Three-dimensional solitary waves in dielectric medium

Abstract

The propagation of the electromagnetic field in a transparent dielectric medium can be considered as the re-radiation of electromagnetic waves by the nonlinear in general waves of the medium polarization. On the other hand, the electromagnetic field in the medium can be presented as a flow of quasiparticles - polaritons. The both classical and quantum nonlinear fields in the medium which Lagrangians are capable to describe spontaneous symmetry breakdown lead to the Goldstone massless bosons and massive quasiparticles. The spontaneous breakdown of the symmetry arises in the system if the symmetry of its ground state is lower than initial symmetry. Thus, the translation group is broken and in the system arise massless collective excitations (bosons), and massive quasiparticles. The collective excitations compensate the breakdown of the initial system symmetry. Therefore, the number of spectrum branches of the Goldstone bosons corresponds to the dimension of the sub-group of the ground state symmetry. Quasiparticles are excitations over the ground (vacuum) state of the system. The three-dimensional solitary waves are the special case of these excitations. The solitary or periodic sinusoidal waves of corresponding quasiparticles can arise in both infinite amorphous dielectric medium and dielectric waveguide. The generation conditions of quasiparticle will be determined by the relation between parameters of the field and the dispersion medium properties. The existence of the field in the form of solitary waves is stipulated by properties of the given system field-medium. The periodic global minima of the potential energy form the topological vacuum with finite magnitude of the field at the minima. In the system, it is possible to select the order parameter which magnitude depends on the relation between parameters of the field and medium.