Date of Award

August 2014

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Engineering

First Advisor

C. Law

Committee Members

A. Mafi, M. Ranji, H. Hosseini, R. Elhajjar

Abstract

The propagation of optical vortices (OVs) in linear and nonlinear media is an important field of research in science and engineering. The most important goal is to explore the properties of guiding dynamics for potential applications such as sensing, all-optical switching, frequency mixing and modulation. In this dissertation, we present analytical methods and numerical techniques to investigate the propagation of an optical vortex in fiber array waveguides. Analytically, we model wave propagation in a waveguide by coupled mode Equations as a simplified approximation. The beam propagation method (BPM) is also employed to numerically solve the paraxial wave Equation by finite difference (FD) techniques. We will investigate the propagation of fields in a 2D triangular lattice with different core arrangements in the optical waveguide. In order to eliminate wave reflections at the boundaries of the computational area, the transparent boundary condition (TBC) is applied. In our explorations for the propagation properties of an optical vortex in a linear and a non-linear triangular lattice medium, images are numerically generated for the field phase and intensity in addition to the interferogram of the vortex field with a reference plane or Gaussian field. The finite difference beam propagation method (FD-BPM) with transparent boundary condition (TBC) is a robust approach to numerically deal with optical field propagations in waveguides.

In a fiber array arranged in triangular lattices, new vortices vary with respect to the propagation distance and the number of cores in the fiber array for both linear and nonlinear regimes. With more cores and longer propagation distances, more vortices are created. However, they do not always survive and may disappear while other new vortices are formed at other points.

In a linear triangular lattice, the results demonstrated that the number of vortices may increase or decrease with respect to the number of cores in the array lattice. In a nonlinear triangular lattice, however, the number of vortices tends to increase as the core radius increases and decrease as the distance between cores increases. Investigations revealed that new vortices are generated due to the effects of the phase spiral around the new points of zero intensity. These points are formed due to the mode coupling of the optical field between the cores inside the array.

In order to understand the dynamics of vortex generation, we examine vortex density, defined as the total number of vortices per unit area of the fiber array. This parameter is to be explored versus the propagation distance, the core radius size and the distance between cores. The Shack-Hartmann wavefront sensor can be employed to find the vortex density and the locations of vortices. Simulation results revealed that the vortex density increases with respect to propagation distance until saturation. It also increases with an increasing radius size but decreases with increasing distance between the array cores for linear and nonlinear regimes.

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