Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

Polarization characteristics of an electromagnetic wave scattered from a slightly random surface: +45° polarized incidence

Abstract

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.     

Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement

The present paper deals with the electromagnetic (EM) scattering from a perfectly conductive, random surface by means of the stochastic functional approach and aims to study the backscattering enhancement associated with co-polarized and cross-polarized scattering. The treatment is based on the stochastic functional theory where the random EM field is represented in terms of a Wiener-Hermite functional of the homogeneous Gaussian random surface. To obtain more precise solutions than the previous works (Nakayama J et al 1981 Radio Sci. 16 831-53), we first establish the reciprocal theorem for vector Wiener kernels which describe the stochastic functional representation of the EM field and, using this, we derive the reciprocal relations for the co-polarized and cross-polarized scattering distribution relative to TE and TM polarizations of incident wave. Solutions for the vector Wiener kernels up to the second are obtained so precisely as to satisfy the reciprocal relations and are expressed in terms of generating matrices, so that complex EM scattering processes described by the vector Wiener kernels are given dear physical interpretations. Compact operator representations are introduced to reformulate the hierarchical kernel equations, the mass operator equation and higher-order kernel solutions. It is shown that the second vector Wiener kernel physically describes a 'dressed double-scattering' process, similar to the scalar theory (Ogura H and Takahashi N 1995 Waves Random Media 5 223-42), and that the 'dressed double scattering', which involves anomalous scattering in the intermediate scattering processes, creates the backscattering enhancement in both co- and cross-polarized scattering for both TE and TM wave incidence.     

Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering

Abstract

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the ‘Brewster scattering angle’, which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a ‘quasi-anomalous scattering’ can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.     

Scattering from an anisotropic cylindrical dielectric shell

The electromagnetic scattering from an anisotropic cylindrical dielectric shell is formulated by using the wave functions for anisotropic media and the boundary-value method. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. Numerical results for the effects of various geometrical and electrical parameters on the bistatic radar cross section are presented.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

An alternative solution of the scattering from an anisotropic cylindrical dielectric shell

A method based on the approximate wave functions for anisotropic media and the mode-matching approach is developed to solve the problem of the electromagnetic scattering from an anisotropic cylindrical dielectric shell. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. The validity of this solution is verified by comparing the numerical results with those in literatures and the previous calculations based on the exact wave functions for anisotropic media. Numerical results show the higher computational efficiency of the present method for bounded anisotropic media.     

Scattering by an array of parallel metallic carbon nanotubes

The scattering of electromagnetic wave by an array of parallel metallic single-walled carbon nanotubes is investigated based on the boundary-value method. Electronic excitations over each nanotube surface are modeled as an infinitesimally thin cylindrical layer of the free-electron gas. The scattering cross section of both transverse magnetic （TM） and transverse electric （TE） uniform plane waves by the system at normal incidences is obtained.     

Scattering and diffraction of a plane wave from a randomly rough strip*

Abstract

This paper deals with plane wave scattering and diffraction from a randomly rough strip using a combination of three tools: the perturbation method, the Wiener-Hopf technique and a group-theoretic consideration based on the shift-invariant property of the homogeneous random surface. The D ^a -Fourier transformation associated with the shift invariance is defined instead of the conventional complex Fourier transformation. For a slightly rough case, Wiener-Hopf equations for the zero-, first- and second-order perturbed fields are derived. They are reduced to a common Wiener-Hopf equation, an exact solution of which is obtained formally by means of the Wiener-Hopf technique. Using the inverse D ^a -Fourier transformation, the scattered wavefield is obtained as a stochastic field. When the strip width is large compared with the wavelength, a uniformly asymptotic representation of the scattered far field is obtained by the saddle point method. For a Gaussian roughness spectrum, several numerical results are calculated and illustrated in figures, based on which the characteristics of scattering and diffraction are discussed.     

Scattering from a slightly random, one-dimensional metal surface: 45° linearly polarized incidence, backscattering enhancement and degree of polarization

The scattering of an electromagnetic wave from a slightly random metal surface which supports the surface plasmon mode at optical frequencies is studied theoretically by means of a stochastic functional approach. In order to investigate the Stokes matrix or the state of polarizations, as well as the intensity of the scattered waves, the rough surface is assumed to be one dimensional, and is illuminated by a+45° linearly polarized plane electromagnetic (light) wave whose plane of incidence is perpendicular to the grooves of the surface. The stochastic wave fields are represented in terms of the Wiener-Hermite functionals, and the approximate solutions of the Wiener kernels are obtained for both TM- and TE-polarized components, from which the Stokes matrix elements can be determined. The dressed or perturbed plasmon mode in the presence of surface roughness is obtained by a mass operator involved in the solutions, and the enhanced backscattering closely related to the plasmon mode is studied in connection with the enhanced peak width and the mass operator for the dressed plasmon mode. The Stokes parameters and the degree of polarization are calculated numerically from various polarized components of the incoherent scattering distribution. To clarify the surface plasmon's association with the scattering characteristics, calculations are made for two kinds of random surfaces, a random surface with a centred Gaussian spectrum and a random grating with twin spectral peaks at the plasmon spatial frequency.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Electromagnetic small-scale modeling of composite panels involving periodic arrays of circular fibers

