Numerical analysis of two-frequency interaction between waves in a nonlinear radiating electromagnetic crystal

Two-frequency interaction between electromagnetic waves in a 2D nonlinear radiating electromagnetic crystal under the conditions of the spatial synchronism of the forward wave at the fundamental frequency and the backward wave at the second harmonic of the fundamental frequency is analyzed. The mathematical model of a 2D radiating electromagnetic crystal is built. The effect of generation of the second harmonic in the case of excitation of this structure by a free-space plane wave is analyzed. The phenomenon of parametric amplification in the case of simultaneous excitation of the electromagnetic crystal by a signal with the fundamental frequency arriving from free space and a planar-waveguide mode with the doubled frequency is studied. The possibility of narrowing the radiation pattern of the structure by means of generation of the second harmonic is shown.