具有余弦-洛伦兹关联结构函数部分相干高斯光束的聚焦性质

Focusing Properties of Partially Coherent Gaussian Beam with Cosine-Lorentz Correlated Structural Function

引入一类新的部分相干光束,其谱相干度或关联结构函数具有余弦-洛伦兹的非传统相关函数形式(即非高斯函数形式),这类部分相干光束满足Gori确定的充分条件,是物理上可实现的光束。基于广义惠更斯-菲涅耳衍射的Collins积分公式,获得了余弦-洛伦兹关联结构函数部分相干高斯光束通过近轴ABCD光学系统传输时其交叉谱密度函数的一般解析表达式,并探讨了光束经过薄透镜聚焦时光强分布的演化特性。结果表明:该类光束在合适的参数条件下能呈现自分裂和自整形等奇异传输特性,且这些传输特性与关联结构函数的性质密切相关;这类光束的自分裂和束斑形状变化是由关联结构函数中的不同因子产生的。因此,调控这类部分相干光束的关联结构函数分布可以有效调制其相干长度和非均匀性,从而可操控光束传输行为。该研究结果为实现4个正方形光束提供了可能方案,在工程技术领域具有重要的应用前景。

We propose a new kind of partially coherent beams whose non-conventional correlation function, also called spectral degree of coherence （SDOC）, contains two nonconventional components, i.e. , a cosine and a Lorentz functions. Such beam meets the sufficient condition established by Gori, and thus it is physically realizable. Analytical expressions of the cross-spectral density function of the proposed beam passing through a paraxial ABCD optical system are derived based on the generalized Huygens-Fresnel diffraction Collins formula. The light intensity distribution properties of beams focused by a thin lens are further analytically investigated. Results show that the proposed beam exhibits extraordinary propagation properties such as self-splitting and self-shaping, and these transmission properties are closely related to the properties of the correlation function. The cosine-function factor of the total SDOC is responsible for the self-splitting behavior and the Lorentz-function factor determines the self-shaping phenomenon. It is clearly shown that modulating the non-conventional SDOC of a partially coherent beam can alter the coherence length and the degree of nonuniformity, and thus provides an effective way to manipulate its focusing properties. Therefore, the results provide an alternative method for realizing four square beam spots, and have important application prospect in the engineering field.