大气湍流中传播涡旋高斯光束的轨道角动量模式演变
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本文主要探讨了通过弱至强大气湍流传播的涡旋高斯光束（Vortex Gaussian Beam）中轨道角动量（Orbital Angular Momentum, OAM）模式的变化。作者 Chunyi Chen、Huamin Yang、Shoufeng Tong 和 Yan Lou 来自长春理工大学光电测量与控制及光学信息技术重点实验室，他们对经过大气湍流传输后，涡旋高斯光束的径向平均功率分布以及OAM模的归一化平均功率进行了理论建模。
研究的核心内容是分析了内禀模式索引（Intrinsic Mode Index）、初始光束半径以及湍流强度在传播过程中对OAM模式变化的影响。他们通过数值计算的方式，评估了现有理论研究中采用的纯相位扰动近似方法的有效性。对比了涡旋高斯光束在湍流作用下的OAM模式混淆与拉盖尔-高斯（Laguerre-Gaussian, LG）光束或纯涡旋光束的混淆现象。
作者发现，随着湍流强度的增强，OAM模式的稳定性逐渐减弱，而初始光束尺寸和内禀模式索引的不同则显著影响了模式的分散程度。此外，他们还揭示了在不同类型的光束结构中，涡旋高斯光束由于其特有的螺旋波前结构，可能会经历更复杂的OAM模式变化特性。这一研究对于理解光束在复杂环境中的传输性能，特别是在光纤通信、自由空间光通信以及量子信息处理等领域具有重要意义。
通过本文的研究，读者可以了解到如何通过精确的理论模型来预测和控制涡旋高斯光束在大气湍流中的行为，这对于设计和优化抗干扰的光通信系统，以及探索高维光信息编码和处理技术具有实际应用价值。这项工作扩展了我们对光束在极端条件下的传输特性的理解，并为进一步的实验验证和工程应用奠定了基础。
extrinsic OAM modes. In the absence of atmospheric turbulence, by employing the Huygens-
Fresnel principle [18,19], the field of the vortex Gaussian beam at a receiver plane separated a
distance L from the transmitter plane can be formulated as follows:
U
(m)
0
(r,L)=a
0
C
(m)
0
A
(m)
(r) exp(im
θ
) (2)
with
C
(m)
0
=
√
π
k
2
8L
2
(−i)
m+1
exp(ikL)
−
ik
2L
(1+ i
α
0
L)
−3/2
, (3)
A
(m)
(r)=rexp
ikr
2
2L
−
ikr
2
4L(1+ i
α
0
L)
×
I
m/2−1/2
ikr
2
4L(1+ i
α
0
L)
−I
m/2+1/2
ikr
2
4L(1+ i
α
0
L)
, (4)
where r is a two-dimensional vector in the receiver plane at angle
θ
, r =
|
r
|
,
α
0
= 2/
kw
2
0
,
k = 2
π
/
λ
is the optical wavenumber with
λ
being the wavelength, I
p
(·) is a modified Bessel
function of the first kind and order p. The superscript m enclosed between parentheses on the
quantities above shows the dependence of these quantities on the OAM mode index m; similar
notation will also be used below; for succinctness, we will not explain it anymore. To formulate
the turbulence-induced changes in the OAM modes of a propagated vortex Gaussian beam in
atmospheric turbulence, below we follow the approach used by Tyler and Boyd [16]. In the
presence of atmospheric turbulence, the field of a propagated vortex Gaussian beam can be
formally expressed by
U
(m)
(r,L)=a
0
C
(m)
0
A
(m)
(r) exp(im
θ
)exp[
ψ
(m)
(r)], (5)
where
ψ
(m)
(r) denotes the turbulence-induced complex phase perturbation. The term
exp[
ψ
(m)
(r)] in Eq. (5) can be expanded into a complex-valued Fourier series
exp[
ψ
(m)
(r,
θ
)] =
∞
∑
n=−∞
c
(m)
n
(r) exp(in
θ
) (6)
with
c
(m)
n
(r)=
1
2
π
2
π
0
d
θ
exp[
ψ
(m)
(r,
θ
)]exp(−in
θ
), (7)
where
ψ
(m)
(·) is expressed in circular cylindrical coordinates. The field U
(m)
(r,L) can also be
expanded into a complex-valued Fourier series
U
(m)
(r,
θ
,L)=
∞
∑
l=−∞
u
(m)
l
(r) exp(il
θ
) (8)
with
u
(m)
l
(r)=
1
2
π
2
π
0
d
θ
U
(m)
(r,
θ
,L)exp(−il
θ
), (9)
where U
(m)
(·) is expressed in circular cylindrical coordinates. Substitution of Eq. (5) with
exp[
ψ
(m)
(r)] given by Eq. (6) into Eq. (9) leads to
u
(m)
l
(r)=a
0
C
(m)
0
A
(m)
(r) c
(m)
l−m
(r) . (10)
#258215
Received 25 Jan 2016; revised 10 Mar 2016; accepted 12 Mar 2016; published 22 Mar 2016
© 2016 OSA
4 Apr 2016 | Vol. 24, No. 7 | DOI:10.1364/OE.24.006959 | OPTICS EXPRESS 6962
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