Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction

Beam coupling influenced by nonlinearly induced diffraction, an effect stemming from the div E-->-term in the wave equations, is stressed in the study. The system considered consists of two beams carried by TE-modes at frequencies of omega and 2omega in quadratic nonlinear planar optical waveguides. The power-conservation law, the Lagrangian and the Hamiltonian of the system, as well as the equations governing its stationary states are derived. It is shown that the nonlinearly induced diffraction modifies the second-order nonlinear terms and acts as an effective third-order nonlinearity. The procedure for dealing with modifications caused by effects like the nonlinearly induced diffraction within the framework of a paraxial approach is discussed. The numerical analysis carried out has the nonlinear wave-number shift and the linear phase mismatch as parameters. The influence of the nonlinearly induced diffraction on the shape (the amplitude and the width) of the solitary waves is demonstrated.