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

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 using the widely used, conventional complex method. Generalized expressions for the electromagnetic fields are also found using both methods, for comparative purposes. Furthermore, the feasibility of bi-complex mathematics is investigated for the derivation of the modal powers and the orthogonality relation.