Abstract
This approach permits in principal to consider propagation over finite lengths of waveguide of general uniform nonlinearity, with arbitrary excitation. At a specific wavelength and angular orientation of the incident beam, the structure "resonate"; namely, complete interference occurs and no light is transmitted. The bandwidth of the resonance is based on parameters such as the grating depth, the thickness of the waveguide layer...etc.
In this paper we present a study of multilayer structure( grating, non linear waveguide and other layers of different materiel), this study based on the development of the actual electromagnetic field in terms of modes of a linear dielectric guide. And we used the nonlinearity parameter (Kerr effect) as a perturbation it means that we analyse the electromagnetic equations in linear waveguide and at the end we add the nonlinear parameter under certain condition.
We analysed the effect of geometric and nonlinear parameters of the structure in the transmission ratio, the results show that the bandwidth can be effected by the intensity of incident beam and it can range from 0.03 nm to several nanometers. Finally we observe that the transmitted intensity can be controlled by these parameters and can be modified by the effect of the last one (nonlinear parameter).