1. 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

2. 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

3. 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

4. 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

5. 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, (2005)

6. 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

7. 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

8. 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

9. 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) ?

10. 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

11. Transmittivity versus collecting angle, at and outside resonance1
-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)

12. Transmittivity and reflectivity with a collecting lens1
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

13. Polarisation s+p
Incident
Réfléchi