Mark Shtaif

Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission

We analyze intrachannel nonlinear effects in high-bit-rate transmission systems based on short optical pulses that are dispersion compensated. We perform an analytical study of a generic example with two pulses, in which case the nonlinearity shifts the pulses in time and results in the generation of leading and trailing pulse echoes. We show that in all the relevant range of parameters, the magnitude of the nonlinear impairments reduces monotonically with the reduction of pulse width and with the increase of the dispersion coefficient.

Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses

We study the properties of symmetric dispersion compensation in optical links using highly dispersed pulse transmission. We show analytically that by splitting the dispersion compensation equally between the input and output of the link, complete cancellation of the timing and amplitude jitter can be obtained in systems where the power profile is symmetric about the center. We explain the dynamics of this cancellation and show, theoretically and experimentaily, that with practical system parameters, symmetric compensation may lead to a considerable improvement in performance.

The statistics of polarization-dependent loss in optical communication systems

In this letter, we study the statistics of polarization-dependent loss (PDL) in optical systems and evaluate its evolution with system length. We show rigorously that within the range of conceivable parameters in optical links, the distribution of PDL is Maxwellian when it is expressed in decibels. The accumulation of the mean-square PDL with system length stays linear in most systems, but may assume an exponential growth in very long systems with large PDL. The analytical results are compared with numerical simulations and an excellent agreement is observed.

Stokes-space analysis of modal dispersion in fibers with multiple mode transmission

Modal dispersion (MD) in a multimode fiber may be considered as a generalized form of polarization mode dispersion (PMD) in single mode fibers. Using this analogy, we extend the formalism developed for PMD to characterize MD in fibers with multiple spatial modes. We introduce a MD vector defined in a D-dimensional extended Stokes space whose square length is the sum of the square group delays of the generalized principal states. For strong mode coupling, the MD vector undertakes a D-dimensional isotropic random walk, so that the distribution of its length is a chi distribution with D degrees of freedom. We also characterize the largest differential group delay, that is the difference between the delays of the fastest and the slowest principal states, and show that it too is very well approximated by a chi distribution, although in general with a smaller number of degrees of freedom. Finally, we study the spectral properties of MD in terms of the frequency autocorrelation functions of the MD vector, of the square modulus of the MD vector, and of the largest differential group delay. The analytical results are supported by extensive numerical simulations.

System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission

We provide accurate analytical estimates of timing- and amplitude-jitter caused by nonlinear pulse interaction in systems based on highly dispersed optical pulses, both for coherent and noncoherent pulse streams. We show that the system penalties reduce monotonically with pulsewidth and with increasing fiber dispersion. We demonstrate that proper dispersion pre-compensation can result in a significant reduction of the nonlinear inpairments and provide analytical tools for obtaining the optimal pre-compensation parameters.

A compensator for the effects of high-order polarization mode dispersion in optical fibers

We present a polarization mode dispersion compensator for the rotation of the principal states with frequency. This compensator requires only two control elements more than existing first-order compensators. These are the position of one polarization controller and the setting of a single delay. With the proposed scheme, compensation for first order can be decoupled from the compensation for higher orders and controlled independently. The effect of the compensator on signal transmission is evaluated with extensive numerical simulations.

Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states

Using the retarded plate model, we derive the correlations and the mean-square values of all orders of polarization mode dispersion (PMD) as well as the autocorrelation function of the PMD vector. Our results provide the signal bandwidth below which the first-order approximation of the principal states of polarization is valid. We show that this bandwidth depends only on the mean value of the differential group delay. Our theoretical results are supported by simulations and experiments.

Analysis of intensity interference caused by cross-phase modulation in dispersive optical fibers

Under a set of broadly justified simplifying assumptions, an analytical approach to the problem of cross phase modulation in optical fibers is presented. Simple analytical expressions describing intensity interference caused by cross-phase modulation (XPM) are derived. It turns out that within a physically realizable range of parameters the power penalties induced by XPM have a linear dependence on the power of the interfering signal. Examples of specific systems are presented and discussed.

Nonlinear propagation in multi-mode fibers in the strong coupling regime

We show that light propagation in a group of degenerate modes of a multi-mode optical fiber in the presence of random mode coupling is described by a multi-component Manakov equation, thereby making multi-mode fibers the first reported physical system that admits true multi-component soliton solutions. The nonlinearity coefficient appearing in the equation is expressed rigorously in terms of the multi-mode fiber parameters.

Analytical solution of wave mixing between short optical pulses in a semiconductor optical amplifier

An analytical solution to the problem of nondegenerate four wave mixing in a semiconductor optical amplifier emphasizing operation with short optical pulses is described. Calculated conversion efficiencies for pulses are significantly larger than for cw fields and are pulse width dependent. Conditions for optimum conversion efficiencies in terms of the pump input energy and the relative temporal alignment between the pulses are presented.