  The mechanism of unidirectional emission of high Q Whispering Gallery mode in
deformed circular micro- cavities is studied and firstly presented in this
paper. In phase space, light in the chaotic sea leaks out the cavity through
the refraction regions, whose positions are controlled by stable islands.
Moreover, the positions of fixed points according to the critical line in
unstable manifolds mainly determines the light leak out from which refraction
region and the direction of the emission. By controlling the cavity shape, we
can tune the leaky regions, as well as the positions of fixed points, to
achieve unidirectional emission high Q cavities with narrow angular divergence
both in high and low refractive index mater
