非高斯湍流对Airy-Schell光束轨道角动量螺旋谱的影响分析

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"该文研究了非高斯 Kolmogorov 涡旋湍流对 Airy-Schell 激光束轨道角动量（OAM）螺旋光谱的影响。通过几何光学近似方法，作者分析了不同条件下的光束传播特性，包括波长、OAM 量子数、主环半径以及任意横截面尺度等参数对光束扩散的影响。在弱湍流环境中，发现较短波长、较小的 OAM 量子数、较大的主环半径和更高的横截面尺度可以减小因衍射导致的光束扩散。此外，Airy-Schell 激光束在径向方向上的模式概率密度振荡频率显著低于 Hankel-Bessel 激光束。文章指出，Airy-Schell 和 Hankel-Bessel 激光束的模式概率密度强烈依赖于波长和 OAM 量子数。为了优化这些特性，文章探讨了如何在非高斯 Kolmogorov 涡旋湍流中保持激光束的稳定性和传输效率。" 本文是光学领域的一篇研究论文，重点关注了非典型 Kolmogorov 涡旋湍流对 Airy-Schell 激光束的螺旋光谱特性的扰动。Kolmogorov 涡旋湍流是一种大气中常见的光学传播环境模型，通常用来描述光在大气中的传播特性。在实际应用中，如远距离通信、天文观测或激光技术，理解这种湍流对光束传播的影响至关重要。 Airy-Schell 激光束是一种特殊的光束类型，结合了 Airy 波前和 Schell 模型的优点，具有独特的传播特性，能够在一定程度上抵抗大气湍流导致的扩散。文章通过数值模拟展示了在水平路径上传播的 Airy-Schell 激光束，揭示了波长、OAM 量子数、主环半径以及横截面尺度等关键因素如何影响光束的扩散程度。其中，较短的波长和较小的 OAM 量子数有助于减小光束扩散，而更大的主环半径和更高的横截面尺度则能提高光束的稳定性。此外，文章还比较了 Airy-Schell 激光束与 Hankel-Bessel 激光束在径向模式概率密度振荡频率上的差异，表明前者在湍流环境中的表现可能更优。这一特性对于选择合适的光束类型用于特定的光学应用，如长距离光通信或自由空间光信息传输，提供了理论依据。这项研究为理解和优化非高斯 Kolmogorov 涡旋湍流环境下的光束传播提供了重要的理论基础，有助于开发更高效、稳定的光学系统。未来的研究可能会进一步探索如何利用这些发现来改善实际应用中的光束质量，并对抗大气湍流带来的影响。

Spiral spectrum of Airy–Schell beams through

non-Kolmogorov turbulence

Yun Zhu (朱云)

1,2

, Licheng Zhang (章里程)

, and Yixin Zhang (张逸新)

School of IoT Engineering, Jiangnan University, Wuxi 214122, China

School of Science, Jiangnan University, Wuxi 214122, China

*Corresponding author: zyx@jiangnan.edu.cn

Received October 20, 2015; accepted January 25, 2016; posted online March 18, 2016

Based on the geometrical optics approximation, we analyze the effects of non-Kolmogorov turbulence on the

spiral spectrum of the orbital angular momentum (OAM) of Airy–Schell beams. Our numerical results of

Airy–Schell beams on the horizontal path show that the beam spreading due to diffraction is smaller for shorter

wavelengths, a smaller OAM quantum number, a larger radius of the main ring, and a higher arbitrary trans-

verse scale in weak turbulence. The oscillation frequency of the mode probability density of Airy–Schell beams

in the radial direction is much lower than that of Hankel–Bessel beams. The mode probability densities of

Airy–Schell and Hankel–Bessel beams are remarkably dependent on the wavelength and OAM quantum num-

ber. In order to improve the mode probability density, Airy–Schell beams with shorter wavelengths and lower

OAM quantum numbers may be the better choice, which is diametrically opposite to Hankel–Bessel beams. Our

research provides a reasonable basis for selecting light sources and precise tracking.

OCIS codes: 100.6640, 210.4770, 180.1790.

doi: 10.3788/COL201614.042101.

According to its exotic features, such as non-diffracting

[1]

self-accelerating

[2–4]

, and self-healing

[5,6]

in vacuum, more

and more attention has been paid to Airy beams. The

propagation properties of Airy beams in atmospheric tur-

bulence, such as scintillation

[7,8]

, evolution

[9]

, thermal

blooming

[10]

, beam wander

[11]

, average intensity distribu-

tion

[12]

, and average spreading

[13]

also have been carefully

investigated. But, as we know, there are almost no discus-

sions with respect to the effects of turbulence on the spiral

spectrum of the orbital angular momentum (OAM) modes

of Airy–Schell (AS) beams.

Considering the needs of precise tracking and significant

deviations from Kolmogorov’s model in certain atmos-

pheric experiments

[14]

, in this Letter, we discuss the radial

distribution of the mode probability density (MPD) and

crosstalk probability density (CPD) of the OAM modes

of AS beams in the horizontal path through the non-

Kolmogorov atmosphere in various situations. To reveal

the distinctive properties of the spiral spectrum of the

OAM of the AS beams in a turbulent atmosphere, we also

compare them with Hankel–Bessel (HB) beams

[15]

On account of the Gaussian-like Airy beam in

far-field region, for long-distance transmissions, both trun-

cated Airy and HB beams become spherical-like beams.

Based on the Retov approximation, in the weak fluc-

tuation region

[16]

, q ¼ z∕kρ

< 1, where qΛ < 1, ρ

is the

spatial coherence radius of a plane wave, k is the wave

number of light, and Λ ¼ 2z∕kW

is the Gaussian beam

parameter characterizing the spot size W at the receiver.

In the half-space z > 0, the complex amplitude of an Airy

beam is given by

Aiðr; φ; zÞ¼Ai

ðr; φ; zÞexp½ψ

ðr; φ; zÞ; (1)

where r ¼jrj, r ¼ðx; yÞ is the two-dimensional position

vector in the source plane, φ is the azimuthal angle,

and z is the propagation distanc e. ψ

ðr; φ; zÞ is the com-

plex phase of waves propagating through turbulence

and Ai

ðr; φ; zÞ is the normalized Airy-Gaussian model

at the z plane with the OAM quantum number l

in free

atmospheric turbulence. In the paraxial approximation,

ðr; φ; zÞ has the form

[17]

ðr; φ; zÞ¼−

ðr

− ω

ÞJ



krr



× exp





expð−il

φÞ; (2)

where ω

is associated with the arbitrary transverse scale,

is the approximate radius of the main ring, and a is the

exponential truncation. J

ðkrr

∕zÞ denotes the l

order

Bessel function of the first kind.

For a paraxial beam, the second-order cross-spectral

density of the partially coherent case is defined by the stat-

istical average over the ensembles as the following

[16,18]

W ðr; r

; zÞ¼hEð r; φ; zÞE



ðr

; φ

; zÞi; (3)

where Eðr; φ; zÞ is the complex amplitude of the AS beams

and hirepresents the ensemble average of the source and

atmospheric turbulence. In free space, Ref. [

19] indicates

that the normalized correlation function of Gaussian–

Schell mode for any distance z is coincident with that

of the original plane (z ¼ 0). Based on the statistical inde-

pendence between the sources and the atmospheric turbu-

lence, the cross- spectral density of AS beams at any

distance z is written as

COL 14(4), 042101(2016) CHINESE OPTICS LETTERS April 10, 2016

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