广义超几何光束在ABCD光学系统中的传播  

The Propagation of Generalized Hypergeometric Beams in ABCD Optical Systems

作　　者：陈建农[1] 于永江[1] 王菲菲[1] 

机构地区：[1]鲁东大学物理与电子工程学院,山东烟台264025

出　　处：《光学学报》2009年第4期902-906,共5页Acta Optica Sinica

基　　金：国家自然科学基金(10601045);校科研基金(20052801)资助课题

摘　　要：新型特殊模式激光束的传播是激光应用研究的基础和重要课题。利用柯林(Collins)积分公式研究了广义超几何光束在ABCD近轴光学系统中的传播行为,得到了光束在输出平面复振幅的解析表达式。结果表明,其传播后的复振幅分布与库默尔(Kummer)函数成正比。通过将Kummer函数展开成级数,获得了光束在输出平面复振幅的模的级数形式,从该级数可以看出,广义超几何光束在ABCD近轴光学系统中传播时的模式结构一般是要发生变化的。作为特殊光学系统,讨论了自由空间传播时近场和远场衍射近似表达式,它们均为一系列同心圆环,空间频率随径向坐标增加而增加,近场衍射时横向模式结构保持不变,而远场衍射时则发生变化。给出了光束的归一化系数,分析了该光束一些简化模式与高斯光束的关系。The study on the propagation of laser beams of new special modes is a fundamental and significant topic in laser application. Based on the Collins integral formula, the propagation of generalized.hypergeometric beams in paraxial ABCD optical systems is studied and the analytical expressions for complex amplitude at output plane are obtained. It is shown that the complex amplitude distribution after propagation in paraxial ABCD optical systems is proportional to Kummer function. By expanding Kummer function as a series,the modulus of this complex amplitude at the output plane could be represented as series summation which shows that the transverse structure of generalized hypergeometric beams propagating in paraxial ABCD optical systems will generally change its form. As a special optical system, the near-field and far-field diffraction behavior in free space is discussed. The transverse structures of both the near-field and far-field are a series of concentric rings and the spatial frequency increases with increase of the radial coordinate. The normalization coefficient was derived and also the relation between simplified modes of hypergeometric mode and Gaussian modes is analyzed.

关 键 词：超几何光束 ABCD光学系统 传播 自由空间 

分 类 号：O436[机械工程—光学工程]