Mathematical simulation of conversion of femtosecond pulses to second harmonic in photonic bandgaps

Summary form only given. We present the results of numerical simulations of the second harmonic generation (SHG) in photonic band gaps (PBG) structures with GaAs/AlAs and GaAs/fused quartz quarter-wave layers under of femtosecond pulse pump. The electromagnetic field inside the slab is presented as a sum of counterpropagating pump and doubled frequency waves. The theoretical consideration is based on the second-order space differential equations for pump and nonlinear transformation waves amplitudes. Simulations of propagating in nonlinear medium are performed by using of method of characteristics. Numerical solution of the equations system was realised by means of fast Fourier transform permitting to take into Account a modification of radiation spectrum after nonlinear transformation of ultrashort pulse. The transmission and reflection coefficients and the density of the optical modes defined as value of the reciprocal group. velocity are calculated. Conversion efficiency reflected and transmitted waves and pulse duration are analysed as a function of the structure period and pump intensity. We show that the value of transmission and reflection coefficients gives a relation between transmitted and reflected waves of the second harmonic whereas the value of the optical modes density determines the nonlinear conversion efficiency. The reflected SHG exceeds transmitted wave for: the PBG GaAs/AlAs more then 30 times. but in the case of PBG GaAs/quartz the intensities of transmitted and reflected pulses were practically identical. The maximum of total conversion efficiency in the both cases occurs for ten periods, and its value is about three percents for pump intensity 400 GW/cm² (PBG GaAs/AlAs). The durations of SHG pulses is less then pump pulses durations in 1/√2