大气湍流对涡旋光束轨道角动量谱的影响

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"Influences of atmospheric turbulence effects on the orbital angular momentum (OAM) spectra of vortex beams" 这篇研究探讨了大气湍流对不同类型涡旋光束（包括拉格朗日-高斯(LG)光束和贝塞尔光束）轨道角动量谱的影响。大气湍流是光学通信、激光传输等领域的一个重要问题，因为它会显著改变光束的传播特性，特别是对于携带轨道角动量的特殊光束。首先，研究者通过数值模拟生成具有不同折射率结构常数的湍流全息图，以模拟不同强度的大气湍流条件。轨道角动量是描述光束旋转性质的物理量，它在量子光学、信息传输以及粒子操控等领域有广泛应用。接着，他们分析了畸变的单模或复用LG光束以及贝塞尔光束的OAM谱。LG光束和贝塞尔光束都是涡旋光束的典型代表，但它们在大气中的行为有所不同。LG光束具有明确的环形光强分布，而贝塞尔光束则呈现无衍射的特性，即使在没有湍流的情况下也能保持较远距离的形状不变。结果表明，与LG光束相比，贝塞尔光束的OAM谱更加分散，这意味着贝塞尔光束在经过大气湍流时受到的影响更大。这种现象可能归因于贝塞尔光束的内在结构使其对环境扰动更敏感。大气湍流会导致光束的传播路径发生随机变化，从而破坏光束的结构，尤其是对于依赖特定模式的OAM值。这一研究的重要性在于，它为理解和优化大气湍流环境下的OAM光束传输提供了理论基础。对于利用OAM进行自由空间光通信或遥感等应用，理解并补偿大气湍流的影响至关重要。此外，这些发现也可能对天文学、遥感技术以及潜在的太空通信系统产生影响，因为这些领域同样需要考虑大气条件对光束传播的影响。这项工作揭示了大气湍流对不同类型涡旋光束OAM谱的具体影响，为未来开发更稳定、抗干扰的光学通信系统提供了新的见解和设计依据。同时，这也为优化大气光学实验和实际应用中的光束传输策略提供了理论支持。

Influences of atmospheric turbulence effects on the

orbital angular momentum spectra of vortex beams

Shiyao Fu and Chunqing Gao*

School of Opto-electronics, Beijing Institute of Technology, Beijing 100081, China

*Corresponding author: gao@bit.edu.cn

Received April 12, 2016; revised June 3, 2016; accepted June 26, 2016;

posted June 27, 2016 (Doc. ID 262979); published July 29, 2016

We investigate the atmospheric turbulence effects on orbital angular momentum (OAM) spectra of different kinds

of vortex beams, including Laguerre–Gaussian (LG) beams and Bessel beams, numerically. We generate the holo-

grams of atmospheric turbulence with different structure constants of the refractive index. The OAM spectra of

distorted single-mode or multiplexed LG beams and Bessel beams are analyzed. Compared with the OAM spectra

of the two kinds of vortex beams, the spectrum of the Bessel beams is more dispersive. The results illustrate that

OCIS codes: (010.1330) Atmospheric turbulence; (050.4865) Optical vortices; (050.1940) Diffraction.

http://dx.doi.org/10.1364/PRJ.4.0000B1

1. INTRODUCTION

Vortex beams such as Laguerre–Gaussian (LG) beams

and Bessel beams are intensively investigated for their

unique performance. It was shown by Allen et al. that the

complex amplitude of a vortex beam comprises an azimuthal

phase term expilϕ, where ϕ is the azimuthal angle, and

l is the topological charge [1]. And each photon in vortex

beams carries the orbital angular momentum (OAM) of lℏ

(ℏ is Planck’s constant divided by 2π).

There have been recent growing interest in applying vortex

beams in free-space optical communications [2,3]. The topo-

logical charge l of a vortex beam, in principle, is an infinite

integer value. In addition, the OAM of an optical beam can

carry an unlimited number of bits. Therefore, vortex beams

can tremendously increase the capacity of optical communi-

cation systems through mode multiplexing. Thus terabit

free-space data transmission has been realized [2]. In general,

LG beams are used as the vortex beams in free-space optical

communication systems. However, another kind of vortex

beam, the Bessel beam, also can be employed in the free-

space multicasting [4]. Compared with LG beams, Bessel

beams have the characteristics of nondiffraction [5], which

means they are capable of recovering by themselves in the

face of obstruction.

In a free-space optical communication system based on vor-

tex beams, the effects caused by atmospheric turbulence

should not be ignored. It is well known that the temperature

and pressure’s inhomogeneities of the atmosphere will con-

tribute to the variations of the refractive index along the trans-

mission path, which may distort the helical wavefront and

increase the bit error rate (BER) of data transmission in

optical communication systems [6]. The aberrant wavefront

distorted by turbulence will also result in the OAM spectrum’s

dispersion [6,7]. The stronger the turbulence is, the more dis-

persive the spectrum will be. Hence, it is significant to evalu-

ate the atmospheric turbulence effect on vortex beams by

studying the variation of their OAM spectra.

Researchers have done a lot in assessing the atmospheric

turbulence influence on vortex beams [6–10]. LG beams and

Bessel beams can be utilized in high-capacity free-space data

transmission through mode-division multiplexing. When they

propagate through turbulent atmosphere simultaneously

under the same condition (beam size, topological charge,

turbulence strength, and so on), the influences of turbulent

atmosphere on the OAM spectra of LG beams and Bessel

beams have not been discussed simultaneously.

In this paper, we numerically study the variation of OAM

spectrum when LG beams and Bessel beams propagate

through atmospheric turbulence under the same condition in

different cases. In addition, the case of transmission through

the same turbulence strength at different propagation distan-

ces and the variation of the desired channel proportion of the

two kinds of vortex beams are also investigated.

2. ATMOSPHERIC MODEL

To study the influence on vortex beams caused by turbulent

atmosphere, the first thing to do is generate phase gratings

that can simulate the turbulent atmosphere. The turbulence

can be modeled by an Nth order matrix of random complex

numbers with statistics that match Kolmogorov turbulence

theory [11]. In our simulation, the turbulence model devel-

oped by von Karman is used [12,13]. It can be shown from

modified von Karman spectrum, which includes the inner

scale introduced by Tatarskii, that the spectrum of fluctua-

tions in refractive index ϕ

κ can be written as

κ0.033C

· κ

 k



−11∕6

exp−κ

∕k

; (1)

where k

 2π∕L

and k

 5.92∕l

. Parameters L

and l

are

the outer and inner scale of turbulence, respectively. In

Eq. (1), κ denotes the spatial wavenumber, and C

is the struc-

ture constant of the refractive index, which represents the tur-

bulence strength. Under the Markov approximation, the phase

spectrum can be expressed as

S. Fu and C. Gao Vol. 4, No. 5 / October 2016 / Photon. Res. B1

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