厄米-高斯模与拉盖尔-高斯模的图像比较

Graphic Comparisons between Hermite-Gaussian Modes and Laguerre-Gaussian Modes

简要地叙述了厄米-高斯模与拉盖尔-高斯模的一些理论,画出了具有代表性的厄米-高斯模与拉盖尔-高斯模在z=0平面的三维图像。为了了解厄米-高斯模与拉盖尔-高斯模的各种模态的关系,分别画出了它们的模态从(0,0)到(2,2)的强度等高线,并从模阶数与峰值、峰值的变化、延伸面积和对称性得到了它们各自的特性,然后进行对比得到它们之间的相同点和不同点。另外通过图像和公式说明了厄米-高斯与拉盖尔-高斯最低阶模(0,0)是一致的,即高斯模。对比了它们之间的电(磁)场和平均坡印廷矢量,不同点与模态有很大关系。画出横截面中振幅强度随传输距离增加而变化的图像,从中得到了束宽和峰值强度与传输距离之间的关系。

The Hermite-Gaussian modes and Laguerre-Gaussian modes are briefly described. The three-dimensional plots of Hermite-Gaussian modes and Laguerre-Gaussian modes in the plane z=0 are drawn. For the sake of revealing the relation among the various modes of Hermite-Gaussian and Laguerre-Gaussian, contour maps for modal orders varying from （0,0） to （2,2） are plotted. The characteristics of the mode order number and the peak value, the change of peak value, the extending area and the symmetry are obtained, respectively. The similarities and differences of the characteristics can also be acquired through the comparisons. The minimum modes of Hermite-Gaussian and Laguerre-Gaussian are consistent, which can be described both in images and formulas. The differences between the electric （magnetic） field and averaged Poynting vector have relationship with the mode. The image of amplitude intensity of the cross-sectional image changes along with the increase of transmission distance. The waist of the beam and peak value also have some connections with the transmission distance.