This thesis concerns polarization mode dispersion (PMD) in optical fiber communications. Specifically, we study fiber birefringence, PMD stochastic properties, PMD mitigation and the interaction of fiber birefringence and fiber nonlinearity. Fiber birefringence is the physical origin of polarization mode dispersion. Current models of birefringence in optical fibers assume that the birefringence vector varies randomly either in orientation with a fixed magnitude or simultaneously in both magnitude and direction. These models are applicable only to certain birefringence profiles. For a broader range of birefringence profiles, 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 first apply these models to single mode fibers. In particular, two existing models and our four more general models are employed for the evolution of optical fiber birefringence with longitudinal distance to analyze, both theoretically and numerically, the behavior of the polarization mode dispersion. We find that while the probability distribution function of the differential group delay (DGD) varies along the fiber length as in existing models, the dependence of the mean DGD on fiber length differs noticeably from earlier predictions. Fiber spinning reduces polarization mode dispersion effects in optical fibers. Since relatively few studies have been performed of the dependence of the reduction factor on the strength of random background birefringence fluctuations, we here apply a general birefringence model to sinusoidal spun fibers. We find that while, as expected, the phase matching condition is not affected by random perturbations, the degree of PMD reduction as well as the probability distribution function of the DGD are both influenced 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 fiber 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 fibers can significantly widen the compensation bandwidth. In the last part of the thesis, we applied the Manakov-PMD equation and a general model of fiber birefringence to investigate pulse distortion induced by the interaction of fiber birefringence and fiber nonlinearity. We find that the effect of nonlinearity on the pulse distortion differs markedly with the birefringence profile.

This thesis concerns polarization mode dispersion (PMD) in optical fiber communications. Specifically, we study fiber birefringence, PMD stochastic properties, PMD mitigation and the interaction of fiber birefringence and fiber nonlinearity. Fiber birefringence is the physical origin of polarization mode dispersion. Current models of birefringence in optical fibers assume that the birefringence vector varies randomly either in orientation with a fixed magnitude or simultaneously in both magnitude and direction. These models are applicable only to certain birefringence profiles. For a broader range of birefringence profiles, 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 first apply these models to single mode fibers. In particular, two existing models and our four more general models are employed for the evolution of optical fiber birefringence with longitudinal distance to analyze, both theoretically and numerically, the behavior of the polarization mode dispersion. We find that while the probability distribution function of the differential group delay (DGD) varies along the fiber length as in existing models, the dependence of the mean DGD on fiber length differs noticeably from earlier predictions. Fiber spinning reduces polarization mode dispersion effects in optical fibers. Since relatively few studies have been performed of the dependence of the reduction factor on the strength of random background birefringence fluctuations, we here apply a general birefringence model to sinusoidal spun fibers. We find that while, as expected, the phase matching condition is not affected by random perturbations, the degree of PMD reduction as well as the probability distribution function of the DGD are both influenced 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 fiber 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 fibers can significantly widen the compensation bandwidth. In the last part of the thesis, we applied the Manakov-PMD equation and a general model of fiber birefringence to investigate pulse distortion induced by the interaction of fiber birefringence and fiber nonlinearity. We find that the effect of nonlinearity on the pulse distortion differs markedly with the birefringence profile.

This dissertation addresses several aspects pertaining to polarization in optical fibers and optical waveguide devices. In particular, the analysis and design of fibers that maintain polarization over long lengths, provide zero polarization-mode dispersion, and function as polarizers or mode filters are presented. First, optimum designs for high-birefringence as well as single-polarization single-mode fibers are studied. For high-birefringence fibers, several index profiles were obtained that provided high birefringence while achieving zero or very small dispersion in 1.3 μm and 1.55 μm windows. Also, few index profiles were found that resulted in single-polarization single-mode operation with zero or very small dispersion at about 1.3 μm and 1.55 μm. A wavelength range of 100 nm to 500 nm was achieved for truly single-mode operation. Second, a comprehensive analysis of polarization-mode dispersion in a multiple-clad fiber due to ellipticity of fiber cross-section is carried out. The analysis results are then used to design large effective area single-mode dispersion-shifted fiber that provides zero polarization-mode dispersion at the wavelength 1.55 μm. Effective area on the order of 122 μm² with mode-field diameter of about 10 μm have been attained for this design. Tolerance analysis on the transmission parameters due to ±1% and ±2% variations in the radii of the fiber layers is carried out. Finally, a wedge-shape dielectric waveguides bounded by conducting planes is introduced and analyzed. Conductor and dielectric losses for the fundamental mode in waveguides with wedge angle of π/n; n ≥ 1, and 2π/3 as a special case with noninteger azimuthal number have been evaluated. These waveguides generally support fewer number of modes for smaller wedge angles and the modes cannot be of TM type. They find applications as mode filters and polarizers.. / Ph. D.

