Optical Fano resonances in photonic crystal slabs near diffraction threshold anomalies

Optical Fano resonances due to resonant eigenmodes in a layered periodically-modulated structure (photonic crystal slab) are investigated theoretically. The special attention is focused on the behavior of the resonances near a diffraction threshold. A new formulation of the resonant mode approximation for the optical scattering matrix near the diffraction threshold anomalies is proposed.