Band structure calculation in two-dimensional Kerr-nonlinear photonic crystals

Using the finite-difference time-domain method, based on the numerical simulation of oscillating dipole radiation, we analyze band structures in two-dimensional Kerr-nonlinear photonic crystals. This method is more thorough at calculating band structures in two-dimensional Kerr-nonlinear photonic crystals than approaches proposed earlier. We find that the band structures calculated for both TE and TM polarizations are dynamically red-shifted with regard to the linear case. For a positive Kerr coefficient, this red-shift increases as the intensity of the oscillating dipole increases.