Leaky-mode expansion of the electromagnetic field inside dispersive spherical cavity

Rigorous justification is presented for a recently introduced method to construct leaky-mode expansions of electromagnetic fields excited inside a spherical cavity filled with a dispersive, lossy medium. In a departure from the traditional approaches, our construction does not rely on Green's functions, rather it starts from a judiciously chosen auxiliary meromorphic function. Convergence of both the series expansions and of the over-completeness relations for the leaky modes is proven for a realistic model of chromatic dispersion.