Gaussian beams in inhomogeneous media: A review
Gaussian beams in inhomogeneous media: A review
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非均匀介质中的高斯光束：综述
DOI：
10.1007/s11200-007-0002-y
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发表时间：
2007
影响因子：
0.9
通讯作者：
P. Berczyński
中科院分区：
文献类型：
--
作者：
Y. Kravtsov;Y. Kravtsov;P. Berczyński
本文概述了近轴复几何光学（CGO）关于高斯光束在光滑非均匀介质中衍射的最重要结果，并讨论了CGO与其他渐近方法之间的相互关系，这些渐近方法将高斯光束衍射问题归结为常微分方程的解，即：（i）Babich方法，它处理简化抛物方程，描述高斯光束的衍射;（ii）复数形式的动态光线追迹方法，它推广了高斯光束的傍轴光线近似;（iii）Pereverzev的傍轴WKB近似，它给出了结果，与Babich的方法非常接近。对于高斯光束，所有方法都导出了类似的常微分方程，即复值非线性Riccati方程和相应的傍轴光线近似复值线性方程组。指出Babich方法为近轴CGO和复值动态射线追迹方法提供了衍射证实。还强调后两种方法在概念上是相互等价的，操作的等效方程，实际上是孪生的，虽然它们的名称不同。本文说明了能力的近轴CGO方法的两个可用的解析解：高斯光束衍射中的均匀和透镜状介质，并通过数值例子：高斯光束反射从一个平面分层介质。
The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method, which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are twins, though they differ by names.The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered medium.