Gutiérrez-Vega Julio C, Bandres Miguel A
Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey, México.
J Opt Soc Am A Opt Image Sci Vis. 2005 Feb;22(2):289-98. doi: 10.1364/josaa.22.000289.
A detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z = 0 is modulated by a Gaussian envelope is presented. We call such a field a Helmholtz-Gauss (HzG) beam. A simple closed-form expression for the paraxial propagation of the HzG beams is written as the product of three factors: a complex amplitude depending on the z coordinate only, a Gaussian beam, and a complex scaled version of the transverse shape of the nondiffracting beam. The general expression for the angular spectrum of the HzG beams is also derived. We introduce for the first time closed-form expressions for the Mathieu-Gauss beams in elliptic coordinates and for the parabolic Gauss beams in parabolic coordinates. The properties of the considered beams are studied both analytically and numerically.
本文对一种任意无衍射光束的传播进行了详细研究，该光束在z = 0平面上的扰动由高斯包络调制。我们将这样的场称为亥姆霍兹 - 高斯（HzG）光束。HzG光束傍轴传播的一个简单闭式表达式被写成三个因子的乘积：一个仅依赖于z坐标的复振幅、一个高斯光束以及无衍射光束横向形状的复缩放版本。还推导了HzG光束角谱的一般表达式。我们首次给出了椭圆坐标下的马蒂厄 - 高斯光束和抛物坐标下的抛物高斯光束的闭式表达式。通过解析和数值方法研究了所考虑光束的特性。
