Phase effects at second-harmonic generation in metamaterials

We develop the theory of second-harmonic generation in metamaterials where fundamental radiation is considered in the constant-intensity approximation taking into account the phase changes of interacting waves. We investigate the second-harmonic wave intensity in metamaterials at different parameters of the problem under consideration. We consider a self-action effect of the light wave in metamaterials in view of the phase changes of all the interacting waves and compare this effect with an analogous effect in usual homogeneous quadratic media. We show that it is possible to change the phase velocity of the pump wave by varying such parameters as the pump intensity, nonlinear medium length, and phase mismatch between the interacting waves. The metamaterials under consideration provide a possibility to change the phase of the fundamental radiation of order of magnitude higher than those in the usual homogeneous quadratic media.