A thesis presented to the University of Waterloo in ful?lment of
the thesis requirement for the degree of Doctor of Philosophy in
Physics.
Waterloo, Ontario, Canada, 2007.
Abstract
This thesis conces polarization mode dispersion (PMD) in optical ?ber communications. Speci?cally, we study ?ber birefringence, PMD stochastic properties, PMD mitigation and the interaction of ?ber birefringence and ?ber nonlinearity. Fiber birefringence is the physical origin of polarization mode dispersion. Current models of birefringence in optical ?bers assume that the birefringence vector varies randomly either in orientation with a ?xed magnitude or simultaneously in both magnitude and direction. These models are applicable only to certain birefringence pro?les. For a broader range of birefringence pro?les, we propose and investigate four general models in which the stochastically varying amplitude is restricted to a limited range. In addition, mathematical algorithms are introduced for the numerical implementation of these models. To investigate polarization mode dispersion, we ?rst apply these models to single mode ?bers. In particular, two existing models and our four more general models are employed for the evolution of optical ?ber birefringence with longitudinal distance to analyze, both theoretically
and numerically, the behavior of the polarization mode dispersion. We ?nd that while the probability distribution function of the di?erential group delay (DGD) varies along the ?ber length as in existing models, the dependence of the mean DGD on ?ber length di?ers noticeably from earlier predictions. Fiber spinning reduces polarization mode dispersion e?ects in optical ?bers.
Since relatively few studies have been performed of the dependence of the reduction factor on the strength of random background birefringence ?uctuations, we here apply a general birefringence model to sinusoidal spun ?bers. We ?nd that while, as expected, the phase matching condition is not a?ected by random perturbations, the degree of PMD reduction as well as the probability distribution function of the DGD are both in?uenced by the random components of the birefringence. Together with other researchers, I have also examined a series of experimentally realizable procedures to compensate for PMD in optical ?ber systems. This work demonstrates that a symmetric ordering of compensator elements combined with Taylor and Chebyshev approximations to the transfer matrix for the light polarization in
optical ?bers can signi?cantly widen the compensation bandwidth. In the last part of the thesis, we applied the Manakov-PMD equation and a general model of ?ber birefringence to investigate pulse distortion induced by the interaction of ?ber birefringence and ?ber nonlinearity. We ?nd that the e?ect of nonlinearity on the pulse distortion di?ers markedly with the birefringence pro?le.
Waterloo, Ontario, Canada, 2007.
Abstract
This thesis conces polarization mode dispersion (PMD) in optical ?ber communications. Speci?cally, we study ?ber birefringence, PMD stochastic properties, PMD mitigation and the interaction of ?ber birefringence and ?ber nonlinearity. Fiber birefringence is the physical origin of polarization mode dispersion. Current models of birefringence in optical ?bers assume that the birefringence vector varies randomly either in orientation with a ?xed magnitude or simultaneously in both magnitude and direction. These models are applicable only to certain birefringence pro?les. For a broader range of birefringence pro?les, we propose and investigate four general models in which the stochastically varying amplitude is restricted to a limited range. In addition, mathematical algorithms are introduced for the numerical implementation of these models. To investigate polarization mode dispersion, we ?rst apply these models to single mode ?bers. In particular, two existing models and our four more general models are employed for the evolution of optical ?ber birefringence with longitudinal distance to analyze, both theoretically
and numerically, the behavior of the polarization mode dispersion. We ?nd that while the probability distribution function of the di?erential group delay (DGD) varies along the ?ber length as in existing models, the dependence of the mean DGD on ?ber length di?ers noticeably from earlier predictions. Fiber spinning reduces polarization mode dispersion e?ects in optical ?bers.
Since relatively few studies have been performed of the dependence of the reduction factor on the strength of random background birefringence ?uctuations, we here apply a general birefringence model to sinusoidal spun ?bers. We ?nd that while, as expected, the phase matching condition is not a?ected by random perturbations, the degree of PMD reduction as well as the probability distribution function of the DGD are both in?uenced by the random components of the birefringence. Together with other researchers, I have also examined a series of experimentally realizable procedures to compensate for PMD in optical ?ber systems. This work demonstrates that a symmetric ordering of compensator elements combined with Taylor and Chebyshev approximations to the transfer matrix for the light polarization in
optical ?bers can signi?cantly widen the compensation bandwidth. In the last part of the thesis, we applied the Manakov-PMD equation and a general model of ?ber birefringence to investigate pulse distortion induced by the interaction of ?ber birefringence and ?ber nonlinearity. We ?nd that the e?ect of nonlinearity on the pulse distortion di?ers markedly with the birefringence pro?le.