# Novel results on propagation characteristics in optical fibers

#### Abstract

A number of new approaches to the understanding of light wave propagation in cylindrical waveguides are described in this study. They include elaborations of known results on fibers with circular cross-section and a new formulation for the understanding of the propagation characteristics of dielectric waveguides with elliptical cross-section.^ The first part is a presentation of a comprehensive review and comparison of the power series expansion and finite difference methods in solving the problem of propagation in cylindrical optical fibers. In particular, a comparison of the accuracy of both methods when calculating the cutoff frequencies of step-index fibers is made. Furthermore, an extension to graded-index fibers by both methods is also shown.^ In the second part, a simple analytic expression is selected to approximate the propagation and delay time of rod waveguides. The explicit formulas yield very small errors in either extreme, i.e. near the cutoff frequency and far away from the cutoff frequency, thus providing much simplification in the estimation of certain optical properties of fibers.^ The third section of the work presents a simple and accurate method to calculate the cutoff frequencies of an optical fiber with elliptical cross-section. This method is easy to implement in a computer program and is applicable to ellipses with any eccentricity. It also allows one to compare the variation of the cutoff frequencies of step-index dielectric waveguides for several differences in the refractive index for a waveguide whose walls are ideal conductors. Finally, the last portion of the research was devoted to extending these results to graded-index fibers. A simple and lucid method to calculate the cutoff frequencies of a graded-index optical fiber with elliptical cross-section is thus presented. The difference between the cutoff frequencies of step-index elliptical fibers and the corresponding cutoff frequencies of graded-index elliptical fibers is found to be relatively small for any given eccentricity. ^

#### Subject Area

Engineering, Electronics and Electrical|Physics, Optics

#### Recommended Citation

Gustavo O Ruiz-Riquer,
"Novel results on propagation characteristics in optical fibers"
(1996).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI9702077.

http://digitalcommons.uri.edu/dissertations/AAI9702077