We introduce a partially coherent beam, called a multi-hyperbolic sine-correlated (MHSC) beam, by employing a multi-hyperbolic sine function to modulate the spectral degree of coherence. Based on the extended Huygens–Fresnel principle and second-order moments of the Wigner distribution function, we derive the analytical expressions for the spectral intensity, the root-mean-square (rms) angular width and the ${M^2}$ factor in turbulent atmosphere. Numerical results show that the intensity profile, which keeps the dark-hollow invariant in free space, will be gradually destroyed by the turbulence along the propagation distance. We believe that the MHSC beams have significant advantage over the hyperbolic sine-correlated beams for reducing the turbulence-induced degradation, especially for the MHSC beams with a higher beam order $N$. The effects of the beams parameters and the turbulent atmosphere on the beam quality are analyzed in detail.

中文翻译：

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多曲率正弦相关光束及其在湍流大气中的统计特性

通过采用多双曲正弦函数来调制光谱的相干度，我们引入了一个部分相干的光束，称为多双曲正弦相关（MHSC）光束。基于扩展的惠更斯-菲涅耳原理和维格纳分布函数的二阶矩，我们得出了光谱强度，均方根（rms）角宽度和$ {M ^ 2} $的解析表达式。湍流大气的因素。数值结果表明，强度分布图在自由空间中保持暗空不变，将被沿传播距离的湍流逐渐破坏。我们认为，MHSC梁有超过减少湍流引起的退化双曲正弦相关梁显著的优势，特别是对于MHSC具有较高的光束阶光束$ N $。详细分析了光束参数和湍流气氛对光束质量的影响。