An Analytical Expression for the Effective Area of the Step-Index Single-Mode Optical Fiber

TL;DR

This paper derives an analytical expression for the effective area of the hybrid HE11 mode in step-index single-mode fibers, linking it to the nonlinear coefficient and electromagnetic field expressions.

Contribution

It provides the first analytical formula for the effective area of the HE11 mode using exact electromagnetic fields, including a simplified approximation.

Findings

Effective area expressed via hypergeometric functions

Simplified formula under weakly-guided approximation

Results agree with established theory

Abstract

The nonlinear coefficient {\gamma} of the step-index single-mode fiber (SMF) is inversely proportional to the effective area of that fiber. An analytical expression for the effective area of the hybrid HE11-mode of the SMF is derived for the first time, using its exact electromagnetic field expressions. The effective area is found in terms of generalized hypergeometric functions. A simpler expression is also deduced under the weakly-guided fiber approximation, and is found to be in agreement with established theory.