This thesis presents the results for the temperature variation of the Differential Group Delay (DGD) measurements of a Dispersion Compensation Module (DCM) and interprets the results with a theoretical DGD model based on glass viscoelastic properties and estimated values of some of glass parameters. The results of our analysis demonstrate the existence of long birefringence relaxation times on the order of many hours in response to temperature changes. These results could be of significance in interpreting the behavior of optical fiber systems.

[pt] Este trabalho visa estabelecer na prática a estatística do ganho dependente da polarização (PDG-Polarization Dependent Gain) em sistemas ópticos com amplificação Raman. A amplificação Raman depende fortemente da polarização relativa entre os fótons de bombeio e de sinal, que tem que ser paralelas para máximo ganho [1]. Portanto, a birrefringência é um importante limitador de desempenho de sistemas de longa distância amplificados por esta técnica visto que modifica os estados de polarização de forma diferente para cada comprimento de onda. A birrefringência varia aleatoriamente de acordo com as flutuações do ambiente onde está a fibra óptica, dando origem à dispersão dos modos de polarização, efeito este conhecido pela sigla PMD. Alguns experimentos recentes mostraram que o amplificador Raman não só depende do estado de polarização do sinal de entrada, mas também que o valor da dependência do ganho com a polarização (PDG- Polarization Dependent Gain) flutua devido a natureza aleatória da PMD [4,5]. É importante conhecer a estatística da PDG, sua relação com a PMD e como a PDG pode ser reduzida a níveis aceitáveis. Nesse trabalho será medida experimentalmente a distribuição estatística da PDG em fibras de dispersão deslocada e os resultados comparados com as previsões teóricas dadas por [2]. / [en] Raman amplifiers are very attractive because they provide a large and relatively flat gain over a wide bandwidth while maintaining a small noise figure, and they can be made using regular silica fiber. However, the Raman Gain coefficient is polarization sensitive and can be up to ten times higher when the signal and pump polarization states are parallel rather than perpendicular [1]. Usually fibers present some degree of residual asymmetry - because the fiber core is slightly out-of-round, or because of mechanical stress on the deployed fiber - and this causes polarization mode dispersion. The light traveling along one polarization axis moves slower or faster than the light polarized along the other axis. This effect distorts the signal and causes polarization fluctuations along the fiber. As the Raman gain is higher when the signal and pump polarization states are parallel these fluctuations of the relative polarization between signal and pump vary the instantaneous value of the Raman gain. So the Polarization Dependence Gain (PMG) is directly related to the PMD. Several experimental studies have shown not only that the gain of raman amplifiers depends on the state of polarization of the input signal but also that this polarization-dependent gain (PDG) fluctuates over a wide range because of the random nature of polarization mode dispersion (PMD) [4,5]. It is important to know the statistics of PDG, its relationship to the PMD, and how the PDG can be reduced to acceptable low levels. In this letter we will demonstrate experimentally the statistical distribution of the PDG given by [2]. This In this work the polarization dependent gain (PDG) fluctuations due to PMD in Raman amplified optical transmissions is experimentally demonstrated.

This thesis examines polarization and polarization mode dispersion (PMD) dynamics in optical fibers as well as the evaluation of probability density functions and bit error rates in a realistic wavelength division multiplexed (WDM) optical communication systems. In the first part of the thesis, experimental studies of the dynamics of polarization in a dispersion compensation module (DCM) are performed in which mechanical shocks are imparted to several different DCMs by dropping a steel ball on the outer casing at different locations and from different heights and the resulting rapid polarization fluctuations are measured. We provide a theoretical model that accounts for the dynamic birefringence generated due to the impact. Next, an experimental technique is proposed to detect the location of temporal polarization activity in WDM systems. It is demonstrated theoretically and in simulations that measurement of both the PMD vector and the Stokes parameters at the WDM frequencies enables the detection of the location of such activity. Different linear prediction procedures are applied to the differential group delay of an optical fiber link assumed to obey the hinge model. The hinges are modeled as polarization rotators with fixed rotation axes and sinusoidally varying rotation angles. Three prediction methods are investigated and consequently compared: an autoregressive model (AR) with Kalman filter, a pattern imitation method and a Taylor expansion technique. The effect of measurement noise on the prediction horizon is also investigated for each prediction method. Using a physically reasonable stochastic model for the hinges, we derive analytical expressions for the temporal autocorrelation functions of the state of polarization (SOP) and the PMD vector. The obtained analytical results are compared to simulations. Finally, we apply the multicanonical method to the probability density function of received symbols and the symbol error ratio (SER) in a dual polarization quadrature phase shift keyed (DP-QPSK) WDM system. We simulate five co propagating channels at a symbol rate of 10.7 GBaud/s and account for PMD and nonlinear effects. We evaluate the performance of the system for two different cases: single mode fibers with full dispersion compensation at the end of the link, effective large area fibers (LEAF) with full dispersion compensation at the end of the link.

