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

Mode-mode coupling theory is presented for the resonant pumping via dynamical tunneling processes in a deformed microcavity. From the steady-state solution of the coupled differential equations of chaotic modes and a high-Q regular mode, pumping efficiency is obtained as a function of pump detuning, coupling constants and decay rates of the involved modes. 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 the regular mode. We also show that the decay rate of the regular mode is enhanced by dynamical tunneling into all chaotic modes. Analysis method to obtain the effective coupling constant from the pumping efficiencies is presented for a two-dimensional deformed microcavity.