In this article, by using the method of finite difference time domain (FDTD) and PML boundary conditions, we have studied the photonic band gaps for TE and TM modes in square and triangular lattices consisting of air holes in dielectric medium and compared the results. In addition, the effect of nonlinearity of the photonic crystal background on the photonic band gaps and comparison with the results of the linear case (holes in a background medium with linear dielectric constant) has been presented. Comparison of the transmission spectrums in linear and nonlinear cases shows a red shift in minimum transmission for both triangular and square lattices.


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