海洋湍流下的CGSM光束传播：光谱特性与参数影响

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本文研究了海洋湍流对余弦-高斯相关谢尔模型（Cosine-Gaussian Correlated Schell Model, CGSM）光束传播的影响。基于扩展的惠更斯-菲涅耳原理，作者推导出了一种解析方法，用于计算在海洋湍流条件下CGSM光束的跨谱密度函数。这种函数反映了光束在不同频率成分之间的相互作用，是评估光束特性如功率分布和相位稳定性的重要指标。研究中，重点考察了三个关键的海洋湍流参数：温度-盐度平衡参数ω、均方温度耗散率χ(T)以及每单位质量ε的能量耗散率。这些参数直接影响光束的光谱密度，即不同频率成分的强度分布，以及光谱相干度，即光束中不同频率成分之间的相关程度。海洋湍流的存在会改变光束的这些特性，使得它们在传播过程中经历衰减、扩散和随机相位变化，从而导致光束的品质恶化。通过数值模拟，作者揭示了这些参数如何具体影响CGSM光束的光谱密度和光谱相干度。例如，温度耗散率的增加可能导致光束中心部分的强度降低，而边缘部分则可能更加分散。平衡参数ω的变化可能引起光束形状的变形，而能量耗散率ε的增加则会加速这种变形和失相干过程。因此，对于在海洋环境下工作的光纤通信系统或者激光测距应用，理解和控制这些效应至关重要，以便设计出抗干扰性能更强的光学系统。本研究深入剖析了海洋湍流对CGSM光束传播的物理机制，为优化光束在复杂海洋环境中的传输性能提供了理论依据。这不仅有助于提升光纤通信系统的可靠性，也对海洋观测、海洋工程等领域中的光学技术发展具有实际意义。

Effect of oceanic turbulence on the

propagation of cosine-Gaussian-correlated

Schell-model beams

Chaoliang Ding, Lamei Liao, Haixia Wang, Yongtao Zhang and

Liuzhan Pan

Department of Physics, Luoyang Normal University, Luoyang 471022, People’s Republic of China

E-mail: dingchaoliang2006@126.com and panliuzhan@263.net

Received 23 December 2014

Accepted for publication 21 January 2015

Published 20 February 2015

Abstract

On the basis of the extended Huygens–Fresnel principle, the analytic expression for the cross-

spectral density function of the cosine-Gaussian-correlated Schell-model (CGSM) beams

propagating in oceanic turbulence is derived and used to investigate the spectral density and

spectral degree of coherence of CGSM beams. The dependence of the spectral density and

spectral degree of coherence of CGSM beams on the oceanic turbulence parameters including

temperature-salinity balance parameter ω, mean square temperature dissipation rate χ

and

energy dissipation rate per unit mass ε is stressed and illustrated numerically. It is shown that

oceanic turbulence plays an important role in the evolution of spectral density and spectral

degree of coherence of CGSM beams upon propagation.

Keywords: ocean optics, coherence, beam characteristics, propagation

(Some ﬁgures may appear in colour only in the online journal)

1. Introduction

In the past few decades, Gaussian Schell-model sources that

have degrees of coherence that have position-independent

Gaussian distribution have been studied comprehensively due

to their tractability and universality [1–4]. Since Gori et al

established the sufﬁcient condition for devising a genuine

correlation function of a scalar or electromagnetic partially

coherent source [5, 6], some other augmented models for

partially coherent sources have been recently introduced in

which the classic Gaussian degree of coherence is modulated

by a well-behaved function such as the J

-correlated Schell-

model sources [7], the non-uniformly correlated sources

[8, 9], the Multi-Gaussian Schell-model sources [10–14], the

Bessel–Gaussian Schell-model sources, the Laguerre–Gaus-

sian Schell-model sources [15], the cosine-Gaussian Schell-

model sources [16], the nonuniformly cosine-Gaussian sour-

ces [17],the specially correlated radially polarized sources

[18] and the sinc Schell-model sources [19, 20] in which

some sources have been generated experimentally

[18, 21, 22]. Surprisingly, the beams generated by these

sources reveal many interesting and useful features in pro-

pagation. In particular, the beams produced by the cosine-

Gaussian Schell-model sources take on the dark-hollow pro-

ﬁle in the far-ﬁeld intensity distribution [16].

In recent years partially coherent dark-hollow beams

have received a lot of attention due to their wide applications

in atomic optics experiments involving optical tweezers, atom

switches and atomic lenses [23, 24]. Some theoretical models

have been proposed to describe partially coherent dark-hol-

low beams [25–29]. However, in these models the dark-hol-

low intensity proﬁles keep invariant for short propagation

distances; they become Gaussian distributions in the far ﬁeld.

In 2013, Z R Mei and O Korotkova introduced a new random

source, i.e. cosine-Gaussian Schell-model sources in which

the intensity is a Gaussian function, but the degree of

coherence is a Gaussian function modulated by the cosine

function [16]. Compared with the classic dark-hollow beams

model, the new model can produce dark-hollow intensity

proﬁles in the far ﬁeld. This feature makes them particularly

Journal of Optics

J. Opt. 17 (2015) 035615 (9pp) doi:10.1088/2040-8978/17/3/035615

Author to whom any correspondence should be addressed.

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