Dispersion-management modeling resolves system-design issues

Jigesh K. Patel

As technologies for dispersion compensation evolve, efficient design of chromatic-dispersion compensation schemes requires simulation studies to evaluate and compare the tradeoffs of available technologies and determine the optimal design solutions.

The evolution of high-speed long-haul networks has generated considerable demand for efficient dispersion-compensation devices. In fact, the slowdown in carrier capital spending has tilted the balance in favor of developing dispersion-compensation components that will enhance the bandwidth capabilities of the installed base of fiber as opposed to solutions that require replacing the existing transport backbones.

The majority of the deployed optical fiber in North America and Europe consists of ITU-T G.652 single-mode fiber (SMF). Dispersion management in such fibers can be accomplished in many ways, though the most widely used approach employs lengths of transport fiber of opposite dispersion characteristics.

Typically a 10- to 20-km length of dispersion-compensating fiber (DCF) is placed before the regenerators, inducing negative dispersion to compensate for the positive dispersion accumulated over the 60- to 80-km length of the SMF. Although the total dispersion over the entire SMF-DCF span can be minimal, net dispersion at any point along the span is non-zero, which keeps the nonlinear mixing effects at minimum levels. While the DCF does not address polarization-mode dispersion, it can still provide for effective dispersion compensation over many channels.

In a DWDM link, DCF is usually set to correct the accumulated dispersion over the central wavelength of the wavelength grid. This arrangement, however, may give inferior compensation for channels on the edge of the wavelength plan. This design is a "continuous" approach to dispersion correction as opposed to the "channelized" dispersion correction, which may be provided by technologies such as fiber Bragg gratings and virtual-imaged phased arrays (VIPAs). Dispersion-compensating-fiber-based compensation can be achieved by either a precompensation configuration, or by the more widely used post-compensation configuration.

SIMULATION CASE STUDIES
The following scenario was simulated using RSoft Design Group' s LinkSIM software program, which illustrated several of the tradeoffs involved in designing a chromatic-dispersion compensation scheme.¹ The simulated topology has a total link-length of 600 km.

Each 100-km span of the four-channel 40-Gbit/s (OC-768) WDM link consists of 80 km of G.652 SMF and 20 km of DCF with a high figure of merit. The wavelength plan is a non-ITU-T grid specifically chosen so as to be able to identify a distinct dispersion slope for each channel. For an uncompensated system the "closed eye" comes as no surprise (see Fig. 1).

On the other hand, the eye-diagram in the link performance when a dispersion post-compensation scheme is employed is much better (see Fig. 2). In a dispersion post-compensation scheme, the unequal accumulated dispersion at the end of each SMF segment for each wavelength is due to the wavelength-dependent dispersion in the fiber, also known as the dispersion slope. The power falls more rapidly in the DCF section than in the SMF section because of the larger attenuation typically associated with the DCF. A closer look at a span dispersion map shows that the net dispersion at the end of the span is non-zero, but minimal, and does not materially affect the simulation results in this example.

An alternate approach is "precompensation," in which a negative dispersion is introduced beforehand in anticipation of the subsequent SMF-induced positive dispersion (see Fig. 3). Comparing the eye diagrams shows that a precompensation scheme produces a slight improvement in performance over the post-compensation scheme.

Precompensation decreases the signal power faster than post-compensation because of the higher attenuation of DCF, and the signal experiences normal dispersion while the signal power is higher, whereas in post-compensation, the signal power falls more slowly in the SMF and experiences anomalous dispersion while the signal power is higher. Precompensation has also been shown to result in pulse compression due to self-phase modulation (SPM), rather than the more detrimental pulse-broadening effect that occurs in post-compensation.^2,3 Because of the interplay between dispersion, nonlinearities, and signal power, the dispersion map strongly affects the pulse evolution in the link.

The dispersion is said to be normal if the group velocity dispersion (GVD) parameter β₂ has positive value. This is also called negative dispersion because the dispersion parameter D is inversely proportional to the GVD parameter β₂. Pulses in silica fiber experience normal or negative dispersion below the zero-dispersion wavelength, which is approximately 1.3 µm for standard SMF.

