Analytical Expressions for Effective Indices of Modes of Optical Fibers Near and Beyond Cutoff

TL;DR

This paper derives analytical formulas for the effective indices of optical fiber modes near cutoff, revealing new properties such as wavelength independence of the EH-mode group index at cutoff in non-dispersive materials.

Contribution

It introduces a first-order Taylor series approximation for mode effective indices near cutoff, enabling the derivation of previously unknown mode characteristics.

Findings

EH-mode group index at cutoff is wavelength-independent in non-dispersive materials

The approximation is valid beyond cutoff where modes are lossy

New mode properties are derived using the analytical expression

Abstract

We derive an analytical expression for the effective indices of modes of circular step-index fibers valid near their cutoff wavelengths. The approximation, being a first-order Taylor series of a smooth function, is also valid for the real part of the effective index beyond cutoff where the modes become lossy. The approximation is used to derive certain previously unknown mode properties. For example, it is shown that for non-dispersive materials the EH-mode group index at cutoff, surprisingly, does not depend on wavelength, core radius, or even radial mode order.