Analysis of nonlinear TE waves in a periodic refractive index waveguide with nonlinear cladding

Formulas are presented for analyzing optical nonlinearity and bistability of TE modes in a periodic refractive index waveguide with nonlinear cladding, both by exact method and by the method of rms approximation. Numerical calculations for realistic periodic refractive index planar waveguide parameters show that the results of the two methods agree excellently when the number of layers of the periodic structure is sufficiently large so that the thin film approximation (the electric field is slowly varying over each period of the periodic structure) is valid. By using rms approximation, the dependence of the modal refractive index on the total power, bistability between core power and total power, and the influence of waveguide parameters on them are discussed.