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.

An updated hoverfly checklist (Diptera: Syrphidae) of the Mascarene island of Réunion, France

A commented and updated checklist of the hoverflies from the Mascarene island of Réunion, France, is presented. A total of 22 species are listed. New data on eight species are provided, two of them new to Réunion: Syritta austeni Bezzi, 1915 and Eristalinus madagascariensis (Hervé-Bazin, 1914). Réunion has 14 species shared with Madagascar and 10 with Mauritius. The present study contributes to better understand the biodiversity of this part of the world.