Heisenberg-Langevin theory of an exciton mirror

We develop a Heisenberg-Langevin theory of an exciton mirror accounting for the retardation and the long-range electron-hole exchange. A particular case of a strong transverse magnetic field is analyzed in detail. The optical bistability due to repulsion between the excitons inside the light cone appears to be prone to a modulational instability towards the non-radiative surface polariton modes. Above the corresponding threshold, the pumped 2D exciton gas acts as an optical parametric generator of twin polariton beams. Conversely, below the threshold, the mirror acquires the phase-conjugating properties.