Electromagnetic analysis of photonic crystal waveguides operating above the light cone

We present a theoretical study of the propagation of light in photonic crystal waveguides operating above the light cone. Air membrane, silicon-on-insulator waveguide, and weakly confined systems on GaAs substrates consisting of a single-line-defect in triangular lattices of holes are analyzed accurately thanks to an original Fourier-modal method. The method that relies on an artificial periodization of the structure and on the introduction of electromagnetic absorbers at the boundaries of the unit cell uses Fourier series to expand the field quantities. For the waveguide geometries investigated in this work and provided that the weakly confined systems are etched deeply into the substrate, attenuations of 10-30 dB/100 μm are predicted over the full bandgap spectral region