Similarity rules for nonlinear Kerr-like slab optical waveguides

It is shown that the stationary waveguiding properties of TE guided waves in a slab optical waveguide with a nonlinear Kerr-like bounding medium can be described in a compact way by means of the usual normalized effective modal index (b) and a set of only four independent normalized parameters: the well-known normalized thickness ( V) and asymmetry measure (a) of the waveguide, the generalized aspect ratio between film and substrate refractive indexes, and a guided power measure. From an analysis starting on Buckingham´s II-theorem, the similarity rules existing between the above waveguiding structures have been investigated. Allowed and forbidden regions in {b,V,a}-space in order that a guided solution exists have been recognized and classified, with the marginal loci separating different regions being a function of only V and a