Waveguide properties of a film with a parabolic profile of the refractive index embedded in a medium with photorefractive nonlinearity

Waveguide properties of a film with a parabolic spatial profile of the refractive index inserted in a medium with diffusion type of photorefractive nonlinearity are described theoretically. Two new types of guided waves with a spatial profile localized along the film boundaries are found. Exact solutions to the wave equation corresponding to even and odd modes are obtained. The wave of the first type attenuates with oscillations in the photorefractive coating media, whereas the wave of the second type attenuates without oscillations. The two wave types also differ from each other by the range of values of the propagation constant. The obtained modes exist at certain discrete values of the propagation constant, which depend on the optical parameters of the system and the film thickness. The total power flow of all types of modes is calculated and the effect of the film thickness is analyzed. Waveguide modes can only be excited when the energy of the exciting beam is greater than the critical value of the wave total power flow. A large fraction of the energy is concentrated in the photorefractive plates at small film thicknesses. The redistribution of energy between the film and the photorefractive plates occurs with an increase in the film thickness.