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In this paper, we introduce the concept of quaternions (which is a generalization of the complex numbers) and quaternion calculus and demonstrate how this theory may be used to simplify the treatment of polarization phenomena in optical fibers. We apply quaternion calculus to two examples: 1) the description of polarization-dependent loss (PDL) elements and concatenation of such and 2) the description of pulse dynamics and broadening in transmission lines with both polarization-mode dispersion (PMD) and PDL. Finally we present some novel results from the investigation of pulse broadening in a simple system comprising a PMD element, followed by a perfect polarizer.
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Karlsson et al. (2004) studied this question.
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