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Abstract

Using the idealized integrable Maxwell-Bloch model, we describe random
optical-pulse polarization switching along an active optical medium in
the lambda-configuration with disordered occupation numbers of its
lower energy sub-level pair. The description combines complete
integrability and stochastic dynamics. For the single-soliton pulse, we
derive the statistics of the electric-field polarization ellipse at a
given point along the medium in closed form. If the average initial
population difference of the two lower sub-levels vanishes, we show that
the pulse polarization will switch intermittently between the two
circular polarizations as it travels along the medium. If this
difference does not vanish, the pulse will eventually forever remain in
the circular polarization determined by which sub-level is more occupied
on average. We also derive the exact expressions for the statistics of
the polarization-switching dynamics, such as the probability
distribution of the distance between two consecutive switches and the
percentage of the distance along the medium the pulse spends in the
elliptical polarization of a given orientation in the case of vanishing
average initial population difference. We find that the latter
distribution is given in terms of the well-known arcsine law.

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This work was partly supported by the National Science
Foundation through grant DMS-1009453.

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