1. Narrow-band filtering with resonant gratings under oblique incidence Anne-Laure Fehrembach, Fabien Lemarchand, Anne Sentenac, Institut Fresnel, Marseille, France Olga Boyko, Anne Talneau Laboratoire de Photonique et de Nanostructures, Marcoussis, France LPN 0 1 R Goal :  =0,2nm~100% efficiency polarization independenceoblique incidence Use with standard collimated incident beam (  =0.2°) Resonant grating  0 1 R 

2. Resonant grating filters: basic principles  k p, p ) x z y   k p, 2  / p ) 2  / 0 light cone ~ p || k inc - K x || ~ Re(k p ) + polarization Coupling condition via the scattering order (-1,0)  - K  k p, 2  / p ) 2  / 0 K=2  /d k inc - K x kpkp 2  / p  k p -K x, 2  / p ) k inc - K x kpkp   ~ p d  k p, p )  k inc s p x z y

3. Resonant grating filters: advantages and limitations  related to the coupling strength between the incident field and the eigenmode: Involved parameters: grating depth h Fourier harmonic   (coupling via scattering order (-1,0) Ultra-narrow bandwidth,  < 0.1nm achievable  2  / 0 k inc - K x kpkp  related to the same parameters (h and   )  = 0.1nm ->  = 0.05° weak angular tolerance (full divergence angle  0.2° for a 1.55  m Gaussian beam with diameter at waist 600  m) coupling condition strongly depends on polarization

4. Angular tolerant + polarization independent resonances requires 4 modes, which are, by pairs: - counter-propagative modes - independent modes 2D square resonant grating under normal incidence 0 1 R     0  2  / 0 K  p, 2  / p ) 0 2  / 0  k inc KyKy E -K y TE guided mode x y z kpkp p polarization Inc. plane KxKx k inc -K x E kpkp TE guided mode x y z s polarization Inc. plane +K x  related to the coupling strength between the two excited eigenmodes Harmonic involved:  2,0 0 1 R      0 locally dispersion-less degenerate modes

5. 2D square resonant grating under oblique incidence TE 1 TE 2 k inc KyKy -K x -K y k p2 KxKx k p1  2  / KxKx -K x KyKy -K y s,p  2  /  1,-1    2,0    1,0 s,p symmetric TE p anti - symmetric TE s p s symmetry plane k inc KyKy k p1 KxKx 2 independent modes 2 counter-propagative modes 2  / KxKx KyKy  spsp  1,-1

6. Design and fabrication design fabrication layers deposition: glass substrate / Ta 2 O 5 / SiO 2 / Ta 2 O 5 / SiO 2 (220nm etched) electronic lithography etching (component size 1mm 2 ) Scanning electron microscopy picture of the grating Top view of the doubly-periodic grating pattern Diameters d B = 347nm d A = 257nm d C = 170nm d/4 d = 890nm A B C A large  2,0 small  1,0 and  1,-1

7. theory Results: resonant grating dispersion relation Minimum of transmittivity versus polar incident angle  and wavelength experimental and theoretical dispersion relation are similar (same gap width ~ 5nm, opening around 5.8°) spectral shift: due uncertainty on layer optical thickness Points A and A’: locally dispersion less degenerate modes Points B et B’: dispersive and non degenerate modes experience A B’ A’ B

8. Results: resonant grating spectra Points A and A’: polarization independence Plane wave:  =0.1nm  =0.17° Gaussian beam: theoretical  =0.2nm experimental  =0.4nm (diameter at waist 580µm, full angle divergence 0.2°) Points B and B’: s and p resonances split and filter performances deteriorated theory experience

9. Conclusion Experimental demonstration of a 0.4nm bandwidth polarization independent resonant grating filter under 5.8° of incidence Performances deteriorations: Theoretically from the plane wave to the Gaussian beam: T min  0 and bandwidth broadening Insufficient angular tolerance: etching in higher optical index layer ? From theory to experience : bandwidth broadening - Grating finite size effects ? - Etching imperfections (write fields stitched error) ?

10. Transmittivity versus collecting angle, at and outside resonance 0.001 0.01 0.1 1 -15.0-10.0-5.00.05.010.015.0 Collecting angle (mrad) transmittivity Rnorm Hrnorm Collecting angle of the detector: 2.7mrad (1mm located at 36cm) diffusion ?

11. Transmittivity and reflectivity with a collecting lens 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 15411541.515421542.51543 longueur d'onde R et T 20% of energy at resonance remains lost pour info: angle de collection 200 mrad en T (lentille) et 60 mrad en R (cube)