  Electromagnetic field interactions in a dielectric medium represent a
longstanding field of investigation, both at the classical level and at the
quantum one. We propose a 1+1 dimensional toy-model which consists of an
half-line filling dielectric medium, with the aim to set up a simplified
situation where technicalities related to gauge invariance and, as a
consequence, physics of constrained systems are avoided, and still interesting
features appear. In particular, we simulate the electromagnetic field and the
polarization field by means of two coupled scalar fields $\phi$,$\psi$
respectively, in a Hopfield-like model. We find that, in order to obtain a
physically meaningful behaviour for the model, one has to introduce spectral
boundary conditions depending on the particle spectrum one is dealing with.
This is the first interesting achievement of our analysis. The second relevant
achievement is that, by introducing a nonlinear contribution in the
polarization field $\psi$, with the aim of mimicking a third order nonlinearity
in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model
framework, whose classical behaviour is analyzed too.
