Generation of difference-frequency radiation in GaAs in the field of a few-cycle laser pulse in the regime of weakly expressed chromatic dispersion

We derive a system of coupled modified Korteweg-de Vries equations in the approximation of unidirectional waves which describe the evolution of electric fields of mutually-orthogonal linearly polarized laser pulses with duration of several optical oscillations in a nonlinear crystal with quadratic nonlinearity in the regime of weakly expressed chromatic dispersion. An isotropic GaAs crystal is considered as a nonlinear crystal, and the direction of propagation of interacting pulses is assumed to coincide with the normal to the 〈110〉 plane of the crystal. The derived system of equations was solved numerically by the finite difference method. We obtained the dependence of the relative shift of the central wavelength of pumping pulse spectrum on the distance travelled. It is shown that the decrease in the crystal thickness down to values commensurate with the coherence length of difference-frequency radiation leads to an increase in conversion efficiency. In particular, it is shown that the efficiency of difference-frequency generation at 4.1 μm and 10 μm for the 30 fs duration of pumping at 1.98 μm and the 100 MV/m amplitude of the electric field is −51 dB and −14 dB, respectively.