具有余弦-高斯关联结构函数部分相干贝塞尔-高斯光束的传输性质及四暗空心光束的产生

基于广义惠更斯-菲涅耳衍射积分公式,获得了余弦-高斯关联结构函数部分相干贝塞尔-高斯光束交叉谱密度函数通过近轴ABCD光学系统传输时的解析表达式.并因此探讨了该类光束经过自由空间传输时光强分布的演化特性.结果表明,余弦-高斯关联部分相干贝塞尔-高斯光束在合适的参数条件下能呈现自分裂等奇异传输特性.特别地,这种自分裂可实现暗空心光束的复制,即从一个暗空心光束获得四个相似的暗空心光束.并且发现这些传输特性和关联结构函数结构密切相关,因此调控关联结构函数分布以实现调制光的相干长度和空间分布性质从而可实现操控光束传输行为.由于暗空心光束在工程技术领域的重要应用价值,本文的研究结果提供了实现四暗空心光束的可能方案,从而在激光通信、微粒操控等方面具有重要的应用前景.

Propagation properties of nonuniform cosine-Gaussian correlated Bessel-Gaussian beam through paraxial ABCD system and generation of dark-hollow beam array

Partially coherent beams with nonconventional correlation functions have been extensively studied due to their wide and important applications in free-space optical communication, particle trapping, image transmission and optical encryption. Here, we study the propagation of nonuniform cosine-Gaussian correlated Bessel-Gaussian beam (cGBCB) in detail. Analytical expressions for the cross-spectral density function of cGBCBs through paraxial ABCD system are derived based on the extended Huygens-Fresnel integral. By use of the derived formulae, the intensity distribution properties of a nonuniform cGBCB on propagation in free space are analytically investigated. Some numerical calculation results are presented and discussed graphically. It is found that when the root-mean-square correlation width δ and the parameter controlling the degree of coherence profiles β are appropriately chosen, the intensity distribution of the nonuniform cGBCB displays self-splitting properties during propagation. We point out that rather than a simple duplication, the self-splitting behaviour consists of a complex process in which the dark hollow pattern for cGBCB is gradually filled in the centre at first, then starts to split with increasing the propagation distance, and most impressively, an evolution process from a single dark hollow beam in the source plane to quadruple dark hollow profiles in certain propagation ranges can be realized. The influence of correlation function on the evolution properties of the intensity distribution is investigated, demonstrating that the values of parameters δ and β of the correlation function play a critical role in inducing the self-splitting effect for nonuniform cGBCB on propagation in free space. Therefore, it is clearly shown that modulating the correlation function of a partially coherent beam can alter the coherence length and the degree of nonuniformity, and thus provides an effective way of manipulating its propagation properties. We also find the evolution speed of the intensity distribution can be greatly affected by the topological charge n of the beam function and the parameter R controlling the hollow size of cGBCB in source plane, e. g. the intensity distribution evolves into quadruple dark hollow profiles more slowly with larger n or smaller R. As is well known, the dark-hollow intensity configurations are useful in many applications and have been extensively studied both theoretically and experimentally. Therefore, the results drawn in the paper develop an alternative way to realize dark-hollow beam array, and further pave the way for dark hollow beam applications in long-distance free-space optical communications.