Harmonics nonlinear interaction in the waveguide with layered periodic walls

Theoretical research of harmonics interaction in nonlinear guiding layer between two periodic layered structures is carried out. We used the method based Green´s formula for the small nonlinearity, i.e. for the case when the nonlinear interaction energy is small compared with the interacting waves energy. The analytical relations for the first and second harmonics amplitude are obtained. It Is shown that nonlinear coefficients become maximal in the point where Bragg resonance condition realize on all structure layers of investigated waveguide including guiding layer. We explain some experimental data using the results obtained