Parametric polariton solitons in coherently pumped semiconductor microcavities

The investigation of exciton-polaritons in semiconductor microcavities operating in the strong-coupling regime is attracting growing interest because of their extraordinary optical properties [1]. Together with the strong excitonic nonlinearities, originating from the Coulomb interaction between excitons, the peculiar dispersion relation of these quasi-particles allows a variety of fundamental effects like optical bistability, low threshold parametric oscillations [2] and formation of robust self-localized states, so-called, cavity polariton solitons (CPSs) [3,4]. It was shown that the inclination of the coherent optical pump (plane wave) endows exciton-polaritons with a kinetic momentum (kx) along one of the orthogonal directions in the plane of the microcavity. It even allows controlling their dispersion. As a result moving 2D CPSs can exist despite the opposite dispersion signs along (x) and orthogonal (y) to the pump momentum directions [4]. In this contribution we provide theoretical evidence of self-localization of polaritons in the direction orthogonal to the pump tilt (y), which is unusual for the defocusing nonlinearity. We study the formation of 1D CPSs excising due to the parametric four-wave mixing of polaritons.