ELECTROMAGNETIC WAVE DIFFRACTION PROBLEM BY PERIODICAL GRATING IN PLANE WAVEGUIDE

Abstract

The problem of an electromagnetic wave diffraction by a periodical grating made of thin conducting screens between two conducting planes is reduced to an infinite set of linear algebraic equations. Three-dimensional case was considered when a field depends on all three spatial coordinates. According to the theorem of unique diffraction problem solution if an original wave is Floquet wave, then the desired solution of the Maxwell equations set can also be only the Floquet wave. We used the expansion of the desired functions along the orthogonal system of functions depending on a transverse coordinate, and the representation in the form of a quasiperiodic function along a longitudinal coordinate. The case when a field does not depend on a transverse coordinate is considered separately. From the boundary conditions and the field conjugation conditions in a grating plane, a pair-wise summatory equation is obtained with respect to the coefficients of the electromagnetic field expansion over an eigenwave of a waveguide. This equation is reduced to an infinite set of linear algebraic equations by the method of integral-summatory identity. An infinite set of linear equations is represented in vector-matrix form: the desired values are two-dimensional vectors, and their coefficients are the square matrices of the second order. Its approximate solution can be obtained by truncation.