We study the frequency up- and down-conversion based on the cascaded process which accompanies large phase mismatching between fundamental and intermediate waves. So, for example, we propose using the cascaded Second-Harmonic Generation (SHG) to implement the frequency conversion process, which is similar to that occurring in a medium with cubic susceptibility. At phase matching between the fundamental wave and the third-harmonic wave, Third Harmonic Generation (THG) occurs with high efficiency (94.5%). We demonstrate that the cascaded process may also influence negatively on the frequency conversion processes. SHG in a medium with combined quadratic and cubic nonlinear response accounting for weak THG at large phase mismatching demonstrates that in some cases, the second harmonic intensity evolution is different, whether we take into account of weak THG process or not. So, then the intensity at doubled frequency may be much lower in certain sections in comparison with those without accounting for THG. We study such an influence of weak THG both for pulses with long duration by developing analytical approach and for short pulses based on computer simulation.
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