Analytical mode normalization and resonant state expansion for optical fibers – an efficient tool to model transverse disorder

We adapt the resonant state expansion to optical fibers such as capillary and photonic crystal fibers. As a key requirement of the resonant state expansion and any related perturbative approach, we derive the correct analytical normalization for all modes of these fiber structures, including leaky modes that radiate energy perpendicular to the direction of propagation and have fields that grow with distance from the fiber core. Based on the normalized fiber modes, an eigenvalue equation is derived that allows for calculating the influence of small and large perturbations such as structural disorder on the guiding proberties. This is demonstrated for two test systems: a capillary and an endlessly single mode fiber.