Why Strong Birefringence In Fibers Helps
Maybe you have heard about polarization-maintaining fibers and know that these have a strong built-in birefringence. However, do you also understand why exactly this birefringence helps to maintain a stable polarization state at the fiber output?
One may simply argue that with a strong built-in birefringence, having a well-defined axis, any random disturbances of the refractive index are comparatively small, so that their influence remains weak. However, this picture is rather vague, and it lacks some of the essential physics, which can be best understood by considering the principle of mode coupling:
Imagine that two propagation modes of the fiber with identical optical frequencies but orthogonal polarization directions, according to the directions of the birefringence, propagate in the fiber. Any random fluctuations of the refractive index cause a coupling between these modes: optical amplitude is shuffled back and forth between them. However, strong birefringence causes the propagation constants of the two modes to differ substantially, so that their relative phase rapidly drifts away. As a consequence of that, the mode coupling becomes inefficient: the optical amplitudes coupled from one mode to the other in subsequent short sections of the fiber will quite precisely cancel each other, rather than constructively add up. The only chance for efficient coupling would be that the refractive index fluctuations evolve (e.g. just by chance) in synchronism with the phase difference of the two modes. This can hardly happen, however, if the birefringence is large enough and the index fluctuations are only slowly varying. For quantitative estimates, one may calculate the average magnitude of the spatial Fourier component corresponding to the birefringent beat period.
In conclusion, the birefringence does not really suppress the local coupling of modes (as the simple argument seemed to suggest), but rather prevents any significant accumulation of coupling effects over some length of fiber. A quite neat principle, isn't it?
This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.
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