Mode-mode coupling theory of resonant pumping via dynamical tunneling processes in a deformed microcavity

It has recently been demonstrated that resonant pumping of a high- Q resonance mode is possible via the dynamical tunneling from a chaotic sea to the high-Q mode in a deformed microcavity laser [J. Yang et al., Phys. Rev. Lett. 104, 243601 (2010)]. The pumping efficiency of a high-Q lasing mode was enhanced by two orders of magnitude whenever the pump was resonant with a high-Q pump mode, which is localized in a regular region in a phase space, separated from the chaotic sea. Since the pump beam, injected by refraction, moves in the chaotic sea, the resonant enhancement must have come from the dynamical tunneling from the chaotic sea to the regular mode. In this article, we present a mode-mode coupling theory for the resonant pumping via the dynamical tunneling processes in a deformed microcavity. From the steady-state solution of the coupled differential equations of uncoupled chaotic modes and an uncoupled high-Q regular mode, pumping efficiency is obtained as a function of pump detuning, coupling constants and decay rates of the involved uncoupled modes. As a main result we show that the pump-excited chaotic modes as a whole can be regarded as a single pump mode with an effective decay rate and an effective coupling constant with respect to the regular mode. Moreover, we show that the decay rate of the regular mode is enhanced by dynamical tunneling into all chaotic modes, from a cavity-quantum-electrodynamics argument and also from an eigenvalue-problem standpoint. Analysis method to obtain the effective coupling constant and the tunneling rate from the observed pumping efficiencies is presented for a two-dimensional deformed microcavity.