Nonlinear Polarization Effects In A Birefringent Single Mode Optical Fiber

Abstract

In this thesis, an investigation is conducted on the nonlinear polarization effects in a birefringent single mode optical fiber. The thesis begins with an introduction that gives current interests as well as a general review of polarization behavior in a birefringent, single mode fiber. The theory on propagation of light in single mode optical fibers is also introduced to serve ~ a basis for understanding the concepts of nonlinear polarization effects. Then Stokes parameters and the Stokes formalism are introduced and related to the traditional measures of light polarization such as ellipticity and azimuth. The use of Stokes parameters to analyze polarization effects as the beam propagates in a birefringent optical fiber forms the central theme of this thesis. The evolution equations for Stokes parameters when the optical fiber is considered linear are derived using the methods of Brown's Unified Formalism for Polarization Optics. Several Mueller matrices which characterize the polarization effects of birefringence and dichroism are obtained analytically. This provides a means to model the evolution of the Stokes parameters as function of fiber length and orientation angle. Graphical illustrations showing the output polarization change are presented in this thesis. Furthermore, general solutions to the Stokes parameters evolution equations when the optical fiber is considered nonlinear have been obtained analytically in terms of the Jacobian elliptic functions. Graphical illustration showing the nonlinear behavior of the output polarization are also presented. A fundamental and noteworthy aspect of the results presented in this thesis is that when the fiber is considered linear the output Stokes parameters are either periodic or constant with length or orientation angle depending on whether the fiber is assumed to have losses or not. When the solutions are periodic, the three Stokes parameters are observed to have the same periods. However, when the fiber response to propagation is considered nonlinear, the output Stokes parameters are generally doubly periodic, and the three Stokes parameters do not have the same periods. Some cases of aperiodicity are observed and presented. Another interesting and novel result presented in this thesis is that when an intense elliptically polarized beam propagating along a birefringent optical fiber undergoes a change in both its shape and orientation, the critical input intensity at which the light induced birefringence cancels the existing fiber birefringence will increase.