Operator method in the waves diffraction problem by a semi-infinite grating of strips placed in parallel planes

Abstract

IntroductionElectrodynamical structures which contain semi-infinite sequences of discontinuities are of interest for a long time. Such structures have a significant feature compared to the infinite ones: they allow to describe the field scattered by the edge of a real finite grating.The approach which supposes that the full field is defined as a superposition of fields scattered by each element with unknown coefficients is widely used in diffraction problems by semi-infinite gratings [1], [2], [3]. Then the coefficients may be represented as a sum of an infinite-array term and an edge effect term. As a result an infinite system of linear algebraic equations is obtained. For the convergence justification the fact that the currents on the conductors which are distant from the end of a semi-infinite grating approach to those of infinite periodic grating is used.In this paper we use the operator method [4]-[8] for study of semi-infinite strip grating. The scattered field is obtained with the help of the reflection operator which is determined from the nonlinear operator equations.