Wan-Jun Wang, Zhen-Sen Wu
J Opt Soc Am A Opt Image Sci Vis. 2018 Jul 1;35(7):1165-1172. doi: 10.1364/JOSAA.35.001165.
The propagation characteristics of annular cos-Gaussian beams and Bessel-Gaussian beams in turbulence have been widely investigated. However, the expression of the average intensity of Bessel-Gaussian beams involves a complex double integral, which requires large computational resources and does not easily ensure accuracy. Under this background, through the general cos-Gaussian beam rotation, a new annular cos-Gaussian beam is proposed which not only has some properties of the general cos-Gaussian beam, but also properties similar to those of the Bessel-Gaussian beam. Moreover, the annular cos-Gaussian beam is simpler in form than the general one and much more time-saving in calculation than the Bessel-Gaussian beams. Based on the extended Huygens-Fresnel principle, the average intensity on a receiver plane of the annular cos-Gaussian beams can be simplified to a summation of several polynomials and it is in good agreement with that of low-order Bessel Gaussian beams. The average radius and the power in the bucket are also derived. In summary, the annular cos-Gaussian beam has promising applications for its quick calculation and simple form among annular beams and hollow beams.
环形余弦高斯光束和贝塞尔高斯光束在湍流中的传输特性已得到广泛研究。然而，贝塞尔高斯光束平均强度的表达式涉及复杂的二重积分，这需要大量的计算资源且不易保证精度。在此背景下，通过对一般余弦高斯光束进行旋转，提出了一种新型环形余弦高斯光束，它不仅具有一般余弦高斯光束的一些特性，还具有与贝塞尔高斯光束相似的特性。此外，环形余弦高斯光束的形式比一般的更简单，计算时比贝塞尔高斯光束更省时。基于扩展的惠更斯 - 菲涅耳原理，环形余弦高斯光束在接收平面上的平均强度可简化为几个多项式的求和，并且与低阶贝塞尔高斯光束的平均强度吻合良好。还推导了平均半径和桶中功率。综上所述，环形余弦高斯光束因其计算快捷、形式简单，在环形光束和空心光束中具有广阔的应用前景。
