Exact theory of nonlinear p-polarized optical waves.

Abstract

Exact calculations are presented of the properties of nonlinear p-polarized waves propagating along the plane boundary between a nonabsorbing, optically self-focusing, nonlinear dielectric and a nonabsorbing positive, or negative, linear dielectric. A nonlinear polarization is used that arises from a number of causes for both Kerr-like and non-Kerr-like saturating media. In the results given here the linear dielectric is a metal, if negative, and is glass if positive. It is found that the variation of the power flow along the guiding surface with effective index, for negative linear dielectrics, will always exhibit a maximum. For data corresponding to copper bounded by, for instance, a self-focusing nonlinear semiconductor, access to this maximum involves such a large change in the refractive index of the nonlinear material, that it is of no practical interest. In the visible better matching of the metal to a nonlinear material can, in principle, be achieved so this maximum may be reached for fairly modest nonlinear changes in the refractive index. A detailed comparison is made with approximations that are based upon a curtailed form of nonlinearity. At low frequencies, for modest nonlinear changes in the refractive index, the dependence of the power flow curve upon the effective guide index is fairly close to several of the earlier published theories. These include a well-known approximation in which the transverse field component is assumed to be dominant. The neighborhood of the maximum, and beyond, becomes accessible at higher operating frequencies and significant differences from earlier approximations may then occur. For positive linear dielectrics the exact theory shows a strong similarity to many more approximate ones, as expected, but the difference between the TM and TE surface wave behavior cannot be discounted. We present several sample calculations of the power flow together with detailed plots of the field components, the magnitude of the nonlinearity, the effect of nonlinearity, and the behavior of the first integral.