In this paper we study the problem of electromagnetic wave propagation in a3-D optical fiber. The goal is to obtain a solution for the time-harmonicfield caused by a source in a cylindrically symmetric waveguide. Thegeometry of the problem, corresponding to an open waveguide, makes theproblem challenging. To solve it, we construct a transform theory whichis a nontrivial generalization of a method for solving a 2-D version ofthis problem given by Magnanini and Santosa.The extension to 3-D is made complicated by the fact that the resultingeigenvalue problem defining the transform kernel is singular both at theorigin and at infinity. The singularities require the investigation ofthe behavior of the solutions of the eigenvalue problem. Moreover, thederivation of the transform formulas needed to solve the wavepropagation problem involves nontrivial calculations.The paper provides a complete description on how to construct thesolution to the wave propagation problem in a 3-D optical waveguide withcylindrical symmetry. A follow-up article will study the particularcases of a step-index fiber and of a coaxial waveguide. In those caseswe will obtain concrete formulas for the field and numericalexamples.
|Numero di pagine||33|
|Rivista||Mathematical Models and Methods in Applied Sciences|
|Stato di pubblicazione||Published - 2004|
All Science Journal Classification (ASJC) codes