ON THE THEORY OF REFLECTIVITY AND TRANSMISSIVITY OF A LOSSLESS NONLINEAR DIELECTRIC SLAB

For the transverse electric polarization case (TE) we present a treatm ent of the optical reflectivity and transmissivity of a slab whose die lectric coefficient is a real valued function of the light intensity. If this function is numerically integrable with respect to the light i ntensity, our treatment can serve as an algorithm for a numerical solu tion of the nonlinear wave equation. If the dielectric function is pro portional to the intensity, an analytical solution of the cubic wave e quation is given for the electric field strength and for the phase of the field in terms of Weierstrass' elliptic functions and first ellipt ic theta functions, respectively. Evaluating this solution by means of a computer algebra system yields the reflectivity, transmissivity and phase dependency on the incident field intensity and on parameters ch aracteristic for the problem. Certain combinations of the parameters l ead to bistable and multivalued behavior. The solution found is used t o determine the relative extrema of the reflectivity and the critical values of the thickness and of the incident intensity. The results are a generalization of linear optics results. Application of the analysi s to the cubic-quintic wave equation yields the general analytic solut ion which is used to determine the reflectivity of a semi-infinite non linear medium.