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

The statistical theory predicts, and experiments confirm, that the differential group delay distribution measured at a particular frequency over a long period of time is identical to the distribution measured at one time over a large range of frequency. This fact allows statistics representing slow time variations to be measured very quickly by gathering data over a wide frequency range. As another result of the statistical model, when several long fiber sections are concatenated, the expected value of differential group delay for the concatenation is given by the root sum of squares of the expected values for the sections, that is,

[Mathematical Expressions Omitted]

As a consequence, [less than][delta][tau][lgreater than][sub.total] grows proportionally to the square root of the fiber length, and the PMD of a long fiber is specified in units of ps/[square root of] km with the understanding that the orientation of [omega] is uniformly distributed. In contrast, the PMD of a short section of fiber or of a fiber manufactured with a consistent birefringence over its length is specified in units of ps/km because it grows proportionally to the fiber length, and the orientation of [omega] is understood to be fixed relative to the physical orientation of the fiber. PMD in components is typically not statistical in origin, and is simply specified in ps.

Measuring PMD

Two polarization modes are transmitted through a device exhibiting significant PMD, each according to its own phase delay and group delay. Owing to the unequal group delays, propagation through such a device will change the mutual temporal coherence between the two polarization modes.

Likewise, the two unequal phase delays lead to a frequency dependent output state of polarization in response to a fixed input state of polarization. These physical characteristics make possible a variety of PMD measurement methods. An interferometric method[5,6] Measures the effect of PMD on mutual coherence, and a wavelength scanning method[7] measures the effect of PMD, through variations of the output state of polarization, on transmission through a fixed analyzer. A method developed by Hewlett-Packard calculates the differential group delay and principal states of polarization as a function of frequency by analyzing Jones matrixes measured at a sequence of optical frequencies.[8,9,10] Most of the techniques currently used to measure PMD are similar in principle to one of these three methods.

A block diagram of the low-coherence interferometric method is shown in Fig. 2a. Collimated light from a broadband light-emitting diode is polarized and split into two mutually coherent beams. One mirror can be scanned in position, creating a differential delay between the two orthogonal polarizations, which are recombined and directed through the device under test (DUT). When photocurrent is measured as a function of the differential interferometer delay, coherent fringes can be observed only when this differential delay is compensated by the differential group delay of the DUT. Fig. 2b shows the envelope of the coherent fringes measured as a function of delay.