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Second harmonic generation in 2D nonlinear photonic crystals based on rectangular symmetry with rectangular motifs has been analyzed theoretically. An approximate solution of the spectral response for the second harmonic generation in any designed 2D nonlinear photonic crystal is obtained within the un-depleted pump approximation. Rapid calculation of the temporal profile of multidirectional second harmonic pulse in such nonlinear lattices has been also shown.

On theory of second harmonic generation in 2D nonlinear photonic crystals with arbitrary structures