  We show that the solution of fully nonlinear lasing equations for stadium
cavities exhibits a highly directional emission pattern. This directionality
can be well explained by a ray-dynamical model, where the dominant ray-escape
dynamics is governed by the unstable manifolds of the unstable short periodic
orbits for the stadium cavity. Investigating the cold-cavity modes relevant for
the lasing, we found that all of the high-Q modes have the emission
directionality corresponding to that of the ray-dynamical model.
