Periodic Structures And Anisotropic Media: A Comparison Of The Numerical Results Obtained By Integral And Differential Methods

Abstract

ABSTRACT When both the integral and differential methods are applicable in the study of anisotropic gratings, we show that they lead to numerical results which are in good agreement. We think that it is a convincing proof of the reliability of our computer programs.This paper must be considered as a companion paper of the one headed Reasearches on gratings made with anisotropic materials: how is the work progressing in our Laboratory presented at the same session by the same authors, and in which the classical differential method (C.D.M.) and the integral method (I.M.) have been depicted. Notations are the same in both papers and will not be exposed again.We consider the following problem (fig. 1), which can be solved by ourthe C.D.M. or the I.M.. An anisotropic dielectric material of permittivitycomputers programs based either on sinusoidal grating made with a x 0 01 0 €y0 , where x= 6.31, y= 6.81, =7.34 is illuminated under zJthe incidence 9=20° by a plane wave. The wave vector of the incident wave lies in the xy plane. We only consider the case where the incident wave is TM polarized. Its wavelength is X = 0.6 urn. The grating period is d = 0.5 urn. Consequently, the grating gives birth to two reflected and four transmitted orders which propagate in the same directions as those described in our companion paper (section 4.3.). There is no change in polarization and the diffracted field is also TM polarized.TM polarization1Figure l.