Propagation Equation and Property of Spectral Degree of Coherence of Partially Coherent Flat-Topped Beams
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摘要: 根据惠更斯-菲涅耳原理,导出了部分相干平顶光束在自由空间中光束空间相干度的传输方程,并通过数值计算研究了光束空间相干度的传输特性.研究表明,部分相干平顶光束空间相干度会出现振荡和相位奇异现象;随光束相关长度和光束阶数的减小,光束空间相干度的振荡减弱,相位奇异点减少;随光束传输距离的增大,光束空间相干度的振荡增强,相位奇异点增多,且宽度增大,即光束的空间相干性变好;光束空间相干度宽度与光强宽度的关系与光束阶数和光束传输距离无关,仅与光束相关长度有关.Abstract: Based on the Huygens-Fresnel principle,propagation equation for the spectral degree of coherence of partially coherent flat-topped beams propagating in a free space was derived,and the properties of the spectral degree of coherence were investigated numerically.The research shows that the oscillatory behavior and phase singularities of the spectral degree of coherence may occur.The oscillatory behavior becomes weaker and pairs of points with the phase singularities become fewer with the decreases of beam spatial correlation length and beam order,but the oscillatory behavior becomes stronger and pairs of points with the phase singularities become more with the increase of propagation distance.The width of the spectral degree of coherence becomes larger with the increase of propagation distance,i.e.,the spatial correlation of partially coherent flat-topped beams is improved with the increase of propagation distance.In addition,the relationship between the width of the spectral degree of coherence and the width of intensity is independent of the beam order and propagation distance,but only depends on the spatial correlation length.
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