Spectral expansions of open and dispersive optical systems: Gaussian regularization and convergence

Abstract Resonant states (RS), also known as quasi-normal modes, arise in spectral expansions of linear response functions open systems. Manipulation these spatially ‘divergent’ oscillating requires a departure from the usual definitions inner product, normalization and orthogonality typical studies closed A multipolar Gaussian regularization method for RS products is introduced context light scattering shown to provide analytical results crucial product integrals problematic region exterior system. We detail applicability this arbitrary geometries while providing semi-analytic benchmark spherical scatterers. This formulation then used highlight lack ‘convergence’ directly truncated necessity adding non-resonant contributions expansions. Solutions difficulties are illustrated case dispersive media spheres, but methods should prove generalizable