Complex stationary-phase points in dynamical-tunneling emissions
In a recent paper [Phys. Rev. A 83, 023827 (2011)] it has been suggested, based on numerical simulation, that tunneling emission in dielectric microcavities can be explained through a two-step process: first dynamical tunneling to reach the critical line and then interference among tangential wave components refractively escaped from the critical line. Here we investigate again the tunneling-emission mechanism by using a stationary-phase method in a circular microcavity. It is shown that the stationary-phase point becomes complex for a tunneling emission and gives a tunneling-ray picture. The imaginary part of the point determines the distance {delta} between the tunneling ray and the cavity surface. In addition, we demonstrate numerically that the two-step tunneling process with a proper window function works very well, even in deformed microcavities.