The fourth harmonic generation in a Bragg resonator on a film with quadratic nonlinearity

In this paper physical effects in a resonator formed by non-periodic Bragg reflector and non-linear film situated on metal plane are theoretically studied. On the first step a linear spatial problem must be solved for each frequency harmonic to obtain transmission matrices of Bragg structure. The second step is devoted to finding on nonlinear film amplitudes of scattered fundamental and higher harmonics if amplitude of direct wave of the fundamental harmonic is known. On the third step amplitudes of all waves on beginning of Bragg structure can be found as functions against direct amplitude of fundamental harmonic on the film. On the fourth step it is possible to find amplitudes of scattered waves as functions against amplitude of the incident wave. Thus linear problem with complicated spatial in homogeneity, time nonlinear problem and problem of hysteresis can be solved separately.