MODIFIED METHOD OF SEPARATION OF VARIABLES FOR SOLVING DIFFRACTION PROBLEMS ON MULTILAYER DIELECTRIC GRATINGS

A modified method of separation of variables is proposed for solving the direct problem of diffraction of electromagnetic wave by multilayer dielectric gratings (MDG). To apply this method, it is necessary to solve a one-dimensional eigenvalue problem for a 2nd- order differential equation on a segment with piecewise constant coefficients. The accuracy of the method is verified by comparison with the results obtained by the commercially available RCWA method. It is demonstrated that the method can be applied not only to commonly used MDG elements with one line in a grating period but also to potentially promising MDG elements with several different lines in a grating period.

Model of Е-polarized wave propagation in a multilayer dielectric structure

This paper addresses the determination of the dielectric constant of multilayer dielectric structures by radiowave interferometry. In the general case, in interferometry measurements to one measured value of the reflection coefficient there may correspond an infinity of dielectric constants. This ambiguity may be resolved by first determining the effect of different parameters of the probing electromagnetic wave on the reflection coefficient. In particular, it is important to have a preliminary estimate of the effect of the incidence angle and the polarization on the range of variation of the reflection coefficient with the variation of one of the structure parameters. This paper considers the case where a plane E-polarized electromagnetic wave, i.e. a wave whose magnetic field is perpendicular to the incidence plane, is incident on a multilayer dielectric structure. The aim of this work is to develop a model of the propagation of an E-polarized electromagnetic wave through a multilayer dielectric structure at an arbitrary incidence angle and to determine the range of variation of the reflection coefficient with the variation of the dielectric constants of the layers. The paper presents a model of the propagation of an E-polarized electromagnetic wave in a two-layer dielectric structure. A metal base, which is an ideal conductor, underlies the structure. The electromagnetic wave is incident from the air at an arbitrary incidence angle. Based on the model, a method is proposed for measuring the relative dielectric constant and the dielectric loss tangent. It is shown that at a normal incidence the reflection coefficient magnitude is the same both for H- and E-polarization. Because of this, determining the relative dielectric constant and the loss tangent from the measured reflection coefficient magnitude calls for measurements not only at a normal incidence, but also at an oblique incidence, at which the reflection coefficient magnitudes will be different for H- and E-polarization.

Synthesis of highly efficient multilayer dielectric diffraction gratings for spectral combining of laser beams

Статья посвящена синтезу многослойных диэлектрических отражательных дифракционных решеток, с высокой эффективностью обеспечивающих спектральное сложение пучков с различной длиной волны в заданном дифракционном порядке. Приводятся результаты решения задачи синтеза многослойных диэлектрических дифракционных решеток, обеспечивающих спектральное сложение в первом или минус первом порядке дифракции. Кроме того, решается задача синтеза для таких решеток с учетом возможных технологических ограничений на высоту профиля (глубину травления). Решение задачи синтеза проводится путем минимизации зависящего от параметров решетки целевого функционала методом Нелдера-Мида. Решение прямой задачи на каждом шаге минимизации осуществляется при помощи комбинации неполного метода Галеркина и метода матриц рассеяния. The paper is devoted to the synthesis of multilayer dielectric reflection diffraction gratings providing high-efficiency spectral combining of the beams with different wavelengths in a given diffraction order. The results are presented for solving the synthesis problems for multilayer dielectric diffraction gratings providing spectral combining in the first or minus first diffraction order. Besides, the synthesis problem for such gratings is solved with account taken of possible technological constraints imposed by the height of the grating profile (etch depth). The solution of the synthesis problem is obtained by means of Nelder-Mead minimization of the merit function depending on the grating parameters. At each minimization step the direct problem is solved using a combination of the incomplete Galerkin method and scattering matrix method.