Title

A method of moments analysis of microstructured optical fibers

Date of Award

2009

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Advisor(s)

Joseph R. Mautz

Keywords

Optical fibers, Dielectric waveguide, Photonic crystal, Chiral core

Subject Categories

Electrical and Computer Engineering

Abstract

A simple yet accurate numerical technique is developed to analyze the problem of electromagnetic propagation guided by dielectric waveguides of arbitrary cross section. Four classes of waveguides are considered: the single dielectric rod, the single chiral rod, the air-hole assisted optical fibers (AHAOF), and the holey fiber (HF). Waveguides of circular, rectangular, triangular and other cross sections are considered as examples.

The chiral rod has a chiral core. All fibers are surrounded by an infinite layer of dielectric cladding. There are a number of air holes in the cladding of AHAOF and in the core of HF.

The circular tube fiber with one air hole, with two air holes, and the Single Material Fiber are analyzed as special cases of HF. A circular core with thirty six air holes is also analyzed. These holes are arranged in a three layer hexagonal pattern.

The surface equivalence principle is used to replace the waveguides by equivalent electric and magnetic surface currents. These currents are placed on various surfaces that define the waveguide. Radiating in unbounded media with proper material parameters, they produce correct fields in different parts of the waveguide. Enforcing the boundary conditions results in a set of coupled integral equations for the surface currents. These equations are solved using the Method of Moments. Pulses and triangular functions are used as expansion functions. An approximate Galerkin's method is used for testing. The propagation constants are identified by monitoring the condition number of the moment matrix. The eigenvector corresponding to the smallest eigenvalue of the matrix contains the expansion coefficients of the surface currents. The fields are computed using these coefficients.

The method developed here is spurious-free for the first three classes of the problems considered. It is almost spurious-free for the HF. The computed results for all the cases considered agree with exact or numerical data available.

The simplicity, accuracy, and spurious-free nature of the developed method are the main contributions of this dissertation. The main limitation of the method is that it cannot be applied to inhomogeneous waveguides. Being based on a nonlinear eigenvalue problem is another disadvantage of the method.

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