Group velocity mismatch at ultrashort electromagnetic pulse propagation in nonlinear metamaterials

The parametric interaction of optical wave pulses in metamaterials is considered in the first approximation of the theory of dispersion. The interaction between the quasi-monochromatic pump wave and the wave pulse at the total frequency with quadratic phase modulation is assumed. The results of calculation of the shape of the spectrum of an excited signal wave at a difference frequency are presented for low frequency pumping. It is shown that the effects of group mismatch in metamaterials lead to a narrowing of the spectrum of the excited wave. With an increase in the modulation degree of a weak exciting wave, the spectrum of the excited wave broadens.