1. Resonant gratings for narrow band pass filtering applications
Olga Boyko, Fabien Lemarchand, Anne Talneau, Anne-Laure Fehrembach and Anne Sentenac
Laboratoire de Photonique et Nanostructures, CNRS UPR20, Route de Nozay, Marcoussis, France
Institut Fresnel, CNRS UMR6133, Aix-Marseille universités, D.U. de Saint Jérome, Marseille, France
Ultra narrowband inverse (notch) filters
FWHM < 1 nm with polarization independence and good angular tolerance

2. NOTCH (INVERSE) FILTERS
Subwavelength grating
Dielectric AR structure
Incident plane wave for R = 1
kxoy
Reflected light R 
at the resonance R = 1 (and T=0)
NOTCH (INVERSE) FILTERS
Incident light Kx z y O x
proj. of the incident wavevector
kg guided mode
evanescent wave
Resonance /coupling condition: |kxoy + m Kx| = kg (m integer)

3. Different configurations for exciting a guided mode
kxoy K kg 1.
A single guided mode kg is excited with a single evanescent wave under oblique incidence
Resonance very sensitive to the incident angle and the incident polarization
Typically  = 5nm for a  = 0.2deg
Bad performances with standard collimated beam

4. Different configurations for exciting a guided modekg
kxoy =0 (normal incidence) 2. -K +K
A single guided mode kg is excited with the two +/-1 evanescent waves under normal incidence
Resonance very sensitive to the incident polarization
The angular tolerance may be good with specific grating profiles

5. Different configurations for exciting a guided modekg
-Kx Kx 3.
kx0y
A single guided mode kg is twice excited with the two +/-1 evanescent waves under oblique incidence
Resonance very sensitive to the incident polarization
The angular tolerance may be good with specific grating profiles

6. Different configurations for exciting a guided mode
kg1
kg2
kxOy 4. K -K
Two guided modes kg are excited with the two +/-1 evanescent waves under oblique incidence
Resonance with a possible good angular tolerance BUT design sensitive to fabrication errors

7. Lamellar grating profiles leading to a good angular tolerance
 (x) x
 (f) f Kx
2Kx
3Kx
4Kx 1 2
Single mode excitation with single evanescent wave: 1
Guide Mode excitation with two evanescent waves: 1 and 2 d d1 d2
d1 and d2  d/2

8. Combining angular tolerance and polarization independence
Angular tolerance: excitation with several evanescent waves and |2| >>|1|
Polarization independence:
excitation with two orthogonal grating vectors Kx and Ky (2D gratings)
kg1
kxOy
kg2
oblique incidence kg
+Kx
+Ky
-Kx
-Ky
normal incidence

9. Design and fabrication
4 DIBS layers
electronic lithography (Leica EBPG 5000+)
272.5nm
365nm
180nm
d/4
d=940nm
SiO2
PMMA

10. Non polarising polarizing beamsplitter
Experimental characterization set-up
reference flux
Non polarising polarizing beamsplitter
tunable laser nm
RGF
T photodiode
Pigtailed collimator
2w0 = 0.58 mm
/2 waveplate
R photodiode

11. Transmittance of the normal incidence notch filter
Here are the transmittivity spectra for a normal incidence filter.
On the left picture you can see the spectral transmittivity. Experimentally we have two curves with squares and stars for two orthogonal polarizations. The spectral width is of 0.4nm and the minimum of transmittance is about 20% which is very close to the theoretical curve with the dots. The calculation is performed for a gaussian incident beam. If we considere a true plane wave the minimum of transmittance is theoretically of 0%.
The angular behaviour is plotted on the right.
The p polarization corresponds to a very large angular tolerance while the s polarization corresponds to the thinnest resonance. The experiment curve with circles correspond to a s+p polarization and is so an intermediate case between the two theoretical curves.

12. Oblique incidence filter: location of the minima of transmittivity versus  and  for s and p polarizations
experience B’ A’
theory A B
experimental and theoretical curves are similar
(same gap width ~ 5nm, opening around 5.8°)
spectral shift: due uncertainty on layer thickness or layer index

13. Experience
Theory (gaussian beam)
Points A and A’: polarization independence
Gaussian beam: diameter at waist 580µm, full angle divergence 0.2°
theoretically Dl=0.2nm (Plane wave: Dl=0.1nm )
experimentally Dl=0.4nm
Points B and B’: s and p resonances split and filter performances deteriorated

14. Conclusion Few number of layers and subwavelength grating
Specific 2D grating design => polarization independence and good angular tolerance
Experimental demonstration of ultra narrowband inverse filters  =0.4nm
Improvement of the maximum R value: larger grating surface (4mm2) and designs with even higher angular tolerance