Energy exchange between electromagnetic waves on the director diffraction grating in planar waveguide with nematic layer

The energy exchange between two coupled TE modes on the diffraction grating of the director in a planar waveguide containing a nematic liquid crystal layer is calculated. The diffraction grating is induced by an external electric field in the nematic layer with periodic anchoring energy at the waveguide surface. The intensity of the signal mode at the output of the nematic layer is calculated as a function of the amplitude and period of the anchoring-energy modulation, the nematic layer sizes, and the electric-field strength. The cases of modes with the same and opposite directions are considered. Analytical expressions for the maximum intensities of the signal mode are derived. In both cases the maximum intensity of the signal mode increases with an increase in the electric-field strength.