Original research articleStatistical properties of twisted Gaussian Schell-model array beams in anisotropic ocean
Introduction
In 1993, Simon et al. introduced a twist phase concept, and added such phase on conventional Gaussian Schell-model beams, named twist Gaussian Schell-model (TGSM) beams [1]. It is demonstrated that the twist phase can exist only in partially coherent beams, and it can rotate the beam spot upon propagation. Inspired by the pioneering work, considerable attentions have been paid on the properties of the TGSM beams [[2], [3], [4], [5], [6], [7], [8], [9], [10]]. Recently, many attempts have been made to attaining genuine twisted non-GSM sources. For instance, Borghi et al. derived the necessary and sufficient condition of the twisted Schell-model beam with axial symmetry [11,12]. Mei et al. modeled bona fide twisted beams through a superposition integral [13]. Gori et al. provided a mathematical procedure to generate genuine twisted sources [14]. Moreover, Nontrivial twisted partially coherent beams such as twisted EM beams with structured correlations, twisted Laguerre-Gaussian Schell-model beams and twisted Gaussian Schell-model array beams were also proposed [[15], [16], [17], [18]].
On the other hand, the evolution behavior of partially coherent optical fields in the presence of random turbulence, such as the Earth’s atmosphere, has been investigated in depth [[19], [20], [21], [22], [23], [24], [25]]. In recent years, another important natural turbulence, turbulent ocean has gained increasing attention due to the development of underwater communicating system [26] and underwater imaging technology [27,28]. In 2000, Nikishov et al. proposed a spatial power spectrum of oceanic turbulence, which is determined by the effects of both temperature fluctuations and salinity fluctuations [29]. By using this model, the second-order statistical characteristics of various partially coherent beams in homogeneous and isotropic sea water have been carried out, such as partially coherent radially polarized beam, multi-Gaussian Schell-model beam, stochastic electromagnetic beam and Gaussian Schell-model vortex beam [[30], [31], [32]]. Moreover, the influence of oceanic turbulence with anisotropy on the intensity and polarization distributions, the beam quality, the orbital angular momentum and the Strehl ratio have also been studied [[33], [34], [35], [36]].
Recently, a class of twisted partially coherent sources for producing Gaussian array profiles has been introduced, termed as twisted Gaussian Schell-model array (TGSMA) sources [17]. Such sources can radiate fields with rotating lattice-like intensity, which are of particular interest for many applications such as beam shaping and complex manipulation of multiparticle [37,38]. To the best of our knowledge, the propagation properties of the novel twisted partially coherent beams in random media have not been reported. In this manuscript, we explore the behavior of the TGSMA beams propagating in the presence of a random medium, for example, the anisotropic oceanic turbulence. The impacts arising from the twist factor, the source coherence and the turbulence parameters on the beam statistical characteristics are investigated.
Section snippets
Analytic solutions for TGSMA beams in oceanic turbulence with anisotropy
The cross-spectral density (CSD) function of a TGSMA field in the source plane , can be expressed as [17]where and are arbitrary two-dimensional position vectors. denotes the beam width, characterizes the strength of source twist, and denotes the degree of coherence. Here, has the from
Numerical examples
In this section, we will numerically analyze the statistical properties of a TGSMA beam propagating through anisotropic oceanic turbulence. Unless other values are specified in captions, the initial parameters are set as follows: , , , , , , , , , and .
Fig. 1 illustrates the evolution of the normalized spectral intensity of a TGSMA beam propagation though oceanic turbulence at several selected distances. It
Conclusion
In this manuscript, we have investigated the behavior of TGSMA beams propagating through turbulent ocean. The analytical formula for the CSD function of such beam on propagation is derived, and used to explore the second-order statistical properties in various oceanic conditions. One sees that the most important oceanic effect is destroying the far zone lattice-like intensity distribution, which can persevere for any large distance for free-space propagation, and the beam spot eventually
Funding
This work was supported by the National Natural Science Foundation of China [grant numbers 11704098, 11974101].
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (38)
- et al.
Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium
J. Opt. Soc. Am. A
(2017) - et al.
Effect of oceanic turbulence on polarization of stochastic beams
Opt. Commun.
(2011) - et al.
Twisted Gaussian Schell-model beams
J. Opt. Soc. Am. A
(1993) - et al.
Interpretation and experimental demonstration of twisted Gaussian Schell-model beams
J. Opt. Soc. Am. A
(1994) - et al.
Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams
Opt. Lett.
(2002) - et al.
Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere
Opt. Express
(2010) - et al.
Orbital angular momentum of partially coherent beams
Opt. Lett.
(2001) - et al.
Spatial correlation properties of twisted partially coherent light focused by diffractive axicons
J. Opt. Soc. Am. A
(2012) - et al.
Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams
Opt. Lett.
(2015) - et al.
Transfer of radiance by twisted Gaussian Schell-model beams in paraxial system
Pure Appl. Opt.
(1996)