Application of Mathieu functions for the study of non-slanted reflection gratings

In this work we prensent an analysis of non-slanted reflection gratings by using exact solution of the second order differential equation derived from Maxwell equations, in terms of Mathieu functions. The results obtained by using this method will be compared to those obtained by using the well known Kogelnik's Coupled Wave Theory which predicts with great accuracy the response of the efficieny of the zero and first order for volume phase gratings, for both reflection and transmission gratings.This work was supported by the “Ministerio de Ciencia e Innovación” of Spain under projects FIS2008-05856-C02-01 and FIS2008-05856-C02-02, and by the “Generalitat Valenciana” of Spain under project PROMETEO/2011/021

Corrected coupled-wave theory for non-slanted reflection gratings

In this work we present an analysis of non-slanted reflection gratings by using a corrected Coupled Wave Theory which takes into account boundary conditions. It is well known that Kogelnik's Coupled Wave Theory predicts with great accuracy the response of the efficiency of the zero and first order for volume phase gratings, for both reflection and transmission gratings. Nonetheless, since this theory disregard the second derivatives in the coupled wave equations derived from Maxwell equations, it doesn't account for boundary conditions. Moreover only two orders are supposed, so when either the thickness is low or when high refractive index high are recorded in the element Kogelnik's Theory deviates from the expected results. In Addition, for non-slanted reflection gratings, the natural reflected wave superimpose the reflection order predicted by Coupled Wave theories, so the reflectance cannot be obtained by the classical expression of Kogelnik's Theory for reflection gratings. In this work we correct Kogelnik's Coupled Wave Theory to take into account these issues, the results are compared to those obtained by a Matrix Method, showing good agreement between both theories.This work was supported by the “Ministerio de Ciencia e Innovación" of Spain under projects FIS2008-05856-C02-01 and FIS2008-05856-C02-02, and by the “Generalitat Valenciana" of Spain under project PROMETEO/2011/021