Asymmetric scattering and nonorthogonal mode patterns in optical microspirals

Quasibound states in an open system do not in general form an orthogonal and complete basis. It is, however, expected that the nonorthogonality is weak in the case of well-confined states, except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the nonorthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly nonorthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.