Exciton-polariton patterns in coherently pumped semiconductor microcavities

摘要

We theoretically study spatially periodic exciton-polariton patterns in a semiconductor microcavity coherently driven by an optical pump. Patterns grow spontaneously in a uniformly pumped cavity above a certain threshold (Turing instability). By means of a perturbation analysis in the vicinity of this bifurcation point, we determine the conditions for pattern formation and predict their properties. The shape of those patterns depends strongly on the detuning of the pump frequency from the system's resonances. For instance, near the bottom of the lower branch of the polariton dispersion relation, a hexagonal pattern is the most favorable periodic solution similar to pattern formation in optical cavities endowed with a defocusing Kerr nonlinearity. Towards the excitonic resonance, the influence of the upper polariton branch becomes important giving rise to a diversity of other solutions, such as roll, labyrinthine, and honeycomb patterns. Our numerical simulations reveal patterns with point and line defects and the formation of disordered patterns of a soliton gas.