拉盖尔高斯涡旋光束对生物细胞的散射特性分析

Analysis of Scattering of Laguerre-Gaussian Vortex Beam by Biological Cells

采用强度矩量分析法得到拉盖尔高斯涡旋光束的波束宽度及发散角。利用复源点方法得到厄米高斯光束的球矢量波函数展开形式，结合厄米多项式与拉盖尔多项式的转换关系，推导得到拉盖尔高斯涡旋光束展开为球矢量波函数的表达式。利用广义洛伦兹Mie理论，研究了拉盖尔高斯涡旋光束对癌细胞的散射特性。数值分析了不同模阶数及不同传输距离的拉盖尔高斯涡旋光束在垂直于传播方向横截面的强度和相位分布。结果表明：随着径向、方位向模阶数及传输距离的增加，拉盖尔高斯涡旋光束的光斑尺寸变大，另外随着传输距离的增加，拉盖尔高斯涡旋光束的相位结构呈现不同于源平面的特点。利用拉盖尔高斯涡旋光束的强度分布特征来解释不同模光束入射的散射强度的角分布特点。

The beam width of Laguerre-Gaussian vortex beam is derived by using intensity momentum method. Using the expression of Hermite-Gaussian beam in terms of spherical vector wave functions by complex source point method, and combining with the transformation between Laguerre polynomial and Hermite polynomial, Laguerre- Gaussian vortex beam is expanded in terms of spherical vector wave functions. Utilizing the generalized Lorenz Mie theory, the scattering of Laguerre-Gaussian vortex beam by cancer cells is investigated. The intensity and phase distribution at cross section perpendicular to the propagation axis with different beam modes and different propagation distances is analyzed numerically. The results show that with the increase of the radial and azimuthal mode index and the propagation distance, the size of the beam increases. The phase distribution of Laguerre-Gaussian vortex presents different characteristics from source plane with the increase of propagation. Stemming from the intensity distribution of Laguerre-Gaussian vortex beam, the scattering properties are interpreted.