Dipole lasing phase transitions in media with singularities in polarizabilities

Abstract

We show that a divergence in the optical polarizability of a heterogeneous medium with nonlinear amplification and a strong dipole-dipole interaction between particles can lead to a phase transition, for which the dipole momentum of the particles or the dipole radiation rate can be taken as order parameters. The "dipole laser" (Phys. Rev. A 71, 063812 (2005)) can be used both as a simple example of such a second-order phase transition and to provide a recipe for its analysis. We show that similar phase transitions may be possible for a nanoparticle on the surface of an optically active medium and at the "Clausius-Mossotti" catastrophe in a bulk heterogeneous medium.