Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles
Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles
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DOI：
10.1364/aop.3.000272
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发表时间：
2011-12-01
影响因子：
27.1
通讯作者：
Alonso, Miguel A.
中科院分区：
文献类型：
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作者：
Alonso, Miguel A.
本教程概述了使用维格纳函数作为建模光场传播的工具。特别强调的是放置在空间传播的固定领域，以及通过色散介质的脉冲的传播。在第一种情况下，维格纳函数给出了场的表示，它类似于系统中所有光线的辐射或权重分布，因为它的参数是位置和方向。在场是傍轴的情况下，并且系统在射线状态中由简单的线性关系描述，维格纳函数在沿着射线传播下是恒定的。在类似的假设下，光脉冲在色散介质中的传播也有一个等价的性质。维格纳函数在这些背景下的几个属性和应用进行了讨论，因为它与其他常见的相空间分布，如模糊函数，频谱图，和胡西米，P，Q，和柯克伍德-里哈切克函数的连接。还讨论了修改的维格纳函数的定义，允许延长财产的保护沿着路径更广泛的问题，包括nonparaxial场传播和脉冲传播一般透明色散介质。(C)2011年美国光学学会
This tutorial gives an overview of the use of the Wigner function as a tool for modeling optical field propagation. Particular emphasis is placed on the spatial propagation of stationary fields, as well as on the propagation of pulses through dispersive media. In the first case, the Wigner function gives a representation of the field that is similar to a radiance or weight distribution for all the rays in the system, since its arguments are both position and direction. In cases in which the field is paraxial and where the system is described by a simple linear relation in the ray regime, the Wigner function is constant under propagation along rays. An equivalent property holds for optical pulse propagation in dispersive media under analogous assumptions. Several properties and applications of the Wigner function in these contexts are discussed, as is its connection with other common phase-space distributions like the ambiguity function, the spectrogram, and the Husimi, P, Q, and Kirkwood-Rihaczek functions. Also discussed are modifications to the definition of the Wigner function that allow extending the property of conservation along paths to a wider range of problems, including nonparaxial field propagation and pulse propagation within general transparent dispersive media. (C) 2011 Optical Society of America