Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE2011 Benidorm, Spain, 26-30 June 2011 Application of Mathieu functions for the study of non- slanted reflection gratings L. Alberto Estepa 1 , Cristian Neipp 1 , Jorge Francés 1 , Manuel Pérez-Molina 1 , Elena Fernández 2 , Augusto Beléndez 1 " Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal Universidad de Alicante, # Departamento de Óptica, Farmacología y Anatomía, Universidad de Alicante $%&&’()%*+’*,’ -./0%&1( ’2-345 ,&3(/3-*6+73(/(8.-8’( Abstract 9* /03( :%&; :’ )&’(’*/ -* -*-4<(3( %7 *%*=(4-*/’+ &’74’,/3%* >&-/3*>( ?< .(3*> ’@-,/ (%4./3%*( %7 /0’ (’,%*+ %&+’& +377’&’*/3-4 ’A.-/3%*B +’&3C’+ 7&%2 D-@:’44 ’A.-/3%*(B 3* /’&2( %7 D-/03’. 7.*,/3%*(8 E0’ &’(.4/( %?/-3*’+ ?< .(3*> /03( 2’/0%+ :344 ?’ ,%2)-&’+ /% /0%(’ %?/-3*’+ ?< .(3*> /0’ :’44 ;*%:* F%>’4*3;1( $%.)4’+ G-C’ E0’%&< :03,0 )&’+3,/( :3/0 >&’-/ - ,,.&-,< /0’ &’()%*(’ %7 /0’ ’77 ,3’*,< %7 /0’ H’&%( -*+ 7 &(/ %&+’& 7%& C%4.2’ )0-(’ >&-/3*>(B 7%& ?%/0 &’7 ’,/3%* -*+ /&-*(23((3%* >&-/3*>(8 8 Key words: diffraction grating, Mathieu equation, volume holograms 1. Introduction E0’ (/.+< %7 /0’ 3*/’&-,/3%* %7 ’4’,/&%2->*’/3, &-+3-/3%* :3/0 +377&-,/3C’ ’4’2’*/( 0-( &’,’3C’+ 2.,0 -//’*/3%* 3* /0’ 43/’&-/.&’ I"=JK8 9* )-&/3,.4-&B (’C’&-4 /0’%&’/3,-4 2%+’4( 0-C’ ?’’* )&%)%(’+ /% -,,.&-/’4< +’(,&3?’ /0’ ?’0-C3%.& %7 +377&-,/3%* >&-/3*>( %7 +377’&’*/ ;3*+8 E0’ -//’*/3%* )%(’+ %* /0’(’ (/&.,/.&’( 3( 3* )-&/ +.’ /% /0’ 7-,/ /0-/ - (3*.(%3+-4 +377&-,/3%* >&-/3*> 3( /0’ (32)4’(/ )’&3%+3, (/&.,/.&’ /0-/ ,-* ?’ &’,%&+’+ %* - )0%/%(’*(3/3C’ 2-/’&3-48 E0’&’7%&’ /0’ ?-(3, )&%?4’2 3* C%4.2’ 0%4%>&-)0< /0’%&< 3( /% +’(,&3?’ -,,.&-/’4< /0’ )&%)’&/3’( %7 /03( ;3*+ %7 (/&.,/.&’(8 L .(.-4 :-< /% ,-4,.4-/’ /0’ ’773,3’*,3’( %7 /0’ +377’&’*/ @CMMSE Page 1302 of 1703 ISBN: 978-84-614-6167-7