On the physics of propagating Bessel modes in cylindrical waveguides

TL;DR

This paper explores the formation of transverse modes in cylindrical waveguides, demonstrating that including Neumann functions is physically necessary for a complete description, challenging traditional assumptions that exclude them.

Contribution

It introduces a geometrical-wave optics approach showing the importance of Neumann functions in describing waveguide modes, offering a new perspective on mode formation.

Findings

Neumann functions are essential for full mode description.

The outside field of the waveguide naturally arises from the analysis.

A physics-focused approach enhances understanding of mode formation.

Abstract

In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical waveguide. In opposition, the physical mathematics solutions (looking at the mathematical problem and then trying to impose a physical interpretation), when studying cylindrical waveguides yields to the Bessel differential equation and then it is argued that in the core are only the Bessel functions of the first kind those who describe the transverse modes. And the Neumann functions are deemed non physical due to its singularity at the origin and eliminated from the final description of the solution. In this paper we show, using a geometrical-wave optics approach, that the inclusion of this function is physically necessary to describe fully and properly the formation of the propagating transverse modes. Also, the field in the outside of a dielectric waveguide arises in a natural way.