Quantization and soliton-like solutions for the $$Phi Psi $$-model in an optic fiber

In the framework of a mesoscopical model for dielectric media we provide an analytical description for the electromagnetic field confined in a cylindrical cavity containing a finite dielectric sample. This system is apted to simulate the electromagnetic field in a optic fiber, in which two different regions, a vacuum region and a dielectric one, appear. A complete description for the scattering basis is introduced, together with field quantization and the two-point function.Furthermore, we also determine soliton-like solutions in the dielectric, propagating in the sample of nonlinear dielectric medium.