涡旋光束二阶非线性效应在简单数学运算中的应用研究

项目名称： 涡旋光束二阶非线性效应在简单数学运算中的应用研究

项目编号： No.61307001

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 丁攀峰

作者单位： 华侨大学

项目金额： 25万元

中文摘要： 涡旋光束具有独特的螺旋相位结构，采用拓扑荷数来表征，如果将涡旋光束作为输入光束进行倍频、和频以及差频，产生光束除了频率改变外，另外一个重要的变化就是光束的拓扑荷数。在通常情况下，涡旋光束的拓扑荷数非常稳定，而且其测量结果准确可靠，不存在近似的问题。因此，从拓扑荷数的角度来看，涡旋光束的倍频、和频与差频分别完成了加倍、加法和减法的数学运算。和强光非线性效应不同，以上过程不要求有较高的输出功率，只要产生光束具有较小的强度，能够测出拓扑荷数即可。因此，涡旋光束二阶非线性的实验条件简单，可以在以前成熟的二阶非线性光学基础上进行，非常方便地实现拓扑荷数的加法、减法运算，为以后在光域内实现复杂的数学和逻辑运算奠定基础。

中文关键词： 拓扑荷数；涡旋光束；数学运算；非线性效应；相干性

英文摘要： Vortex beam possesses special spiral phase structure, which can be interpreted by the topological charge. If vortex beam is used to further the process of SHG, SFG and DFG, the frequency of the produced optical beam will change. Besides, another important change is the topological charge. Generally, the topological charge of a vortex beam is very stable on common conditions and its measurement is exact and reliable, which is not approximate at all. So from the point of view of the topological charge, it can be regarded that the process of SHG, SFG and DFG fulfill the mathematic calculation of doubling, addition and subtraction, respectively. The process is quite different from that of the strong nonlinear optics. It does not need high output optical power. The produced beam with properly small power can govern the measurement of the topological charge. So the experiment of second order nonlinear effects for vortex beam can be easily put in practice. And it can be done on the prevenient base for traditional second order nonlinear optics. In this way the calculation of addition and subtraction of the topological charge can be easily realized. The research may provide guidance of complex calculation of math and logic in optical domain.

英文关键词： topological charge；vortex beam；mathematic calculation；nonlinear effect；coherence