Nonlinear directional coupler with variable coupling coefficient and variable nonlinear refractive index coefficient

In this paper, we report on the study of the coupled mode equations for nonlinear directional coupler (NLDC) in which both linear coupling coefficient and nonlinear refractive index coefficient are functions of propagation distance. We show, for the first time, to the best of our knowledge, that the equations for the general case can be transformed to those for the NLDC with constant linear coupling coefficient and that they can also be transformed to equations describing NLDC with constant nonlinear refractive index coefficient but extra loss or gain as long as the original nonlinear coefficients are the same for the two constituent waveguides. Combining the two transformations, we conclude that the equations for a general NLDC can be transformed to a conventional NLDC with extra loss or gain as long as the original nonlinear coefficients are the same for the two constituent waveguides. The potential applications of the proposed transformations are also discussed.