidence

The scattering properties of woven fibrous materials are examined in this paper and a simple model is presented to account for the interactions between the scattered radiation from different individual fibers. The case of a normally incident plane electromagnetic wave is considered. Fiber sizes in the Rayleigh regime are considered for developing closed-form solutions. Previous studies in the literature that have addressed the scattering properties of fibrous materials have mostly ignored the effect of constructive or destructive addition of scattered waves from individual fibers, the exception being the case of parallel fibers. The difference in the effects of interference on scattering properties of parallel fibers and of woven fabrics arises from the additional interaction of radiation scattered from mutually perpendicular fibers in the latter case, which further complicates the analysis.

Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization

The problem of scattering by a finite array of infinitely long perfectly conducting circular cylinders located on the surface of a conducting ground plane or partially buried into it due to an obliquely incident plane electromagnetic wave is solved by an exact procedure based on the method of images. The incident field, the reflected field from the ground plane in the absence of cylinders and the scattered fields from different cylinders and their images are expressed in terms of cylindrical vector wavefunctions. The boundary conditions of the vanishing of the tangential electric field on each one of the cylinders are then imposed and this procedure leads to a set of coupled infinite systems of equations for the even and odd mode expansion coefficients of the scattered fields originating from each cylinder. These equations are truncated at a large fixed number and the coefficients are determined by a Gaussian elimination procedure. The scattered far field from the array is then determined by summing contributions from each cylinder. The variation of the scattered field with the different parameters of the array like the electrical radius, spacings between cylinders, height parameter and the angle of incidence is studied in detail. Numerical results are presented for the TM polarization in a three-cylinder configuration for those cylinders whose electrical radius is in the Rayleigh and lower resonance regions.

Modulation of optical radiation by reflection from a film structure under the conditions of excitation of an interface polariton at a metal—semiconductor boundary

A numerical calculation is reported of the reflection coefficient of a plane electromagnetic wave incident on a multilayer asymmetric planar metal—semiconductor structure, which forms a Schottky barrier at the interface. The slope of the modulation characteristic of the reflection coefficient is calculated for the case when the thickness of a depletion layer in the contact region is controlled by an external voltage. This slope is shown to be considerably less than the value reported by other authors. An explanation is given of this discrepancy and methods for increasing the slope of the modulation characteristic are suggested.

Inverse scattering for anisotropic mirror image symmetric media

An inverse medium scattering problem for a homogeneous slab of anisotropic dispersive medium is presented. The inverse problem is to recover the dyadic susceptibility kernel from the dyadic reflection kernels for obliquely incident transient electromagnetic plane waves. A time domain technique, based on wave splitting and invariant imbedding, is used. Mirror images enter into the formalism in a natural way and are therefore discussed. This leads to a simplified problem for a class of mirror image symmetric media. This is solved numerically and the stability of the algorithm is tested using noisy data.