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A Geometrical Perspective on the Coherent Multimode Optical Field and Mode Coupling Equations

机译:相干多模光场和模耦合方程的几何透视

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The generalization of the Poincaré sphere to modes is the ()-dimensional complex projective space CP(). There is a minimal set of Stokes vector components that determine the coherent multimode optical field. These are obtained from the inverse stereographic projection of coordinate hyperplanes in CP() into a sphere, just as in the case. We derive -mode analogs of Poole’s optical fiber polarization-mode dispersion (PMD) equations that involve only independent variables. This is achieved by means of an explicit generalized coherent state representation of the optical field, which enables the components of the PMD vector to be expressed in terms of the optical state and its frequency derivatives. Poole’s equations describe mode coupling as a flow on CP(). We give general constraints on the mode-coupling matrix and Stokes vector components. The group delay operator is shown to be a rank-2 perturbation of a diagonal matrix.
机译:庞加莱球面到模式的一般化是()维复投影空间CP()。最小的斯托克斯矢量分量集决定了相干多模光学场。这些都是从CP()中坐标超平面到球体的逆立体投影中获得的,就像在这种情况下一样。我们推导了Poole的光纤偏振模色散(PMD)方程的模态类似物,该方程仅涉及独立变量。这是通过光学场的显式广义相干状态表示来实现的,该状态表示使PMD矢量的分量可以根据光学状态及其频率导数来表示。普尔的方程式将模式耦合描述为CP()上的流。我们给出了模式耦合矩阵和斯托克斯矢量分量的一般约束。组延迟算子显示为对角矩阵的2级扰动。

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