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

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

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A single guided mode kg is twice excited with the two +/-1 evanescent waves under oblique incidence Different configurations for exciting a guided mode 3.3. Resonance very sensitive to the incident polarization The angular tolerance may be good with specific grating profiles kx0y Kx-Kx kg

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Two guided modes kg are excited with the two +/-1 evanescent waves under oblique incidence Different configurations for exciting a guided mode 4.4. Resonance with a possible good angular tolerance BUT design sensitive to fabrication errors K kg 1 -K kxOy kg 2

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Lamellar grating profiles leading to a good angular tolerance (x) x (f) f Kx2Kx3Kx4Kx 11 22 Single mode excitation with single evanescent wave: 1 d d1 d2 d1 and d2 d/2 Guide Mode excitation with two evanescent waves: 1 and 2

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

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Design and fabrication 4 DIBS layers SiO 2 PMMA 272.5nm 365nm 180nm d/ nm d=940nm d/4 electronic lithography (Leica EBPG 5000+)

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

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Transmittance of the normal incidence notch filter TT

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

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

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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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