arXiv subjects

W. Astar

Publications and source records attributed to W. Astar.

5 recordsLinked to original sources

arXiv2024

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 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

physics.optics↗

arXiv2023

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

The nonlinear coefficient γ 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.

physics.optics↗

arXiv2021

New Analytical Expressions for the Levi-Civita Symbol and Its Treatment as a Generalized Function

New analytical expressions are found for the Levi-Civita symbol using the Kronecker delta symbol. The expressions are derived up to 3 dimensions, extended to higher dimensions, and confirmed in Matlab for 5 dimensions. The expressions can be re-cast in terms of elementary and/or special functions, which lead to the conclusion that the Levi-Civita Symbol can be treated as a generalized, discrete function

math.GM↗

arXiv2021

The Z-Transform of the Levi-Civita Symbol

A derivation of the Z-transform of the Levi-Civita symbol is carried out up to 3 dimensions, and generalized to higher dimensions. Using its Z-transforms, corresponding expressions for the Laplace transform are also found, using Tustin's transform

math.GM↗

arXiv2020

A New Compact Expression for the Powers of Hybrid Modes of the Step-Index Optical Fiber

A new, compact, and exact general expression is developed for the powers of hybrid EH- and HE-modes of the standard step-index optical fiber. The expression is found with the help of the Pauli matrices. The expression is reducible to widely used approximate forms for hybrid mode powers of weakly-guided fibers.

physics.optics↗