Tovar A A
Physics and Engineering Programs, Eastern Oregon University, La Grande, Oregon 97850-2899, USA.
J Opt Soc Am A Opt Image Sci Vis. 2000 Nov;17(11):2010-8. doi: 10.1364/josaa.17.002010.
New exact solutions to the paraxial wave equation are obtained in the form of a product of Laguerre polynomials, Bessel functions, and Gaussian functions. In the limit of large Laguerre-Gaussian beam size, the Bessel factor dominates and the solution sets reduce to the modes of closed resonators, hollow metal waveguides, and dielectric waveguides. In the opposite limit the solutions reduce to Laguerre-Gaussian modes of open resonators and graded-index waveguides. These solutions are valid for electromagnetic waves traveling through free space, and they are valid for propagation through circularly symmetric optical systems representable by ABCD matrices as well. An interesting feature of the new solution set is the existence of three mode indices, where only two are required for an orthogonal expansion. As an example, Laguerre-Gaussian beam propagation through an optical system that contains a Bessel-like amplitude filter is discussed.
通过拉盖尔多项式、贝塞尔函数和高斯函数的乘积形式，得到了傍轴波动方程的新精确解。在拉盖尔 - 高斯光束尺寸很大的极限情况下，贝塞尔因子起主导作用，解集合简化为封闭谐振器、空心金属波导和介质波导的模式。在相反的极限情况下，解简化为开放谐振器和渐变折射率波导的拉盖尔 - 高斯模式。这些解对于在自由空间中传播的电磁波是有效的，并且对于通过由ABCD矩阵表示的圆对称光学系统的传播也是有效的。新解集合的一个有趣特征是存在三个模式指数，而正交展开仅需要两个。作为一个例子，讨论了拉盖尔 - 高斯光束通过包含类贝塞尔幅度滤波器的光学系统的传播。
