On the physics of propagating Bessel modes in cylindrical waveguides

• Published in: American journal of physics Vol. 85; no. 5; pp. 341 - 345
• Main Authors: Gómez-Correa, J. E., Balderas-Mata, S. E., Coello, V., Puente, N. P., Rogel-Salazar, J., Chávez-Cerda, S.
• Format: Journal Article
• Language: English
• Published: Woodbury American Institute of Physics 01-05-2017
• Subjects: Dielectrics; Differential equations; Optics; Physics
• ISSN: 0002-9505; 1943-2909
• DOI: 10.1119/1.4976698

In this paper, we demonstrate that by using a mathematical physics approach—focusing
attention on the physics and using mathematics as a tool—it is possible to visualize the
formation of the transverse modes inside a cylindrical waveguide. The opposite
(physical mathematics) approach looks at the mathematical problem and then tries to impose
a physical interpretation. For cylindrical waveguides, the physical mathematics route leads to
the Bessel differential equation, and it is argued that in the core of the waveguide there are only
Bessel functions of the first kind in the description of the transverse modes. The Neumann
functions are deemed non-physical due to their singularity at the origin and are
eliminated from the final description of the solution. In this paper, by combining geometric optics and
wave optics concepts, we show that the inclusion of the Neumann function is physically
necessary to describe fully and properly the formation of the propagating transverse
modes. With this approach, we also show that the field outside a dielectric waveguide arises in a
natural way.