Electromagnetic modeling of composite panels as planar multilayers involving a periodic set of circular cylindrical fibers in each constitutive layer is considered. As a first step, the case of a single layer is studied. Combining multipole method and plane-wave expansion leads to full-wave field representations in all space, yielding in particular reflection and transmission coefficients for TE/TM oblique plane-wave illuminations. Gaussian beams are accounted for via a Fourier transform and numerical quadrature scheme. Comparisons with data available for photonic crystals show the accuracy of the method, while results for fiber-reinforced composites illustrate its effectiveness.     

Scattering of electromagnetic wave from perfect electromagnetic conductor cylinders placed in un-magnetized isotropic plasma medium

The two dimensional analytical formulation of scattering of electromagnetic wave from a perfect electromagnetic conductor (PEMC) cylinder placed in un-magnetized isotropic plasma medium is presented. The extended classical scattering theory is used. The incident wave is taken as linearly polarized wave. The analytical theory is formulated for parallel polarization (TM) and also for perpendicular polarization (TE). The numerical computation results show that backscattering and forward scattering are sensitive to electron density and effective collision frequency of plasma medium. We placed different types of cylinders (PEC, PMC and PEMC) in un-magnetized plasma medium and concluded that stealth capability of plasma increases with the placement of PEMC cylinder in plasma medium.     

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM₀₀ mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM₀₀ mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM₀₀ mode.     

Observation of phase-matched electromagnetic scattering in an active dielectric cylinder

A theoretical investigation of oblique plane-wave electromagnetic scattering in an active dielectric cylinder predicted the existence of anomalous resonances at discrete plane-wave angles of incidence. These resonances may be understood as being due to a leaky-wave phase-matching boundary condition. Experiments were performed with active dielectric cylinders to confirm the existence of discrete resonances. Cross coupling between TE and TM modes was clearly detected for both active and passive scattering. Enhancement of active scattered field intensities was observed in experiments with finite-diameter pump and probe laser beams. Optical pumping of a dye solution was used to provide the gain.     

A Theoretical Model to Explain the Mechanism of Electromagnetic Wave Propagation Along Cylindrical Micelles

A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.     

A Theoretical Model to Explain the Mechanism of Electromagnetic Wave Propagation Along Cylindrical Micelles

A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.     

TM plane wave scattering and diffraction from a randomly rough half-plane: (part II) An evaluation of the diffraction kernel

In a previous paper (part I), it has been shown that a random wavefield from a randomly rough half-plane for a TM plane wave incidence is written in terms of a Wiener-Hermite expansion with three types of Fourier integrals. This paper studies a concrete representation of the random wavefield by an approximate evaluation of such Fourier integrals, and statistical properties of scattering and diffraction. For a Gaussian roughness spectrum, intensities of the coherent wavefield and the first-order incoherent wavefield are calculated and shown in figures. It is then found that the coherent scattering intensity decreases in the illumination side, but is almost invariant in the shadow side. The incoherent scattering intensity spreads widely in the illumination side, and have ripples at near the grazing angle. Moreover, a major peak at near the antispecular direction, and associated ripples appear in the shadow side. The incoherent scattering intensity increases rapidly at near the random half-plane. These new phenomena for the incoherent scattering are caused by couplings between TM guided waves supported by a slightly random surface and edge diffracted waves excited by a plane wave incidence or by free guided waves on a flat plane without any roughness.     

Scattering of an electromagnetic wave from a planar waveguide structure with a slightly 2D random surface

This paper deals with the scattering of an electromagnetic (EM) wave from a waveguide structure with a slightly rough surface. The waveguide structure is a dielectric film on a planar, perfectly conductive surface, and the top of the film is a two-dimensional (2D) homogeneous Gaussian random surface. The treatment is based on the stochastic functional theory where the random EM field is represented in terms of a Wiener - Hermite functional of the random surface. Numerical calculations show that enhanced backscattering and cross-polarization occur, but that no enhanced satellite peak appears for a 2D random surface, in contrast to the case of a 1D surface. The enhanced backscattering is caused by the interference of two double-scattering processes and is attributed to the existence of guided waves in the scattering structure.