I examine two methods for modeling the temporal dynamics of optical communication networks that rapidly and accurately simulate the statistics of unlikely but physically significant system configurations. First, I implement a fiber emulator based upon a random uniform walk over the Poincaré sphere that reproduces the expected polarization temporal autocorrelation statistics with a small number of emulator sections. While easy to implement numerically, the increased computational efficiency afforded by this approach allow simulations of the PMD temporal dynamics to be preferentially biased towards regions of low probability using standard multicanonical methods for the first time. Then, in a subsequent study, I present a general transition matrix formalism that additionally applies to other time-dependent communication systems. I compare the numerical accuracy of several transition matrix sampling techniques and show that straightforward modifications of the acceptance rule can significantly increase computational efficiency if the numerical parameters are chosen to ensure a small self-transition probability within each discretized histogram bin. The general applicability of the transition matrix method is then demonstrated by calculating the outage dynamics associated with the hinge model of polarization evolution and, separately, fading in wireless communication channels. Further, I develop a Magnus expansion formalism for the rapid and accurate estimation of the frequency dynamics of optical polarization that extends the work of Ref.[94] to systems with PMD and PDL. My approach reproduces the power-series expansion and differential equation solution techniques of previous authors while also preserving the required symmetries of the exact solution in every expansion order. This significantly improves the bandwidth of high estimation accuracy, making this method well-suited to the stochastic analysis of PMD and PDL induced system penalty while also yielding physically realizable operator expansions applicable to the joint compensation of PMD and PDL. Finally, I employ high-speed polarimetery to demonstrate experimentally that low-amplitude mechanical excitations of commercially available dispersion compensation modules can excite high-frequency, > 75,000 rotations/s, polarization transients that are nearly invariant between successive measurements. I extend this procedure to measurements of the transient evolution of PMD.

This thesis examines polarization and polarization mode dispersion (PMD) dynamics in optical fibers as well as the evaluation of probability density functions and bit error rates in a realistic wavelength division multiplexed (WDM) optical communication systems. In the first part of the thesis, experimental studies of the dynamics of polarization in a dispersion compensation module (DCM) are performed in which mechanical shocks are imparted to several different DCMs by dropping a steel ball on the outer casing at different locations and from different heights and the resulting rapid polarization fluctuations are measured. We provide a theoretical model that accounts for the dynamic birefringence generated due to the impact. Next, an experimental technique is proposed to detect the location of temporal polarization activity in WDM systems. It is demonstrated theoretically and in simulations that measurement of both the PMD vector and the Stokes parameters at the WDM frequencies enables the detection of the location of such activity. Different linear prediction procedures are applied to the differential group delay of an optical fiber link assumed to obey the hinge model. The hinges are modeled as polarization rotators with fixed rotation axes and sinusoidally varying rotation angles. Three prediction methods are investigated and consequently compared: an autoregressive model (AR) with Kalman filter, a pattern imitation method and a Taylor expansion technique. The effect of measurement noise on the prediction horizon is also investigated for each prediction method. Using a physically reasonable stochastic model for the hinges, we derive analytical expressions for the temporal autocorrelation functions of the state of polarization (SOP) and the PMD vector. The obtained analytical results are compared to simulations. Finally, we apply the multicanonical method to the probability density function of received symbols and the symbol error ratio (SER) in a dual polarization quadrature phase shift keyed (DP-QPSK) WDM system. We simulate five co propagating channels at a symbol rate of 10.7 GBaud/s and account for PMD and nonlinear effects. We evaluate the performance of the system for two different cases: single mode fibers with full dispersion compensation at the end of the link, effective large area fibers (LEAF) with full dispersion compensation at the end of the link.

This thesis presents the results for the temperature variation of the Differential Group Delay (DGD) measurements of a Dispersion Compensation Module (DCM) and interprets the results with a theoretical DGD model based on glass viscoelastic properties and estimated values of some of glass parameters. The results of our analysis demonstrate the existence of long birefringence relaxation times on the order of many hours in response to temperature changes. These results could be of significance in interpreting the behavior of optical fiber systems.

Polarization division multiplexing (PolDM) is a promising way to improve the spectral efficiency of fiber-optic communication systems. However, PolDM systems suffer greatly from polarization mode dispersion (PMD), especially in long-haul systems. PMD is time-varying and is intrinsically hard to compensate. Current PMD compensators are complicated and expensive to build, adding to the cost and complexity of practical PolDM systems. We propose a new differential polarization time coding scheme combined with controlled polarization rotation to increase the system tolerance to PMD. An encoding algorithm, a differential receiver design, and a decoding algorithm are described in detail. Controlled polarization rotation is achievable using conventional Mach-Zehnder interferometers that are used to modulate the signal. Simulation results show that significant improvement in PMD tolerance can be achieved with little added complexity. Given a certain transmission distance, our proposed system can also increase the achievable data rate compared to a PolDM differential quadrature phase shift keying system.