We study the non-Markovian quantum dynamics of an emitter inside an open multimode cavity, focusing on the case where the emitter is resonant with high-frequency cavity modes. Based on a Greens function technique suited for open photonic structures,
we study the crossovers between three distinct regimes as the coupling strength is gradually increased: (i) overdamped decay with a time scale given by the Purcell modified decay rate, (ii) underdamped oscillations with a time scale given by the effective vacuum Rabi frequency, and (iii) pulsed revivals. The final multimode strong coupling regime (iii) gives rise to quantum revivals of the atomic inversion on a time scale associated with the cavity round-trip time. We show that the crucial parameter to capture the crossovers between these regimes is the nonlinear Lamb shift, accounted for exactly in our formalism.
The angular emission pattern of a random laser is typically very irregular and difficult to tune. Here we show by detailed numerical calculations that one can overcome the lack of control over this emission pattern by actively shaping the spatial pum
p distribution. We demonstrate, in particular, how to obtain customized pump profiles to achieve highly directional emission. Going beyond the regime of strongly scattering media where localized modes with a given directionality can simply be selected by the pump, we present an optimization-based approach which shapes extended lasing modes in the weakly scattering regime according to any predetermined emission pattern.
