Polarization independent ultra-sharp filtering at oblique incidence with resonant gratings Anne-Laure Fehrembach, Fabien Lemarchand, Anne Sentenac, Institut Fresnel, Marseille, France Olga Boyko, Anne Talneau Laboratoire de Photonique et de Nanostructures, Marcoussis, France LPN Goal : Dl=0.2nm ~100% efficiency with standard collimated incident beam (Dq=0.2°) polarization independence oblique incidence Resonant grating l q 1 R l

Resonant grating filters: basic principles (kp , lp) x z y q l kinc kx (kp, 2p/lp) 2p/l light cone kinc kinc (-1) p s (kp , lp) E d kinc (-1) kp kx ky l ~ lp kx - K 2p/l K=2p/d kinc (-1) kp 2p/lp Advantages and limitations: ultra-narrow bandwidth: Dl < 0.1nm achievable weak angular tolerance: Dq < 0.05° strong polarization sensitivity

Angular tolerant configuration Perturbative model: Dl  e1 Dq  e2 2p/l kx x y z kinc (-1) (+1) kx (-1) kinc 2p/l kx 2p/l kinc (-1) kinc (-1) (+1) TE2 TE1 kx 2p/l 2 counter propagative modes, small e1 , large e2

Polarization independent configuration symmetric TEp anti - symmetric TEs p s symmetry plane kinc (0,1) (1,0) symmetry plane 2p/l k s p e1,-1 Symmetry plane, small e1,-1

Angular tolerant and polarization independent oblique incidence configuration Symmetry plane, 2 counter propagative modes k 2p/l e1,-1 p s kx 2p/l e1,-1 p s kinc (0,1) (-1,0) (0,-1) TE2 (1,0) TE1 symmetry plane Dq  e2,0 Dl  e1,0 small e1,-1, small e1,0 , large e2,0 Fehrembach, Sentenac, Appl. Phys. Lett., 86, 121105 (2005)

Design and fabrication design  "Doubly periodic patern" fabrication layers deposition: glass substrate / Ta2O5 / SiO2/ Ta2O5 / SiO2 (220nm etched) electronic lithography etching (component size 1mm2) Diameters dB = 347nm dA= 257nm dC= 170nm d/4 d = 890nm A B C small e1,-1, small e1,0 , large e2,0 Scanning electron microscopy picture of the grating

Results: resonant grating dispersion relation Minimum of transmittivity versus incident angle and wavelength theory experience A B A’ B’ experimental and theoretical dispersion relations are similar (same gap width ~ 5nm, opening around 5.8°) Points A and A’: polarization independent, angular tolerant resonance Points B et B’: weak angular tolerance, polarization sensitivity

Results: resonant grating spectra diameter at waist 580µm, full angle divergence 0.2° Theory q=5.5° q=5.8° Experience q=5.5° q=5.8° Points B and B’: s and p resonances split up, wide bandwidth, low efficiency (Dq=0.02°) Points A and A’: polarization independence, narrow bandwidth, quite good efficiency

Results: experience vs theory Plane wave Theory, Gaussian beam divergence 0.2° Experience Dl=0.1nm Dq=0.17° R=100% T=0% R+T=100% Performances deterioration: Etching imperfections (write fields stitching errors) ? little diffusion at resonance but 20% energy is lost Dl=0.4nm Dl=0.2nm R=65% T=35% R+T=100% R=28% T=52% R+T=80% Grating finite size effects (1mm²) ?

Conclusion Experimental demonstration of a resonant grating filter with 0.4nm bandwidth polarization independence under 5.8° of incidence Performances deterioration: weak angular tolerance and finite size effect Etching in high index, over a wide area New component: Dl=0.2nm, Dq=0.6°, etched over 3mm²

Transmittivity versus collecting angle, at and outside resonance 1 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 Rnorm Hrnorm 0.1 diffusion ? Collecting angle of the detector: 2.7mrad (1mm located at 36cm) transmittivity 0.01 diffusion ? 0.001 Collecting angle (mrad)

Transmittivity and reflectivity with a collecting lens 1 0.9 0.8 0.7 pour info: angle de 0.6 collection R et T 200 mrad en T (lentille) 0.5 et 60 mrad en R (cube) 20% of energy at resonance remains lost 0.4 0.3 0.2 0.1 1541 1541.5 1542 1542.5 1543 longueur d'onde

Polarisation s+p Incident Réfléchi