  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.
