Outer resonances and effective potential analogy in two-dimensional dielectric cavities

Outer resonances are studied as one type of quasinormal modes in two-dimensional dielectric cavities with refractive index $n>1$. The outer resonances can be verified as the resonances which survive only outside the cavity in the small opening limit of the dielectric disk. We have confirmed that the outer resonances universally exist in deformed cavities irrespective of the geometry of cavity and they split into nearly degenerate states in slightly deformed cavity. Also we pointed out that the effective potential analogy is inapplicable to the description of outer resonances. Since most outer resonances in the dielectric cavities have quite high leakages, they would affect to the broad background in the density of states. Especially, for TE polarization case, relatively low-leaky outer resonances exist and it presents the possibility that they can interact with the inner resonances and affect lasing modes.