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.

Recoverable silica-gel supported binam-prolinamides as organocatalysts for the enantioselective solvent-free intra- and intermolecular aldol reaction

Silica-gel supported binam-derived prolinamides are efficient organocatalysts for the direct intramolecular and intermolecular aldol reaction under solvent-free conditions using conventional magnetic stirring. These organocatalysts in combination with benzoic acid showed similar results to those obtained under similar homogeneous reaction conditions using an organocatalyst of related structure. For the intermolecular process, the aldol products were obtained at room temperature and using only 2 equiv of the ketone with high yields, regio-, diastereo- and enantioselectivities. Under these reaction conditions, also the cross aldol reaction between aldehydes is possible. The recovered catalyst can be reused up to nine times providing similar results. More interestingly, these heterogeneous organocatalysts can be used in the intramolecular aldol reaction allowing the synthesis of the Wieland–Miescher and ketone analogues with up to 92% ee, with its reused being possible up to five times without detrimental on the obtained results.