Resonant gratings

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Fano resonance and applications
When a grating engraved on a dielectric or metallic layer is illuminated by an incident wave, a peak in the reflectivity, transmittivity or absorption spectrum can be observed, under certain circumstances. This phenomenon, known as Fano resonance, is due to the excitation of an eigenmode of the structure, a guided mode in the dielectric case, and a surface plasmon in the metallic one. The resonance peak is very narrow spectrally and can reach 100% (in reflection, transmission or absorption). The applications are filtering, in reflection (notch filter), or transmission (band-pass filter), sensors, polarization splitting...
For filtering applications, the peak is unfortunately polarization dependant and has an angular acceptance too narrow, as compared to the angular divergence of the beams used in practice.

Method
To be able to find solutions to these problems, we have led a theoretical work in depth based on the use of an home made numerical code (Fourier Modal Method, see the section on the Numerical Methods for Periodic Media), a rigorous study of the scattering matrix (energy conservation, reciprocity theorem …), a vectorial perturbative method (expression of the eigenmodes and scattering matrix of the structure with respect to that of a planar reference structure, and the parameters of the structure).

Results
This approach gave us an in-depth understanding of the guided mode resonances in gratings and to propose original configurations for practical needs, some of which have been experimentally and successfully tested :
-a reflection filter with 0.28nm bandwidth at 1550nm (experiment), polarization independent under normal incidence (fig. 1)
-a reflection filter with 0.4nm bandwidth at 1550nm (experiment), polarization independent under oblique incidence (fig. 2)
-a reflection filter with 0.12nm bandwidth at 1550nm (theory), polarization independent, with a 90nm tunability with respect to the angle of incidence around 15° (fig.3).

Fig.1

Fig.2

Fig.3

Current works and prospects
The current works on this subject are the tunability with electro-optic materials (fig.3). In addition, the method that have been developed and the acquired knowledge could be applied successfully to other structures, for other applications :
-transmission filters,
-resonant gratings surrounded with Bragg reflectors,
-broadband mirrors…

Collaborations : LPN-CNRS Marcoussis, LAAS-CNRS Toulouse, CNES