arXiv 1203.42392012-03-19physics.optics

简并共振光学介质中的随机脉冲开关

Stochastic Pulse Switching in a Degenerate Resonant Optical Medium

Ethan P. Atkins, Peter R. Kramer, Gregor Kovacic, Ildar R. Gabitov

DOI：: 10.1103/PhysRevA.85.043834

摘要：

利用理想化的可积麦克斯韦-布洛赫模型，描述了沿λ位形有源光学介质的随机光脉冲偏振开关，其低能子能级对的占据数无序。该描述结合了完全可积性和随机动力学。对于单孤子脉冲，我们以封闭的形式导出了沿介质给定点的电场极化椭圆的统计特性。如果两个较低的子能级的平均初始布居数差为零，我们表明，脉冲偏振将切换之间的两个圆偏振，因为它沿着介质传播间歇。如果这种差异不消失，脉冲最终将永远保持在圆偏振中，这取决于平均哪个子能级被更多地占据。我们还导出了偏振开关动力学统计的精确表达式，如两个连续开关之间的距离的概率分布和脉冲沿介质的距离的百分比花费在给定方向的椭圆偏振的情况下，平均初始布居数差为零。我们发现，后者的分布是根据著名的反正弦定律。

英文摘要：

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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