Jitter can be generally modeled as a superposition of an unbounded random component that follows a Gaussian distribution and a bounded deterministic component. It is usually assumed that the probability distribution of total jitter for very large values of jitter tends to a purely Gaussian distribution. The standard deviation of this Gaussian distribution is identical to the standard deviation of the random component and the mean value of the distribution is related to the deterministic component. A mathematical justification for this assumption is, however, lacking in the literature. In this work, a general asymptotic expression is derived for the tail of the total jitter distribution. It is shown that, to first order, the tail of the distribution can be expressed as a Gaussian function divided by a power function of jitter. Asymptotic expressions for the cumulative distribution function and the Q-scale are also derived. The implications of these results for the accuracy of broadly accepted tail fitting routines are discussed.

An improved method for decomposition of random and deterministic jitter measurements using tail fitting of the probability density function of total jitter is proposed. The currently employed techniques assume that the tails of the probability density function tend to a Gaussian function. We show that to be inaccurate by deriving analytical expressions for the accurate asymptotic form of the probability density and cumulative distribution functions. In doing so, we prove that the tails approach a Gaussian function multiplied by a term that is inversely proportional to the total jitter. Monte Carlo simulations of jitter consisting of a combination of random and deterministic components are performed and nonlinear least squares fits to the derived asymptotic forms are used to estimate the root mean square of the random component and the bounds of the deterministic component for a few examples.

The design of application-specific integrated circuits (ASIC) is at the core of modern ultra-high-speed transponders employing advanced digital signal processing (DSP) algorithms. This manuscript discusses the motivations for jointly utilizing transmission techniques such as probabilistic shaping and digital sub-carrier multiplexing in digital coherent optical transmissions systems. First, we describe the key-building blocks of modern high-speed DSP-based transponders working at up to 800G per wave. Second, we show the benefits of these transmission methods in terms of system level performance. Finally, we report, to the best of our knowledge, the first long-haul experimental transmission - e.g., over 1000 km - with a real-time 7 nm DSP ASIC and digital coherent optics (DCO) capable of data rates up to 1.6 Tb/s using two waves (2 x 800G).

This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.

AbstractThe multicanonical method is applied to the calculation of the symbol error ratio (SER) as a function of the optical signal to noise ratio (OSNR) at the receiver for a polarization multiplexed quadrature phase shift keying (PM-QPSK) wavelength division multiplexed (WDM) system. We improve upon previous calculations by including polarization mode dispersion (PMD) and subsequently verifying the numerical accuracy of our calculations. Our numerical studies demonstrate that acceptable accuracy can be achieved even when advancing the polarization through the fiber with relatively large propagation step lengths.

We present analytic expressions for the temporal autocorrelation functions (ACF's) of the polarization mode dispersion (PMD) vector, the squared differential group delay (DGD) and the state of polarization (SOP) in the hinge model for stochastically varying hinges. We also derive the continuous limit of the temporal ACF of the squared DGD. Our studies demonstrate that for large time offsets, the ACF of the PMD vector approaches a constant value that depends principally on the DGD of the last fiber section but is also affected to a diminishing degree by the DGD of preceding fiber sections. We also show that sinusoidal perturbations of the hinge rotation angles do not significantly alter the results. The accuracy of the procedure is further established through comparison with numerical simulations.

We demonstrate that within the framework of the hinge model, the polarization mode dispersion (PMD) vector correlation function averaged over time and wavelength is only appreciably affected by the position of the last hinge. Further, the correlation function width is found within the context of a standard hinge model to decrease nearly monotonically with the number of hinges. We finally derive, through a theoretical analysis, an upper bound for the mean squared differential group delay of the last fiber section in the link in terms of the correlation function.

We propose a method for determining the spatial position of fast polarization changes in a WDM system. In particular, we demonstrate that the PMD (polarization mode dispersion) vector and Stokes parameters for each WDM (wavelength division multiplexing) channel can be employed to find with an accuracy, shown to be less than 15% in most simulated cases, the position of the sources of rapid polarization fluctuations in a link with a mean DGD (differential group delay) greater than 15 ps. The technique can also be applied to locate hinge positions provided that only a single hinge is active at any given time.

We simulate the time evolution of differential group delay (DGD) in a fiber link in the hinge model with time series forecasting procedures, in particular, autoregressive (AR) models with Kalman filter, pattern imitation, and a Taylor expansion. In these studies, the furthest prediction horizon was attained with the AR accompanied by the Kalman filter procedure. We further discuss the influence of measurement noise on the prediction horizon. We also apply these methods to the measured DGD on 40 Gb/s fiber links and discuss the results.

We examine both theoretically and experimentally rapid polarization transients generated by mechanical impacts on dispersion compensation modules (DCMs). In our experiments, the transient response of the output polarization to sudden mechanical impacts is found to remain constant among successive measurements. That is, the Stokes vector traces the same path over the Poincaré sphere provided that the interval of time between measurements is less than the time associated with the slow thermal drift of the fiber birefringence profile. Experimentally we can measure angular velocities (AVs) of the Stokes vector over the Poincaré sphere exceeding 100 krad∕s. We demonstrate theoretically with a simple model for the excitation that the patterns of the AV observed in experiments can be reproduced through simulation and that the amplitude of the AV increases with the volume of the fiber affected by the impact. Our model is sufficiently simple to be employed in system simulations.

Submitted for the MAR10 Meeting of The American Physical Society Rapid Polarization Activity in Optical Communication Systems DAVID YEVICK, MICHAEL REIMER, GEORGE SOLIMAN, Department of Physics, University of Waterloo — We have recently analyzed the high-speed polarization and polarization-mode-dispersion (PMD) transients associated with mechanical impacts on a dispersion compensation module consisting of several km of optical fiber. These generate in our experiments rotational frequencies of up to several hundred radians/sec on the Poincare sphere that can severely degrade the performance of both standard and non-conventional communications systems. Accordingly, we implemented several procedures for performing high-speed polarization measurements, employed these to analyze small and large amplitude excitations and compared the results with a heuristic fiber model. Theoretically, we extended our previous work on applying the Magnus expansion to the analysis of the dependence of the PMD and polarization-dependent-loss (PDL) on frequency. From these, we obtained simple procedures for modeling polarization behavior over a wide frequency range from a small number of experimental measurements. Finally, we analyzed the applicability of various models of stochastic time-dependent refractive index variations to system outage prediction. David Yevick Department of Physics, University of Waterloo Date submitted: 20 Nov 2009 Electronic form version 1.4