摘要:
在圆柱坐标系中研究了傍轴线偏振拉盖尔-高斯光束在两种各向同性介质界面反射和折射后光强质心的偏移.基于菲涅耳近似和泰勒级数展开,分别得到了部分反射和全反射两种情形下,质心的横向偏移和纵向偏移与光束拓扑荷的解析关系式.研究表明,部分反射时,反射和折射光束的横向偏移的大小与光束的拓扑荷成正比,方向由拓扑荷的符号决定;而纵向偏移仅仅大小与光束的拓扑荷有关.全反射时,反射光束质心偏移不受拓扑荷影响.通过数值模拟验证了解析结果的正确性,并得到了解析公式的适用条件.拉盖尔-高斯光束的质心偏移特性可应用于测量光束的径向节点数和拓扑荷,对利用拉盖尔-高斯光束进行信息编码和传输具有重要意义.
Abstract:
We study shifts of the beam centroid of linearly polarized paraxial Laguerre-Gaussian beams reflected and refracted at an interface of isotropic dielectric in the cylindrical coordinate system.According to the Fresnel approximation and the Taylor series expansion,we derive analytical expressions for transverse and longitudinal shifts and their general relationship with topological charge in the cases of partial and total reflection,respectively.It is shown that in the partial reflection regime,transverse shifts of both reflected and refracted beams are in proportion to the topological charge of beams and their directions are determined by the sign of the topological charge,while only the value of longitudinal shift is related to the topological charge.In the regime of total reflection,the shift of reflected beam centroid is independent of topological charge.To verify our analytical results,we perform numerical simulations of the shifts of reflected and refracted beams directly and indicate the applicable condition of the analytical expressions.The shifts of the beam centroid can be applied to the measurement of the topological charge and radial node number of Laguerre-Gaussian beams,which is of significance for information encoding and communication.
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