James P. Gordon

Jones matrix for second-order polarization mode dispersion

A Jones matrix is constructed for a fiber that exhibits first- and second-order polarization mode dispersion (PMD). It permits the modeling of pulse transmission for fibers whose PMD vectors have been measured or whose statistics have been determined by established PMD theory. The central portion of our model is a correction to the Bruyère model.

Measurement of polarization mode dispersion vectors using the polarization-dependent signal delay method

We describe a new time-domain method for determining the vector components of polarization-mode dispersion from measurements of the mean signal delays for four polarization launches. Using sinusoidal amplitude modulation and sensitive phase detection, we demonstrate that the PMD vector components measured with the new method agree with results obtained from the more traditional Müller Matrix Method.

Effect of guiding filters on the behavior of dispersion-managed solitons.

We show that guiding filters fundamentally alter the behavior of dispersion-managed soltions by making the pulse energy nearly independent of path-average dispersion (D?) in the neighborhood of D?=0 . This fact enables one to design maps permitting adequate pulse energy with narrow-bandwidth, temporally broad pulses for the attainment of high spectral efficiency and reduced nonlinear penalties in wavelength-division multiplexing.

Scheme for the characterization of dispersion-managed solitons

We give a simple new derivation of the ordinary differential equations that describe approximately the behavior of dispersion-managed solitons, and a new scheme for their solution in which the nonlinear dispersive and spectral effects are clearly apparent.

Dispersion-managed solitons for terrestrial transmission

We describe a scheme involving the insertion of segments of dispersion-compensating fiber, pumped to yield Raman gain, at one or more intermediate points within each 80-km-or-greater span between amplifier huts. With dispersion-managed solitons, the scheme is expected to allow for error-free, many-channel wavelength-division multiplexing, with high spectral efficiency, over transmission distances of many thousands of kilometers.

Statistical properties of polarization mode dispersion

Abstract Polarization mode dispersion (PMD) is one of the effects which limit bit rates in optical communications systems. The statistics of PMD is complicated because it is multi-dimensional, however, many useful results have been obtained. Much work has been done, but the subject is not yet closed, as witnessed by the existence of this conference. In this talk I will review the way some statistical equations are treated. I will briefly discuss the methods of Ito and Lax, and their application to the PMD problem.

The inverse PMD problem

When a fiber is characterized by measured polarization mode dispersion (PMD) vector data, inversion of these data is required to determine the frequency dependence of the fiber’s Jones matrix and, thereby, its pulse response. We briefly review approaches to PMD inversion and discuss three second-order models used for this purpose. We report extension of inversion to fourth-order PMD using higher-order concatenation rules, rotations of higher power designating higher rates of acceleration with frequency, and representation of these rotations by Stokes vectors.

Wavelength Division Multiplexing with Ordinary Solitons

This chapter discusses wavelength-division multiplexing (WDM) with ordinary solitons. There is no net exchange of energy or momentum of solitons after the collisions among ordinary solitons. This transparency makes ordinary solitons ideal for use in dense WDM. But, the loss and varying dispersion of real fibers destroy the symmetries necessary for such transparency, so that the emerging solitons suffer frequency shifts and loss of energy. These defects can be corrected through the use of fibers whose dispersion profile tracks the loss/gain-induced intensity profile. Step-wise approximations to such exponentially dispersion-tapered spans have allowed for successful experimental demonstration of six-channel WDM. The chapter further provides a comparison of the different scaling properties of collisions of ordinary solitons with dispersion-managed solitons. In the experiments described in the chapter, sliding-frequency guiding filters provided a very strong and useful control over the WDM with ordinary solitons in several different ways.

Dispersion-managed Solitons

This chapter provides an overview of dispersion management and dispersion-managed solitons. With dispersion management, the transmission line consists of segments of fiber whose individual dispersion parameters (Dl ocal ) are of alternating algebraic sign: D + local and D - local. Furthermore, this arrangement, or dispersion map, is ideally periodic. For each map period, the accumulated dispersions of the two segments nearly cancel, so that the path-average dispersion parameter of the map, D, is usually much smaller than either: D + local or ׀D - local׀. To support solitons, D is also positive. In response to the relatively large, alternating D local values, the pulse width tends to undergo a large fractional change, periodic with the map. This pulse breathing is accompanied and promoted by a similarly periodic variation in the chirp parameter, with the chirp passing through zero at or near the center of each fiber segment. To obtain dispersion-managed solitons, the pulse intensity must be increased until self-phase modulation produces a phase shift across the pulse that just cancels out the net phase shift produced by the dispersive term within each map period. This periodic cancellation of phase shifts eliminates the net pulse broadening from D, so that the pulse behavior becomes truly periodic.

Wavelength Division Multiplexing with Dispersion-managed Solitons

This chapter discusses wavelength-division multiplexing (WDM) with dispersion-managed solitons. It explains how dispersion management tends to render the jitter from collisions so small that the performance of a dense WDM system becomes nearly indistinguishable from that of a single, isolated channel. Collisions between pairs of solitons consist of fast, repeated, and minicollisions that individually produces small displacements of the pulses in frequency and time. But when the ratio of local-to-path-average dispersion is very high, then the colliding pair tends to undergo a very large number of such mini-collisions before the solitons cease to cross each others paths. Thus, the net length for an overall collision tends to be long. The chapter outlines a quasi-analytic model, based on observation of exact numerical simulations, and on analytic treatment of the simpler constituent elements. This model provides the basis for a satisfactory mathematical model of the all-important timing jitter that result from the collisions.