Oblique Incident Plane Wave Research Articles

New scheme for introducing an oblique incidence plane wave to layered media in finite-difference time-domain

In the application of two-dimensional finite-difference time-domain (2D-FDTD) method to the analysis of scattering by an object embedded in layered media，the obliquely incident wave along the total field-scattered field (TF-SF) contains the incidence pulse and the reflected and multiple-reflected wave，which can not be introduced by use of the traditional method. To solve this problem，a hybrid scheme using different ways to treat the four TF-SF boundaries is presented. The modified 1D-FDTD including oblique incidence angle is used to treat the longitudinal side boundaries，which can produce the reflected and multiple-reflected wave to layered interface automatically. The longitudinal side boundaries are extended downwards，such that the TF-SF lower boundary is located in the perfectly matched layer (PML) completely，thus the transmission wave and scattered wave are both outward-going waves in the lowest PML layer，and are absorbed by PML. The TF-SF upper boundary is located in free space; the incidence wave along it is in fact a properly time-delayed duplication of the waveform at the corner of TF-SF upper longitudinal boundary. The computational results show the reliability and applicability of the presented hybrid scheme.

DESIGN AND OPTIMIZATION OF PLANAR MULTILAYER ANTIREFLECTION METAMATERIAL COATINGS AT KU BAND UNDER CIRCULARLY POLARIZED OBLIQUE PLANE WAVE INCIDENCE

In this paper, planar multilayered antireflection coatings composed of isotropic and dispersive common materials and metamaterials (DPS, DNG, ENG, and MNG) are designed and optimized at Ku band under circularly polarized oblique plane wave incidence by a full-wave method and combination of the method of least squares (MLS), genetic algorithm (GA) and conjugate gradients (CG). The body on which the coating is applied may be selected as PEC, plexiglas, or any other material. As a result a new class of radar absorbing materials (RAM) are obtained, which may be effectively used for antireflection coatings. Furthermore, guidelines are presented for the selection of correct signs for the real and imaginary parts of propagation constant k and intrinsic impedance η.

Mechanically Tunable Frequency Selective Surface with Square-Loop-Slot Elements

The mechanically tunable characteristics of double-layer FSS (frequency selective surface) with square-loop slot elements is studied, under normal incidence and 45° oblique incidence of plane wave with TE and TM polarization. The simulation and measurement results show that FSS has good stability for different incidence angles; the actual tunable range covers 1.90∼3.20 GHz, corresponding to 54.17% shift of resonant frequency for 2.40 GHz in designing; this method is easy realization and good tunable regularity; it is low cost with potential wider applications.

Validation of Modal/MoM in Shielding Effectiveness Studies of Rectangular Enclosures With Apertures

This paper discusses the validation of Modal/method of moments (MoM) including cases when the apertures are made as big as the wall of the enclosure (equivalent to having one side of the cavity open). The validation is done using field computations involving bodies of arbitrary shape (FEKO), a commercially available code. The results show that Modal/MoM predicts the results close to the analytical results of Robinson et al. Electron. Lett., 32 (17), 1996; Robinson et al., IEEE Trans. Electromagn. Compat., 40 (3), 240-247, 1998 for single-aperture cases and for most double-aperture cases. Also, for the cases of considering oblique incident plane waves, through validation, it has been found that Modal/MoM can predict the shielding effectiveness close to measured results for smaller angles and not for larger angles of incidence due to the edge effects. In this work, the shielding effectiveness is calculated at only one point, the center of the cavity assuming it to be the worst case. This work discovers the limitation of Modal/MoM for certain applications.

Optimization of the Method of Auxiliary Sources (MAS) for Scattering by an Infinite Cylinder Under Oblique Incidence

ABSTRACT This paper presents a rigorous accuracy analysis of the method of auxiliary sources (MAS) for the problem of oblique incidence plane wave scattering by a perfectly conducting, infinite circular cylinder. For this particular scattering geometry, it is shown that the MAS matrix is inverted analytically, via eigenvalue analysis, and an exact mathematical expression for the discretization error is derived. Furthermore, the computational error, resulting from numerical matrix inversion, is calculated and compared to the analytical one, showing perfect fit for a wide range of the auxiliary sources' locations. The irregular behavior of the computational error for small values of the auxiliary sources' radii is explained by the corresponding high values of the linear system's condition number. It is also demonstrated that specific source locations, associated with the characteristic eigenvalues of the scattering problem, should be avoided, because then both computational and analytical error increase very abruptly. The dependence of the computational and analytical error on the angle of incidence is thoroughly investigated. Finally, the optimal location of the auxiliary sources is determined on the grounds of error minimization.

