Relation between efficiency of second harmonic generation and spectral properties of a one-dimensional photonic crystal

Numerical calculation of second harmonic generation in a photonic crystal consisting of alternating quarter-wave layers of ZnS and SeF₂ pumped by a femtosecond tunable laser is carried out. The results are compared with the spectral characteristics of the photonic crystal obtained with the use of a matrix method for calculating transmission coefficients. It is shown that the maximum efficiency of conversion to the second harmonic takes place at a minimum group velocity mismatch of the pump and second harmonic waves, corresponding to pump frequencies in the range below the band gap edge of the photonic crystal.