Theory and Computation of Scattering Resonances of Photonic Microstructures

The optical properties of microstructured photonic waveguides are governed, in the scalar approximation, by a Schroedinger equation with a high contrast and oscillatory potential. We outline a Schroedinger scattering resonance perturbation theory for this non-selfadjoint eigenvalue problem. The imaginary parts of the scattering resonance "eigenvalues" correspond to the radiative approach to the study of such waveguides in the scalar approximation. We implement a multiple scale approach to the study of such waveguides in the scalar approximation.