Analysis of hard surfaces of cylindrical structures of arbitrarily shaped cross section using asymptotic boundary conditions

The surface equivalence principle is used to formulate the problem of infinitely long cylindrical structures of arbitrary cross section and loaded with metallic strips. The strips are tilted by an angle with respect to the cross section plane. Special cases are considered when the strips are directed along or transverse to the cylinder axis. The excitation is an oblique plane wave incident with arbitrary polarization. The asymptotic strip boundary condition (ASBC) is used to simplify the problem. The surface integral equations are solved using the method of moments. The numerical solution is verified with the series solutions of the circular cylinders loaded with helical strips. Several applications of hard surfaces are presented for structures loaded with tilted strips such as the struts loaded with tilted strips to reduce the equivalent blockage width of the struts and make it polarization independent.

Conical diffraction by periodic structures: Variation of interfaces and gradient formulas

AbstractThis paper studies the dependence of solutions to conical diffraction problems upon geometric parameters of non–smooth profiles and interfaces between different materials of diffractive gratings. This problem arises in the design of those optical devices to diffract time–harmonic oblique incident plane waves to a specified far–field pattern. We prove the stability of solutions and give analytic formulas for the derivatives of reflection and transmission coefficients with respect to Lipschitz perturbations of interfaces. These derivatives are expressible as contour integrals involving the direct and adjoint solutions of conical diffraction problems.

Analytical model for regular dense arrays of planar dipole scatterers — Abstract

An analytical boundary condition for modeling the electromagnetic properties of planar regular dense arrays of dipole particles for oblique incidence of plane waves is developed. The regular array is assumed to be dense which means that the dipole particles are close to each other. The interaction between the dipole particles is taken into account by interaction constant. The expression for the interaction constant is written in analytical form and is used for developing a transmission‐line model for arrays of planar dipole scatterers. The regular dense array is modeled as a shunt impedance which is different for TM and TE polarizations.

Analytical Model for Regular Dense Arrays of Planar Dipole Scatterers

An analytical boundary condition for modeling the electromagnetic properties of planar regular dense arrays of dipole particles for oblique incidence of plane waves is developed. The regular array is assumed to be dense which means that the dipole particles are close to each other. The interaction between the dipole particles is taken into account by interaction constant. The expression for the interaction constant is written in analytical form and is used for developing a transmission-line model for arrays of planar dipole scatterers. The regular dense array is modeled as a shunt impedance which is different for TM and TE polarizations.

Electromagnetic analysis of axially symmetric diffractive optical elements illuminated by oblique incident plane waves.

We present an analysis of axially symmetric diffractive optical elements illuminated by off-axis or oblique incident plane waves. The analysis is performed with a finite-difference time-domain method that has been formulated to exploit axial symmetry yet accommodate off-axis illumination. This approach is compared with a full three-dimensional formulation and is found to be more efficient in both memory requirements and computational time. Validation and applications of this method are presented.

Scattering from a coated cylindrical shell comparison of ray and exact computations

We discuss sequentially the following: a homogenized shell theory and how it differs from uniform shell theory; high-frequency analysis of the quasi-P and S membrane wave solutions; the application of ray and coupling theory to the coated shell to predict the scattered response for oblique plane wave incidence; and numerical benchmarking against the exact code for thick coated shells. The shell theory is based on composite plate theory, with shell stresses modeled by the Kirchhoff assumption. The ray theory generalizes the theory developed for uniform thin shells, and accounts for the simultaneous P and S supersonic waves, and resulting resonances. The numerical comparisons demonstrate that the ray theory is accurate for undamped coatings, for which the excited resonances are strong. With damping present in the coating two unexpected discrepancies arise in the ray theory predictions. First, the damping of the excited structural waves is underestimated, even for relatively low damping in the coating, on the order of 0.1. At higher damping, e.g. 0.5, the same problem persists and is exacerbated by the degeneration of the background or specular approximation that is used in the asymptotic ray theory model. Refinements of the model to successfully address these is discussed.

Multilayer anisotropic bi-periodic diffraction gratings

The formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73 (1983) 901] treating the diffraction on planar multilayered 1D anisotropic gratings is extended to the diffraction on anisotropic 2D multilayer grating structures bi-periodic in the plane parallel to the interfaces. In addition to the oblique incidence of plane waves, the case of normal incidence is also treated. The goal of the paper is to provide a basis for the formal analysis of 2D patterned multilayers with natural or induced anisotropies. For example, such structures are of interest in the design of new magnetic and magneto-optic devices. In view of the fact that the anisotropies have often a negligible effect on the energy distribution among diffracted modes with respect to the isotropic case the optical response is alternatively expressed in terms of the ellipsometric parameters of diffracted waves. The present analysis represents generalization of the problem of electromagnetic wave interactions in planar multilayers consisting of layers characterized by a general permittivity tensor treated by Yeh [J. Opt. Soc. Am. 69 (1979) 742].

Simple wave solutions for the Maxwell equations in bianisotropic, nonlinear media, with application to oblique incidence

We analyze the propagation of electromagnetic waves in nonlinear, bianisotropic, nondispersive, homogeneous media using simple waves and six-vector formalism. The Maxwell equations are formulated as an eigenvalue problem, whose solutions are equivalent to the characteristic propagation directions. We solve the oblique incidence of plane waves in vacuum on a half space of nonlinear material, and present a method to calculate the reflected and transmitted fields for all angles of incidence and all polarizations of the incident field. Numerical examples for reflection and transmission illustrate the field dependence of the Brewster angle, and the birefringence of an anisotropic material.

