Incident femtosecond pulse chirp influence on nonlinear localization of laser energy in 2D photonic crystal

We investigate laser energy localization in 2D photonic crystal with Kerr nonlinear response in dependence of the incident femtosecond pulse chirp. Such kind of energy localization appears due to soliton formation in certain elements of photonic crystal. Their positions, in which the soliton appear, depend on the incident pulse chirp and the pulse intensity. It is important to emphasize that a soliton occur in separate elements of the photonic crystal. Therefore, their sizes must be less than sizes of the photonic crystal elements. Consequently, an intensity of the incident pulse must be greater than certain crucial value. A process of energy localization strongly depends on relation between the wave packet carrier frequency and a frequency characterizing a photonic crystal. These solitons move with slow velocity inside the PC elements. Under certain conditions, the soliton can stop. The problem under consideration is described by a nonlinear Schrodinger equation with respect to amplitude slowly varying in time only. We investigate a femtosecond pulse interaction with photonic crystal numerically and analytically.