New Generalized Expressions for the Electromagnetic Fields of the Hybrid Modes of an Optical Fiber Using Complex and Bi-Complex Mathematics

TL;DR

This paper introduces a bi-complex mathematical approach to derive simplified and generalized expressions for the electromagnetic fields of hybrid modes in optical fibers, improving analytical clarity and computational efficiency.

Contribution

It presents a novel bi-complex mathematical framework for analyzing optical fiber modes, offering simpler expressions and generalized formulas compared to traditional methods.

Findings

Bi-complex mathematics simplifies electromagnetic field expressions.

Generalized formulas for modal powers and orthogonality are derived.

Feasibility of bi-complex approach for weakly-guided fibers is demonstrated.

Abstract

The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized expressions for the electromagnetic fields are also found using both formulations for comparative purposes. Furthermore, the feasibility of bi-complex mathematics is investigated for the derivation of the modal powers, orthogonality relations, and the weakly-guided fiber approximation