Existence and stability of TE modes in a stratified non-linear dielectric

Starting from Maxwell's equations for a stratified optical mediumwith a non-linear refractive index, we derive the equationsfor monochromatic planar TE modes. It is then shown that TEmodes in which the electromagnetic fields are travelling wavescorrespond to solutions of these reduced equations in the formof standing waves. The equations of the paraxial approximationare then formulated and the stability of the travelling wavesis investigated in that context.