Semi-infinite nonlinear electromagnetic crystal

The excitation of a 2D semi-infinite electromagnetic crystal with nonlinear capacitive elements by plane waves is considered in the case of a relatively weak nonlinearity. The method of successive approximations is combined with the Wiener-Hopf method to derive an analytical solution to the boundary problem. The second-harmonic excitation, parametric amplification, and the specific conditions for the interaction of waves of the nonlinear electromagnetic crystal under which the method of successive approximations is incorrect are analyzed. The solution to the boundary problem is derived in the approximation of the 1D electromagnetic crystal and a homogeneous medium.