Simplified Electromagnetic Field Expressions for Optical Fibers

A recent paper titled "New Generalized Expressions for the Electromagnetic Fields of the Hybrid Modes of an Optical Fiber Using Complex and Bi-Complex Mathematics" by W. Astar presents a reformulation of the electromagnetic fields associated with hybrid modes in optical fibers. The study employs bi-complex mathematics, which simplifies the expressions compared to traditional complex methods.

The paper outlines the derivation of generalized expressions for these electromagnetic fields using both bi-complex and conventional complex methods, allowing for a comparative analysis. Additionally, the feasibility of bi-complex mathematics is explored in the context of deriving modal powers and orthogonality relations.

This work is significant as it may enhance the understanding and application of optical fibers in various technologies, potentially leading to improvements in telecommunications and data transmission. The simplified mathematical expressions could facilitate more efficient designs and analyses in optical engineering, impacting both academic research and practical applications in the field.

The full paper can be accessed at arXiv:2409.00027.