Measurement of polarization-mode dispersion - includes related articles on Jones calculus, the Poincare Sphere, and the HP 8509A/B Lightwave Polarization Analyzer - Technical

Hewlett-Packard Journal, Feb, 1995 by Brian L. Heffner, Paul R. Hernday

Polarization-mode dispersion is defined and characterized, using Poincare sphere and Jones matrix concepts. Interferometric, wavelength scanning, and Jones matrix eigenanalysis measurement methods are described. Instrumentation, especially the HP 8509B lightwave polarization analyzer, is discussed.

New generations of high-speed undersea telecommunication systems and cable TV distribution systems feature an important new player: the erbium-doped fiber amplifier, or EDFA. Moving quickly from laboratory to mainline application, the EDFA will lower the cost and increase the reliability of long-haul telecommunications and greatly increase head-end distribution power for CATV.

In contrast to older systems in which propagation loss was compensated by detecting the optical signal and retransmitting it at higher power (regeneration), the EDFA-based system is a continuous glass pathway with amplification provided at intervals by short lengths of pumped, erbium-doped fiber. The absence of pulse regeneration must be offset by improvements in the dispersive characteristics of the pathway.

Historically, polarization-mode dispersion, or PMD is the third of a series of dispersive effects in optical fiber. The bandwidth of multimode fiber is limited because light separates into spatial modes of many different lengths. Single-mode fiber solves that problem but is limited by chromatic dispersion, in which the transmission medium allows adjacent wavelengths to travel at slightly different speeds. PMD, a more subtle effect, arises from slight physical asymmetry in the index of refraction, called birefringence. In fiber, it is caused by stresses induced by fiber manufacture, packaging, and deployment and is strongly influenced by environment.

When chromatic dispersion is sufficiently reduced, the pulse distortion and signal fading produced by PMD can be observed. In CATV systems, the combination of PMD in fiber and components, frequency chirp in the transmitter, and polarization dependent loss near the receiver produces composite second-order distortion. For high-speed, long-haul telecommunications, and high-channel-capacity CATV systems to realize their potential, PMD must be understood and controlled.

Polarization-mode dispersion is a fundamental property of single-mode optical fiber and components in which signal energy at a given wavelength is resolved into two orthogonal polarization modes of slightly different propagation velocity. The resulting difference in propagation time between polarization modes is called the differential group delay, commonly symbolized as [delta][tau.sub.g], or simply [delta][tau]. In most optical components, the polarization modes correspond to physical axes of the component and the differential group delay (and therefore the PMD) is nearly independent of wavelength. In practical lengths of optical fiber, differential group delay varies randomly with wavelength and the specification of PMD must be statistically based. Long-fiber PMD is commonly expressed as either the average value or the rms value of differential group delay over a wide wavelength range. For fibers that exhibit a large degree of coupling of energy between polarization modes, PMD scales with the square root of fiber length and is often specified in picoseconds per root kilometer.

How much PMD is too much? For modest impact, the instantaneous differential group delay of a telecommunication system must be kept below one tenth of a bit period, or 20 ps for a 5-Gbit/s NRZ pulse stream.

Characterizing PMD

PMD in many real systems varies over time and is best characterized by a statistical picture to account for its changing details. For the moment, however, let's consider how to characterize the PMD of a stable device or system that exhibits no time variation. Differential group delay, the most direct measure of the signal-distorting effects of PMD, does not tell the whole story. The PMD of a system is completely characterized by specifying any of the following three quantities as a function of wavelength or optical frequency:

* A pair of principal states of polarization and a differential group delay * A three-dimensional polarization dispersion vector * A Jones matrix (see page 28).

If a polarized, tunable optical wave is transmitted through a device, the polarization at the device output will in general trace out an irregular path on the Poincare sphere[1] (see page 29) as the optical radian frequency [omega] is tuned, as shown in Fig. 1. Over a small range of frequency, any section of the irregular path can be approximated as an arc of a circle on the surface of the sphere. The center of such a circle, projected to the surface of the sphere, locates a principal state of polarization. A second, orthogonal principal state of polarization is located diametrically opposite on the sphere. The principal states of polarization are significant because they summarize how any output state of polarization evolves with frequency. As a function of frequency, all output states rotate about a diameter connecting the two principal states of polarization. The rate of rotation is determined by the differential group delay.