Atomically thin semiconductors as nonlinear mirrors

We show that a transition metal dichalcogenide monolayer with a radiatively broadened exciton resonance would exhibit perfect extinction of a transmitted field. This result holds for s- or p-polarized weak resonant light fields at any incidence angle, due to the conservation of in-plane momentum of excitons and photons in a flat defect-free two dimensional crystal. In contrast to extinction experiments with single quantum emitters, exciton-exciton interactions lead to an enhancement of reflection with increasing power for incident fields that are blue detuned with respect to the exciton resonance. We show that the interactions limit the maximum reflection that can be achieved by depleting the incoming coherent state into an outgoing two-mode squeezed state.