Sergey B. Panin

Elliptical to Linear Polarization Transformation by a Grating on a Chiral Medium

The phenomenon of wave polarization conversion occurs when an electromagnetic wave of elliptical polarization is incident upon a layered structure comprising a strip grating, magnetodielectric layer, chiral layer, and screen. For suitable choice of structural parameters, we discovered regimes where the specularly reflected wave is nearly totally transformed into a linearly polarized wave. Due to the presence of a chiral medium, the corresponding diffraction problem is an intrinsically vectorial problem.It is solved using an analytical regularization procedure based on the Riemann-Hilbert problem method and the obtained solution thus admits an effective numerical treatment.It is shown that a nearly total polarization transformation can be realized for different elliptical polarisation parameters of the incident wave over a rather wide range of incident wave angles. The exhibition of polarization transformation is affected by the resonance properties of the grating-screen volume and by the grating. The purity of polarization conversion may be effectively controlled by careful choice of the structure parameters.

Regularization of the Dirichlet Problem for Laplace's Equation: Surfaces of Revolution

Abstract Based on the idea of analytical regularization, a mathematically rigorous and numerically efficient method to solve the Laplace equation with a Dirichlet boundary condition on an open or closed arbitrarily shaped surface of revolution is described. To improve the convergence of the series for the single-layer density, we extracted and evaluated in an explicit form the singularity of the density at the surface edge. Numerical investigations of canonical structures, such as the open prolate spheroid and the open surface obtained by the rotation of “Pascals Limaçon” or the “Cassini Oval,” exhibit the high accuracy and wide applicability of the method.

Diffraction from a Grating on a Chiral Medium: Application of Analytical Regularization Method

Theoretical results on the electromagnetic wave difiraction from a periodic strip grating placed on a chiral medium are obtained. Analytical Regularization Method based on the solution to the vector Riemann-Hilbert boundary value problem was used to get robust numerical results in the resonant domain, where direct solution methods typically fail. It was shown that in the case of normal incidence of linearly polarized wave the cross-polarized fleld appears in the re∞ected fleld. For elliptically polarized incident wave the difiraction character essentially depends on the polarization direction of the incident wave. These difiraction peculiarities are more pronounced in the resonant domain. In∞uence of the dichroism caused by chiral medium losses is thoroughly studied. The combination of a chiral medium and a grating can be efiectively used for a frequency and polarization selection and for a mode conversion.

Electromagnetic-wave diffraction by a strip grating with a layer of planar-stratified medium

A new solution approach to problem of wave diffraction by an inhomogeneous magnetodielectric layers, whose permittivity and permeability are piecewise continuous functions of a single spatial coordinate, was proposed in [1]. The approach is based on the reduction of the Helmholtz equation to the Riccati differential equation. The original numerical algorithm using a robust recurrence formula was constructed to calculate the solution integrals of the Riccati equation.In this work utilizing the results [1] we develop a high-performance method of the diffraction characteristics calculation for a periodic strip grating lying on an inhomogeneous dielectric layer. The excitation by an obliquely incident plane electromagnetic wave is considered.

Benchmark problems for coupling and scattering with cavities of general form

The need for reliable and accurate prediction of electromagnetic wave coupling to, or scattering from, structures arises in many contexts. General-purpose computational codes have been extensively developed in the last few decades as computing power and resources have become widely available; they have had a significant impact in providing numerical solutions and insight into important coupling and scattering mechanisms. However, their accuracy, particularly for objects of some complexity, incorporating edges and re-entrant structures, can be difficult to assess. The strongly resonant features of cavity-backed apertures can present difficulties in accuracy and computational cost for such general-purpose numerical codes. This chapter presents a method of analytically regularizing the underlying integral equation governing diffraction from the structure, so that a well-conditioned system of equations is obtained. It generalizes the process of analytical regularization applied to cavities of spherical and other canonical shape [2, 3] in which the basic equations are transformed to a second-kind Fredholm matrix equation. It applies to axisymmetric bodies, and examples confirm that the condition number of the resultant system is well controlled even near-resonant frequencies and that solutions of guaranteed accuracy can be efficiently obtained.

Resonant diffraction from a grating on a paramagnetic layer with frequency dispersion

Plane electromagnetic wave diffraction by a strip periodic grating lying on a paramagnetic dispersive layer, the permeability of which possesses negative real part in the microwave band, is solved by Analytical Regularization based on the solution to the Riemann-Hilbert problem. The effect of the resonant transmission accompanied by extremely high absorption is thoroughly studied across the frequency band of the surface waves of the paramagnetic layer placed in the biasing magnetic field. This effect is caused by the surface waves of the layer excited resonantly by the plane incident wave with the diffraction grating present. The resonant frequency is electronically tuned by the biasing magnetic field.

Coupling and scattering from axisymmetric bodies, open and closed: Regularisation methods

An accurate and numerically efficient solution is developed for the scalar wave diffraction problem from an arbitrary shaped body of revolution, either closed or having an aperture. The Dirichlet boundary condition is considered. Based on analytical regularization, the method transforms the standard surface integral equation to an algebraic system that may be truncated to well-conditioned system that produces solutions of prescribed and guaranteed accuracy.

Analytical regularization for diffraction problem: Open shell of revolution

A rigorous and numerically efficient approach for solving the scalar diffraction problem for open arbitrarily shaped shell of revolution is developed, when Dirichletpsilas boundary condition is imposed. The approach is based on the analytical regularization method. Seeking the solution by its integral representation, we determine the singular features of the kernel, and decompose it into the singular canonical part, and a regular remainder. Then, utilizing an appropriate technique, the problem is equivalently reduced to integral equation of the first kind, and then - to an infinite system of linear algebraic equations of the second kind. The last is well conditioned always, and its solution can be efficiently obtained to any pre-specified accuracy.

Diffraction from Arbitrarily Shaped Open Shells of Revolution: Dynamic Case

A mathematically rigorous and numerically efficient approach is developed for solving the Laplace equation with Dirichlet boundary condition on a closed or open arbitrary shaped surface of revolution. Although important in itself, the problem also provides a first step towards the solution of the related wave scattering problem. The generalized method of analytical regularization transforms the problem to a well-conditioned infinite system of linear algebraic equations of the second kind. This provides a robust numerical solution with any desired accuracy.

Diffraction by a screened chiral layer with a grating

Polarization characteristics of the reflecting structure like a chiral layer combined with a dielectric layer, both in between a diffraction grating and a screen, are considered. Due to the analytical regularization procedure derived from the Riemann-Hilbert problem method, the correspondent diffraction vector problem is solved in the form available for effective numerical treatment. The numerical investigation shows a number of new diffraction features caused by the chiral medium presence.