Yu. V. Shestopalov

Reflection and transmission of a plane TE-wave at a lossless nonlinear dielectric film

Abstract A general analytical solution of the Helmholtz equation describing the scattering of a plane, monochromatic, TE-polarized wave with a film exhibiting a local Kerr-like nonlinearity is presented. The film is situated between two semi-infinite media. All media are assumed to be non-absorbing, non-magnetic isotropic and homogeneous. The results derived contain conditions for unbounded field intensities expressed in terms of the imaginary half-period of Weierstrass’ elliptic function ℘ . The reflectivity R is calculated as a function of the film thickness and the transmitted intensity. The critical values of R are determined. The results are a generalization of the linear optics results.

Logarithmic Integral Equations in Electromagnetics

Elements of the theory of integral operators: integral operators with purely logarithmic kernel integral operators in Holder spaces logarithmic integral operators and Chebyshev polynomials integral operators defined on a set of intervals integral operators with fixed logarithmic singularities elements of spectral theory abstract pole pencils logarithmic integral operators in Sobolev spaces integral operators with kernels represented by series methods of small parameter approximate inversion approximate semi-inversion. Generalized potentials with logarithmic kernels: generalized potentials Greens potentials examples for canonical domains half-plane rectangle circle exterior of a circle ring. Summation operators: matrix representation Galerkin methods and basis of Chebyshev polynomials summation operators in the spaces of sequences matrix representation of logarithmic integral operators. Boundary value problems: formulation of the problem uniqueness and existence theorems canonical problems - diffraction by strips and slots diffraction by a slot diffraction by a strip diffraction by a screen with a rectangular slotted cavity scattering by a circular slotted cylinder eigenoscillations of open and closed slot resonators closed rectangular slot resonator open rectangular slot resonator slotted resonator with circular cross section the integral and summation equations for the strip problems summation equations in the problem on eigenfrequencies.

Permittivity Reconstruction of Layered Dielectrics in a Rectangular Waveguide from the Transmission Coefficients at Different Frequencies

Determination of electromagnetic parameters of dielectric bodies of complicated structure is an urgent problem. However, as a rule, these parameters cannot be directly measured (because of composite character of the material and small size of samples), which leads to the necessity of applying methods of mathematical modeling and numerical solution of the corresponding forward and inverse electromagnetic problems. It is especially important to develop the solution techniques when the inverse problem for bodies of complicated shape is considered in the resonance frequency range. In this paper we develop a method of solution to the inverse problem of reconstructing (complex) permittivity of layered dielectrics in the form of diaphragms in a waveguide of rectangular cross section from the transmission coefficients measured at different frequencies. The method enables in particular obtaining solutions in a closed form in the case of one-sectional diaphragm. In the case of an n-sectional diaphragm we solve the inverse problem using numerical solution of a nonlinear equation system of n complex variables. Solvability and uniqueness of the system are studied and convergence of the method is discussed. Numerical results of calculating (complex) permittivity of the layers are presented. The case of metamaterials is also considered. The results of solution to the inverse problem can be applied in nanotechnology, optics, and design of microwave devices.

Solutions to the Helmholtz equation for TE-guided waves in a three-layer structure with Kerr-type nonlinearity

We study certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation on the line describing waves propagating in a nonlinear three-layer structure consisting of a film surrounded by semi-infinite media. All three media are assumed to be lossless, nonmagnetic, isotropic and exhibiting a local Kerr-type dielectric nonlinearity. The linear component of the permittivity is modelled by a continuous real-valued function of the transverse coordinate. We show that the solution of the Helmholtz equation in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating the equivalent Volterra equation. The associated dispersion equation has a simple root (if the semi-infinite media are linear and if the nonlinearity parameter of the film is sufficiently small) that uniquely determines this solution.

Uniqueness of complex permittivity reconstruction in a parallel‐plane waveguide

The paper presents a statement and a proof of uniqueness of solution to the inverse problem of determination of permittivity of a lossy dielectric inclusion in a parallel-plane waveguide from the r ...

A Nonlinear Multiparameter EV Problem

We investigate a generalization of one-parameter eigenvalue problems arising in the theory of wave propagation in waveguides filled with nonlinear media to more general nonlinear multi-parameter ei ...