What optical fiber modes reveal: group velocity and effective index for external perturbations

Abstract

Precise control of fiber modes and their dispersion is essential, particularly for fields such as nonlinear frequency conversion or biosensing, both of which often require extensive and time-consuming simulations for design optimization. Here, we develop a first-order perturbation theory for predicting the effective index of bound and leaky fiber modes that is applicable for arbitrary global perturbations as long as the perturbations in the external surrounding are constantly homogeneous and isotropic deviations from the unperturbed fiber. This includes changes not only in permittivity and permeability, but also in wavelength. Thus, we are able to calculate the group velocity solely from the field distributions of the fiber modes at a single wavelength, which therefore allows for large-scale parameter sweeps for accurately managing dispersion. We demonstrate the capabilities of our theory for various trial systems such as step index fibers, photonic crystal fibers, and light cages.