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

TL;DR

This paper introduces an efficient analytical method combining mode normalization and resonant state expansion to model the effects of transverse disorder in optical fibers, including leaky modes, improving the understanding of fiber perturbations.

Contribution

It adapts the resonant state expansion to optical fibers and derives the correct analytical normalization for all fiber modes, enabling accurate modeling of structural disorder effects.

Findings

Successfully models perturbations in capillary and photonic crystal fibers.

Provides a new eigenvalue equation for calculating disorder effects.

Demonstrates the method on two fiber types.

Abstract

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 properties. This is demonstrated for two test systems: a capillary fiber and an endlessly single mode fiber.