The spectrum of the second-harmonic of a powerful laser pulse with the account of cubic nonlinearity in metamaterial

In the non-stationary process of doubling the frequency of high-power laser radiation in metamaterials, the effects of self- and cross-phase modulation, related to the cubic nonlinearity of the medium, are considered. It is assumed that the pump wave propagates in a region with negative refraction. It is shown that in the case of a nonlinear optical process of frequency doubling of an intense light wave in a metamaterial, it is important to take into account the influence of a powerful pump wave. It is shown that the frequency shift of the maximum of the harmonic spectrum in the metamaterial is related to the cubic nonlinearity of the medium. It is shown how the width of the spectrum of the second-harmonic depends on the pump intensity, linear and nonlinear phase detuning. In addition, analytical expressions are obtained for the optimal values of frequency detuning and group velocities on which the maximum of the harmonic spectrum is obtained for non-stationary generation in a metamaterial. Estimations of the quasistatic interaction lengths and the frequency shift of the second-harmonic spectrum are given. By varying the linear phase detuning or the pump intensity, it is possible to manipulate the frequency shift of the maximum of the harmonic spectrum, and from here one can realize a smooth rearrangement of the central frequency of the harmonic spectrum.