In the previous chapter, we discussed devices based on deliberately introduced birefringence in an optical fiber, thus utilizing the polarization effects to our advantage. In Chapter 10, we discuss the detrimental aspect of birefringence in optical fibers - namely, polarization mode dispersion (PMD).
The existence of birefringence in a fiber implies that the fiber supports two orthogonally polarized modes that have different effective indices and hence propagate with different group velocities in the fiber. An optical pulse launched into such a fiber would be split into two orthogonally polarized pulses, which would then propagate with different propagation constants and group velocities. The two pulses thus reach the output end of the fiber at slightly different times and with different phases. The superimposition of these two pulses leads to the generation of an optical pulse that is now temporally more broadened as compared to the input pulse. Thus, the pulse becomes dispersed due to the effect of fiber birefringence, and the phenomenon is called polarization mode dispersion. PMD is a serious limitation in the case of ultrahigh-bit-rate (> 10 Gb) fiber communication links, as it puts a cap on the bit rate of the link as well as causes errors in data transmission. In the following, we discuss some basic concepts involved in the understanding of PMD in optical fibers.
10.2 PMD in Short-Length and High-Birefringence Fibers
In short-length SMFs or Hi-Bi fibers, one can assume that the birefringence is constant in magnitude as well as in direction so that there is no polarization mode coupling. In such cases, the two polarization modes - namely, slow and fast - are fixed, so PMD is completely deterministic and not random. If ns and nf are the effective indices of the slow and fast modes, respectively, the corresponding propagation constants will be given by
where ω is the angular frequency.