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**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

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**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)

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**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

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**Different configurations for exciting a guided mode**

kg 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

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**Different configurations for exciting a guided mode**

kg -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

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**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

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**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

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**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

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**Design and fabrication**

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

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**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

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**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.

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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

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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

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**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

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