A hybrid implicit-explicit FDTD scheme for solving the scalar wave equation in non-linear optical waveguides

Because of its versatility the finite-difference time-domain (FDTD) method has become the method of choice for solving electromagnetic propagation and scattering problems. Extension of the method to handle non-linear media has also been reported, but potential problems with stability and model accuracy may arise due to the usage of explicit discretization. A hybrid implicit-explicit FDTD scheme is proposed which eliminates these problems in regions of non-linear media while retaining the computational simplicity of the explicit scheme in linear regions. Preliminary simulation results for a non-linear slab waveguide are presented and compared with those obtained from a purely explicit scheme.