This invention relates to optical communications and the processing of optical signals. More particularly, the invention relates to optical processing methods and systems that address polarization effects such as polarization mode dispersion (PMD) and polarization dependent loss (PDL).
The transmission of information over optical fibers is becoming pervasive. This is motivated, at least in part, because optical fiber offers much larger bandwidths than electrical cable. Moreover, optical fiber can connect nodes over large distances and transmit optical information between such nodes at the speed of light. Among factors limiting transmission rates and distances in high-speed fiber systems, however, are polarization effects such as polarization mode dispersion (PMD) in optical system such as optical fiber.
Polarization-mode dispersion arises from small random birefringences in optical fibers. For sufficiently short sections of fiber, the birefringence may be considered uniform, and light traveling along the fast and slow axes of the fiber experiences different propagation delays. For longer sections of fiber, however, the orientation and amplitude of the birefringence varies, leading to a phenomenon called polarization-mode coupling which eventually randomizes the polarization state of the propagating lightwave. The fiber length over which the polarization state is randomized is known as the correlation length Lc. Typical lengths for Lc range from meters to perhaps a few hundreds of meters. Therefore, high-speed fiber transmission systems, with lengths ranging from tens of kilometers to thousands of kilometers, are long compared to the correlation length.
In this long fiber limit, one may model a fiber as a series of wave plates with random orientations of fast and slow axes. Any single wave plate is characterized by the differential delay δτ between its two axes. For a large number of wave plates, N, the total delay is a random variable whose statistics are governed by a random walk process. Therefore, the variance of the delay scales as δτ√{square root over (N)}. For this reason, one measure of PMD is in units of ps km−0.5. Modern high quality fibers may have PMD coefficients below 0.1 ps km−0.5. On the other hand, much older embedded fiber has much higher PMD, which can be on the order of several ps km−0.5 or higher. In such a fiber, PMD will cause severe impairments at 10 Gb/s in fiber spans of only 100 km.
Much research on PMD in lightwave systems focuses on PMD-related timing shifts and pulse broadenings significantly below the bit period, because in the absence of PMD compensation, this is the only regime where high quality communications is possible. In these situations PMD may be understood in the “high coherence” limit, where the coherence time of the lightwave signal exceeds the PMD-related broadening. In this limit the leading effect is termed first-order PMD. In the first order PMD picture, there exists a pair of orthogonal, input principal states of polarization (PSPs) for which the output polarization does not change with frequency (to first order). These PSPs correspond to the fastest and slowest propagation through the fiber, respectively. The differential group delay (DGD) between the two PSPs is denoted Δτ. Both the PSPs and Δτ are random variables. The PMD can be represented compactly by introducing a polarization dispersion vector{right arrow over (Ω)}=Δτ{right arrow over (s)}  (1)whose magnitude gives the DGD and whose direction {right arrow over (s)} is a unit vector in the Poincare sphere representation specifying the orientation of the PSPs. In the first order limit, pulse broadening and distortion due to PMD can be described in terms of the output signal being split into two replicas with relative delay Δτ. Characterizing PMD in terms of a coefficient with units ps km−0.5 actually refers to <Δτ>, the statistical mean of Δτ.
In the first-order PMD limit, compensation can be accomplished by using a polarization controller and polarization beam splitter to separate the fiber output into the two PSPs, passing one of the separated beams into a variable delay stage, and then recombining the two beams with a relative delay opposite to the DGD. Compensating for higher-order PMD, however, is clearly more difficult.
Another polarization effect that can limit performance of high-speed fiber systems is polarization dependent loss (PDL) and polarization dependent gain (PDG). PDL arises in passive devices wherein the loss is polarization dependent. PDG arises in optical amplifiers where the gain is polarization dependent. In either case, the polarization effects lead to intensity fluctuations in the fiber system, which degrade performance. Moreover, like PMD, these polarization effects typically vary with lightwave frequency.