Bandres Miguel A, Gutiérrez-Vega Julio C
California Institute of Technology, Pasadena, California 91125, USA.
Opt Express. 2008 Dec 8;16(25):21087-92. doi: 10.1364/oe.16.021087.
A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others.
给出了椭圆柱面坐标下傍轴波动方程的一个非常一般的光束解。我们将这样的场称为椭圆光束（EB）。EB的复振幅由广义英斯函数或惠特克 - 希尔函数描述，并且在最一般的情况下由四个复参数表征。详细研究了通过复ABCD光学系统的传播以及平方可积条件。EB的特殊情况包括标准、优美和广义的英斯 - 高斯光束、马蒂厄 - 高斯光束等。
