Transference matrix method for non slanted holographic reflection gratings

Cristian Neipp; Jorge Francés; Manuel Pérez-Molina; Sergio Bleda; Augusto Beléndez

doi:10.1117/12.854277

14 May 2010 Transference matrix method for non slanted holographic reflection gratings

Cristian Neipp, Jorge Francés, Manuel Pérez-Molina, Sergio Bleda, Augusto Beléndez

Proceedings Volume 7717, Optical Modelling and Design; 771706 (2010) https://doi.org/10.1117/12.854277
Event: SPIE Photonics Europe, 2010, Brussels, Belgium

Abstract

In this work we present an analysis of non-slanted holographic reflection gratings by using a matrix method. A transfer matrix which relates the values of the electric field and its derivatives is obtained for a permittivity which varies cosenoidally for one period. The coefficients of this matrix can be calculated in terms of Mathieu's functions and their derivatives. Then the matrix of the entire medium is obtained as the Nth power of the matrix for one period. Since the reflectance and transmittance coefficients are related to the coefficients of the medium matrix, it is possible to calculate the efficiencies of orders -1 (reflected) and 0 (transmitted) by using this method. The results obtained by using the Trensference Matrix Method are compared to those obtained using Kogelnik's expressions for the transmission and diffraction efficiency. As will be seen there is good agreement between the results obtained by the Transference Matrix Method and those of the Coupled Wave Theory.

Citation Download Citation

Cristian Neipp, Jorge Francés, Manuel Pérez-Molina, Sergio Bleda, and Augusto Beléndez "Transference matrix method for non slanted holographic reflection gratings", Proc. SPIE 7717, Optical Modelling and Design, 771706 (14 May 2010); https://doi.org/10.1117/12.854277

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