Photonic Band Gap Resonant Gratings : Tailoring Radiation from Specular Structures

1. 0,1nm R 1 103 0,4° R 1  (µm) 1,52 1,55 1,57 Einc (ainc,linc) R s et p s et p periodd , K=2p/d ainc p p h q (°) q0 # 0° eigenmode(ap,lp) s s linc b PBG +K -K ainc # 0 a ainc TE1 TE2 TE1 TE2 2p/l aref1 (l) aref2 (l) TE1 TE2 a K -K K/2 TM TE linc ainc # 0 symmetry plane h # 0 : no more degeneracy TE1s TE1p h = 0 : the band is degenerated 2p/l Einc (ainc,linc) (p,s) symmetric (p) ainc TE1 antisymmetric (s) p-polarised mode s-polarised mode a = b a = b 2p/l TE2 (s,p) TE1 (s,p) Degeneracy +PBG TE1 TE2 a = b Photonic Band Gap Resonant Gratings : Tailoring Radiation from Specular Structures A.L. Fehrembach, A. Sentenac, anne.sentenac@fresnel.fr The resonance phenomenon When the incident spatiotemporal frequencies (ainc,2p/linc) are close to that (ap,2p/lp) of an eigenmode there is an anomaly in the reflectivity curves The resonance peaks are described with a Phenomenological theory The mode dispersion relation is studied with a weak-potential method The periodic modulation acts as a grating coupler and a photonic cristal for the modes Using PBG resonant grating for free-space DWDM filters * Oblique incidence * Narrow spectral bandwidth * Polarisation independent * Angular tolerance Modifying the shape of the resonance peaks by exciting simultaneously two modes antisymetric symetric The structure supports symmetric and antisymmetric modes whose effective index are as close as wanted. Increasing the angular tolerance of the resonance by flattening the mode dispersion relation The angular width does not depend on the spectral width The planar waveguide support two TE modes : The dispersion relations intersect outside the edge of the Brillouin zone A dual-pitch grating is used for coupling the incident wave into the mode and creating a Photonic Band Gap Polarisation independent resonances require mode degeneracy Degeneracy TM TE TE TM h # 0 h = 0 degeneracy a = b (2003) A. L. Fehrembach et A. Sentenac 'Study of waveguide gratings eigenmodes for unpolarized filtering applications' J. Opt. Soc. Am. A,20, 481 (2002) A. L. Fehrembach, D. Maystre et A. Sentenac 'Phenomenological theory of filtering by resonant dielectric gratings' J. Opt. Soc. Am. A, 19, 1136-1144 (1999) F. Lemarchand, A. Sentenac, E. Cambril et H. Giovannini ‘Study of the resonant behavior of waveguide gratings : Increasing the angular tolerance of guided-mode filters’, Journal of Optics A : Pure and Applied Optics, 1, 545-551