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Polarization mode dispersion (PMD) has been a major impediment in achieving higher speeds in optical fiber communication systems. Various approaches and techniques for the basic theoretical analysis, modeling, simulation, and compensation of PMD have been proposed in the literature. In this paper, we present a novel and fresh approach to the modeling, emulation and inversion of PMD in optical fibers. In our approach, we first build a full PMD model based on coupled mode theory as a continuous-time, lumped and lossless system. We then develop systematic model dimension reduction techniques, adapted from Krylov-subspace based methods for large electronic systems, in order to obtain compact and low complexity PMD models. The reduced complexity models produced by our technique match the full PMD model over a specifiable frequency range of interest, have the same structure as the full model, and are amenable to efficient software and low complexity hardware implementations for emulation and inversion. Furthermore, the reduced compexity PMD modeling framework we develop in this paper can serve as a general formalism for studying the compressibility of PMD models and emulators.