If the GVD parameter has negative value, the dispersion is said to be anomalous, which is the case for pulses in the entire 1.55-µm band in standard SMF. In anomalous dispersion, the lower-frequency (red-shifted) components of an optical pulse travel slower than the higher-frequency (blue-shifted) components. For DSF, the dispersion zero lies in the 1.55-µm band. As a result, pulses in one part of the 1.55-µm band experience normal dispersion, and the pulses in the other part of the band experience anomalous dispersion. In the normal dispersion regime, the SPM causes increased broadening of the pulse. On the other hand, the effect of SPM in the anomalous regime is influenced by the amount of dispersion present.

UNDERSTANDING THE EFFECTS OF DISPERSION
To understand the basic phenomenon that leads to improved performance in the precompensated system, let us investigate how the input pulse propagates in these spans. In post-compensated spans, the input pulse is compressed after the 80 km of SMF because of the SPM in the anomalous dispersion regime. The 20-km of DCF following the SMF then severely distorts the pulses.

The power is reduced as the result of attenuation after 80 km of SMF, thereby reducing the nonlinear interactions. Hence the pulse broadening occurs because of the large dispersion of the DCF. In precompensated spans, the DCF-induced dispersion in the normal regime causes significant pulse broadening. The following 80 km of SMF then compresses them to a narrower width.⁴

It is interesting to note that a conventional DCF has a very small effective-mode area as compared to the standard SMF. This may cause additional constraints in its power handling capacity, thereby affecting the supportable channel count and data rates in a DWDM system. Modified DCF and non-zero dispersion-shifted fiber (NZDSF) are now available with larger effective-mode areas and with better dispersion characteristics.

Hence, for effective control over the dispersion in an optical link, it is very important to plan on an appropriate set of SMF, NZDSF, and DCF with carefully considered effective-mode areas, dispersion slopes, and zero-dispersion wavelengths (&#lambda;₀). This requirement can be illustrated by comparing bit-error rate (BER) curves in an 80-km, 40-Gbit/s, 10-channel DWDM link with 50-GHz interchannel spacing (see Fig. 4).

In this link, the ranges for the zero-dispersion wavelength and the effective area were chosen to represent currently available nonlinear fibers. High bit-rate DWDM systems tend to exhibit higher penalties due to cross-phase modulation (XPM) rather than four-wave mixing (FWM).⁵ Since different zero-dispersion wavelengths can lead to different FWM/XPM components, it is possible for other channels to have a BER performance slightly different from what can generally be anticipated. Because of the complex interactions between dispersion, nonlinearities, and signal power, a comprehensive simulation is vital to select appropriate fibers that produce an optimum tradeoff between nonlinear effects and chromatic dispersion, and to design a dispersion map scheme that optimizes system performance.

DEVELOPMENTS AND PROSPECTS
A number of alternative approaches for dispersion compensation are currently under laboratory investigation and field trial. Several of the most promising dispersion-compensation modules are based on specialty DCF,⁶ dispersion-compensation gratings, high-order mode (HOM) fibers,⁷ and VIPAs.⁸

Recently, new types of DCF have been proposed that have dispersion characteristics exactly opposite those of SMF and hence can be cabled with the SMF in a 1:1 length ratio. These are also known as reverse-dispersion fibers or inverse-dispersion fibers.

FIGURE 4. Tradeoffs between fiber selection and its influence on dispersion and nonlinear effects are apparent in BER curves. Since different zero-dispersion wavelengths can lead to different FWM/XPM components, it is possible for other channels (top) to have a BER performance slightly different from what can generally be anticipated (bottom).

Future flexible manufacturing processes are also expected to produce fiber Bragg gratings with negligible group-delay ripple that will fulfill the wideband compensation needs of long-haul WDM applications. High-order-mode fibers offer low insertion loss and can tolerate higher input optical power without generating nonlinear effects. Spatial-mode transformers would be used to transform the energy in a fiber from the basic single mode into the higher mode of a negative-dispersion HOM fiber and vice versa.

Virtually imaged phased-array-based dispersion-compensation modules can serve as tunable compensators for dispersion and have shown encouraging results in recent field trials for OC-768 systems. The recent agreement on a common specification is expected to help commercial availability of VIPA-based dispersion-compensation modules in 2002.

ACKNOWLEDGMENTS
The author wishes to thank his colleagues Brent K. Whitlock, Mike Steel, Rob Scarmozzino, Jim Doty, Bulent Kose, Feng Ma, Jim Morikuni, Pablo Mena, and Andrea Papa for their inputs and stimulating discussions.

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Jigesh K. Patel is an application engineer at RSoft Design Group, 200 Executive Boulevard, Ossining, NY 10562. He can be reached at [email protected].