EXISTENCE, UNIQUENESS AND REGULARITY FOR SOLUTIONSV OF THE CONICAL DIFFRACTION PROBLEM

This paper is devoted to the analysis of two Helmholtz equations in ℝ2 coupled via quasiperiodic transmission conditions on a set of piecewise smooth interfaces. The solution of this system is quasiperiodic in one direction and satisfies outgoing wave conditions with respect to the other direction. It is shown that Maxwell's equations for the diffraction of a time-harmonic oblique incident plane wave by periodic interfaces can be reduced to problems of this kind. The analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for solutions corresponding to electromagnetic fields with locally finite energy. Special attention is paid to the regularity and leading asymptotics of solutions near the edges of the interface.

Obliquely incident wave coupling on finite-aperture waveguide gratings

The problem of oblique incidence of plane waves and Gaussian beams on finite-aperture gratings (the number of grooves and their length and depth are all finite) in slab waveguides is analyzed by means of a four-wave two-dimensional coupled-mode theory (2D-CMT). This model considers the finite aperture of the gratings and the correct simultaneous interaction among all four relevant waves (TE+,TE-,TM+, and TM-) by means of Bragg diffraction at oblique incidence. The grating’s geometry and boundary conditions are properly accounted for, and the problem is solved numerically by a finite-difference method. Near-field and far-field distributions, as well as reflection and transmission (power) coefficients (as functions of the plane-wave incidence angle), are calculated. The model is compared with the degenerate case of two-wave coupling that considers interaction only between pairs (e.g., TE+↔TE-), and significant differences may be observed. Compatibility and differences between the 2D-CMT and the one-dimensional CMT (grooves with infinite length) are also presented, in addition to the influence of the beam width and the groove length on the emerging waves. The analysis is general and can be performed on many kinds of realistic beams, grating shapes, and applications.

High-Frequency Electromagnetic Currents of Transition Region of an Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

High-Frequency Electromagnetic Currents of Transition Region of an Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

Analysis of electromagnetic scattering by periodic strip grating on a grounded dielectric/magnetic slab for arbitrary plane wave incidence case

A new type of integral equation that is coupled with strip-electric and slot-magnetic currents is applied to the analysis of electromagnetic scattering by a periodic strip grating on a grounded dielectric/magnetic slab for an oblique incident plane wave with arbitrary polarization. In the analysis, the electric and magnetic currents are expanded into a product of a series of cosine functions and a function satisfying the edge condition. Coupled linear equations for the unknown electric and magnetic currents are obtained. From the coupled linear equations, explicit expressions for the reflection coefficients are derived by the use of a single edge-mode expansion. The validity of the method is examined by numerically calculated boundary conditions. A comparison between the calculated results from the present method and a previous method by measured ones shows that the accuracy of the method is excellent. Numerical calculations show that the method converges very rapidly with reasonable accuracy.

Interaction of an Oblique Incident Elastic Wave With a Pair of Surface-Breaking Cracks

In this paper, the authors study a two-dimensional in-plane problem in the context of an oblique incident plane wave in the presence of two (parallel) surface-breaking vertical cracks. An analytical approach is developed that permits reducing the problem to a system of two integral equations with respect to the normal and tangential opening of the crack faces. The system is investigated numerically for a wide range of the frequency parameter. It is shown that with the choice of an appropriate pair of cracks it is possible to arrange the control of the free-surface vibrational amplitude.

Scattering of a horizontally polarized oblique wave by a pair of surface-breaking cracks

Antiplane scattering is studied in the context of an oblique incident plane wave in the presence of two (parallel) vertical cracks. In particular, the influence of these cracks on the oscillation of a free surface for various values of physical and geometrical parameters is investigated. The developed model is solved numerically for a wide range of the frequency parameter. The amplitude of the surface oscillations can be reduced by choosing appropriate values of the geometrical parameters, leading to possible solutions of problems of importance in seismology.

Wave scattering by periodic arrays of breakwaters

Oblique incidence of plane waves upon an infinite array of in-line periodic screens or breakwaters in finite water depth is considered using linear water-wave theory. The number of reflected or transmitted waves is a function of the angle of incidence and the ratio of wavelength to array periodicity. A simple matrix formulation is provided for all the reflection and transmission coefficients arising from a particular set of parameters, using a formulation based either on the unknown velocity through a gap or on the unknown pressure difference across a breakwater screen. Integral properties of functions related to these unknowns form the basis of the matrix structure, the functions themselves satisfying a set of integral equations which are solved using a Galerkin approximation that gives highly accurate approximations with very few terms in the expansion. The problem is extended to consider two identical parallel arrays and it is shown that there exists zeros of both reflection and transmission. Finally, a wide-spacing approximation is derived for two arrays based on the accurate results found from the single array problem, where the two arrays do not have to be identical, but must have the same periodicity.