Steady state electromagnetic wave propagation in weakly nonlinear media

A theory of steady state nonlinear wave propagation is developed using a Volterra series formalism. Under the term “steady state wave propagation” we imply a state in which wave parameters remain constant in the time- and space-domain. Detailed consideration is given to quadratic homogeneous medium. Conditions for the existence of such a state in static and dynamic meanings are investigated. It shown that the main condition is a smallness of the total wave energy. Other necessary factors are medium dispersive properties and a correlation between nonlinearity and dispersion values. An estimate for high harmonics´ amplitudes ratio in a steady state is obtained for a case with a negligible small dispersion. But in such a case this state turns out to be unachievable in evolutionary processes. Sufficient closed form conditions for dispersive properties providing the dynamic achievability of a steady state are obtained