Solitons and vortex lattices with microcavity polaritons

I am going to report our recent results on two aspects of nonlinear physics of microcavity polaritons. First, is the two-dimensional localization of exciton polaritons in a coherently pumped semiconductor microcavity operating in the strong-coupling regime. 2D polariton-solitons  can exist despite the fact that the effective mass of linear  polaritons has the opposite signs along the orthogonal directions in the momentum space. Nonlinearities compensating the opposing mass signs have different physical origin, but act simultaneously. They are due to  repulsion of polaritons, which compensate the negative mass effects,  and due to parametric four-wave mixing, which compensate the positive mass effects.  Both of these nonlinearities  support their respective families of one-dimensional solitons, which coexist one with another and with 2D solitons. Second part of my talk is about vortex lattices of exciton polaritons in microcavities operating in the four-wave mixing regime. These lattices  can be practically seeded by a weak signal pulse formed by a superposition of three interfering beams and can be either very robust or can melt through annihilation of vortex-antivortex pairs.