Band Structures for 2D Photonic Crystals in Presence of Nonlinear Kerr Effect Calculated by Use of Nonlinear Finite Difference Time Domain (NFDTD) Method

In this paper, we report the simulation results for impact of nonlinear kerr effect on band structures of a two dimensional photonic crystal (2d-phc) with no defect, a phc based w1-waveguide (w1w), and also coupled-cavity waveguides (ccws). all phc structures are assumed to a square lattice of constant a made of gaas rods of radius r=0.2a, in an air background. the numerical simulation was performed using the nonlinear finite difference time domain (nfdtd) technique. in doing so, we have normalized the electric field and the electric flux density vectors, and used a multi probe procedure. these have resulted in very accurate dispersion relations that, in turn, have enabled us to make some novel observations. for instance, simulations show that with an increase in the input light intensity (in the nonlinear regime) the band edges for all three phc structures experience some red shifts. the red shifts observed for ccws are, of course, larger than the red shifts experienced by other two structures. furthermore, the numerical results for ccws also show that the larger the light input intensity, the smaller the corresponding maximum light group velocity becomes. to the best of our knowledge, this is the first instance that such observations on the impact of the nonlinear kerr effect on the band diagram of 2d-phc waveguides are reported.