Peculiarities of periodic and aperiodic energy-exchange regimes in the cascade quasi-synchronous parametric frequency conversion

The domains of existence and peculiarities of exact analytic solutions of the problem of quasi-synchronous interaction of four plane collinear monochromatic waves — modes in a quadratically nonlinear medium during cascade frequency conversion are analysed. It is shown that the unusual types of multicomponent cnoidal and solitary soliton-like waves (of periodic and aperiodic energy-exchange regimes) are realised. Two of the four components of the latter are proportional to the real and imaginary parts of the well-known Lorentzian dependence, which is commonly used to describe the dispersion of contributions from resonance transitions to the complex permittivity in the case of homogeneous line broadening.