Elsevier

Optik

Volume 211, June 2020, 164612
Optik

Original research article
Statistical properties of twisted Gaussian Schell-model array beams in anisotropic ocean

https://doi.org/10.1016/j.ijleo.2020.164612Get rights and content

Abstract

The effect of anisotropic oceanic turbulence on propagation characteristics of twist Gaussian Schell-model array beams is investigated. The analytical expression for the cross-spectral density function of such beam propagating through turbulent ocean is derived and used to explore the evolution behavior of the spectral intensity and the degree of coherence. An example illustrates the fact that, the most important oceanic effect is destroying the far zone lattice-like beam profile, and the beam shape eventually converges into Gaussian profile. Besides, after passing through the turbulence at sufficiently large distances from the source, the twist phase modulation of the second-order statistical properties is shown to be suppressed by the turbulence fluctuation, the spectral intensity evolves in the same way with different twist strength, and so is the case for the degree of coherence. The impacts, which arise from the source coherence and the turbulence parameters on beam characteristics are analyzed in detail.

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 z=0, can be expressed as [17]W(0)(ρ1,ρ2,0)=expρ12+ρ224σ02gρ1ρ2expiux1yx2y,where ρ1=(x1,y1) and ρ2=(x2,y2) are arbitrary two-dimensional position vectors. σ0 denotes the beam width, u characterizes the strength of source twist, and g denotes the degree of coherence. Here, g has the fromgρ1ρ2=expx1x222δx2expy1y222δy2×nx=PPcos2πnxRxδxx1x2ny=QQcos2πnyRyδyy1y2,

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: λ=632nm, Nx=Ny=3, σx=δx=1mm, σy=δy=0.3mm, Rx=2Ry=3mm, u=2mm, ξ=2, w=2.5, χT=107K2/s, ε=109m2/s3, and η=1mm.

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.

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