Propagation of laser beams through air-sea turbulence channels

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Propagation of laser beams through
air-sea turbulence channels
Minghao Wang, Xiuhua Yuan, Omar AlHarbi, Peng
Deng, Tim Kane
Minghao Wang, Xiuhua Yuan, Omar AlHarbi, Peng Deng, Tim Kane,
"Propagation of laser beams through air-sea turbulence channels," Proc.
SPIE 10770, Laser Communication and Propagation through the Atmosphere
and Oceans VII, 1077003 (18 September 2018); doi: 10.1117/12.2323302
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California,
United States
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Propagation of laser beams through air-sea turbulence channels
Minghao Wang1,2, Xiuhua Yuan1, Omar AlHarbi2,3, Peng Deng2, Tim Kane2
1School of Optical and Electronic Information, Huazhong University of Science and Technology,
Wuhan, Hubei 430074, China
2Department of Electrical Engineering, The Pennsylvania State University,
University Park, PA 16802, USA
3Department of Electrical Engineering, College of Engineering
Majmaah University, Majmaah 11952, Saudi Arabia
ABSTRACT
Reliable communication between aerial and undersea vehicles is a challenging issue because radio frequency signals are
attenuated drastically in sea water while acoustic waves are not preferable in terrestrial links. Located in the
transmittance windows of both sea water and the atmosphere, blue-green laser based free-space optical communication
systems are capable of providing high speed, low latency data links for this very scenario. Apart from the absorbing and
scattering attenuations in the air-water channel, another limiting factor impacting efficient laser beam propagation is the
turbulence induced intensity fluctuations. Pure attenuation in sea water restricts the laser communication distance to
~100 meters, which will further reduce to ~10 meters in the presence of oceanic turbulence. Meanwhile, atmospheric
turbulence can also substantially degrade the beam quality if the aerial vehicle is at high altitude. In this study, we focus
our effort on the turbulence effects on beam propagation in the air-water two-stage links, not taking into account media
attenuation or water surface distortions. Considering the complexity of the depth dependence of salinity and temperature
in sea water and the altitude dependence of air refractive-index structure constant, we use numerical methods to simulate
the beam propagation through the two-stage turbulence channel, which is modeled by discrete phase screens generated
with parameterized atmospheric and oceanic turbulence power spectrums. On that basis, beam spread, area scintillation
and SNR penalty at the receiver end are analyzed for the uplink as well as the downlink transmission.
Keywords: radial partially coherent beams, turbulence propagation, air-sea hybrid link, wave optics simulation
1. INTRODUCTION
With the rapid development of autonomous underwater vehicles (AUVs) and unmanned aerial vehicles (UAVs)1-3,
there is an increasing need for reliable communication means between these two types of platforms for efficient
information exchange. Traditionally acoustic waves are extensively used in underwater navigation and communications,
but the modulation bandwidth of acoustic waves is rather narrow, not capable of meeting the demands of modern
network traffic. Besides, the large propagation delay and the random reflection at the ocean surface add to the
intractability of the acoustic approach4, 5. On the other hand, electromagnetic waves are of high bandwidth and thus
widely used in terrestrial communication systems. Unfortunately, the high electrical conductivity makes sea water
attenuate electromagnetic waves so intensely that one meter of sea water is more than enough to extinguish any typical
radio frequency (RF) signals6.
As a decent compromise, optical waves (in the blue-green wavelength) can propagate up to ~100 m in relatively
clear sea water7-10. Moreover, laser beam based free-space optical communication (FSOC) systems can provide Gbps
data links11, 12. Therefore FSOC is a feasible means for data transmission between AUVs and UAVs. Nonetheless, the
air-sea hybrid channel poses several challenges for laser beam propagation, among which the extinction caused by
absorption and scattering can be and can only be compensated by launching more power at the optical transmitter. Yet
another major adverse factor is the atmospheric turbulence and the oceanic turbulence along the optical path, which are
essentially refractive index inhomogeneities that can severely distort the wavefront. Turbulence induced intensity
fluctuations (also known as optical scintillations) and beam wander determines the SNR ceiling to a great extent, which
is not possible to break by simply increasing the launching power since turbulence is a source of multiplicative noise.
The propagation of coherent laser beam in the turbulent atmosphere has been extensively studied in the last few
decades13-18. Research on oceanic turbulence propagation has also been rather active in recent years19-24. Nonetheless, the
Laser Communication and Propagation through the Atmosphere and Oceans VII, edited by Jeremy P. Bos,
Alexander M. J. van Eijk, Stephen M. Hammel, Proc. of SPIE Vol. 10770, 1077003
© 2018 SPIE · CCC code: 0277-786X/18/$18 · doi: 10.1117/12.2323302
Proc. of SPIE Vol. 10770 1077003-1
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20 km
15 km
10 km
5 km
0
20 m
40 m
60 m
-H-V C n2 profile
+Phase screen position
air
4sea
problem with coherent beams is that they are very prone to turbulence induced wavefront perturbations. To better
alleviate the scintillation phenomena, partially coherent beams are introduced in the context of FSOC25-27. By sacrificing
some extent of directionality, partially coherent beams (PCBs) are more resistant to turbulence induced wavefront
distortions, and thus benefit the reception performance. As a widely used partially coherence source, the Gaussian
Schell-model (GSM) beam can be easily generated by a rotating ground glass or a spatial light modulator loaded with
digital phase screens28,29. Recently, a class of nonuniformly correlated beams called radial partially coherent beams
(RPCBs) were proposed, which have a convex shape in the complex degree of coherence (DoC)29. It is found that this
type of DoC distributions will result in free-space self-focusing, leading to better axial power concentration property so
that the scintillation is reduced and the SNR is improved29,30.
To date, the issue of optical communications in air-sea hybrid links has not been fully addressed. In this study, we
will limit our scope to the turbulence effects in such links, while neglecting the path attenuation as well as the random
reflection of the ocean surface31. By use of wave optics simulation (WOS), we analyze the reception performance of
GSM and RPCB beams in vertical air-sea paths through scintillation index and SNR. The propagation of these PCBs in
air-sea hybrid channels with various path parameters will be examined, both uplink and downlink. The rest of this paper
is structured as follows. In Section II the channel model is introduced in a numerical manner and the basics of wave
optics simulation is briefly explained. Section III firstly provides an experimental demonstration of how the RPCB self-
focuses during propagation, then the simulation results of RPCB propagation through different ranges of air-sea
channels, from the perspective of aperture-averaged scintillation and ensembled receiver SNR, and some discussions
concerning the obtained results are also included in this part. Section IV is a summary.
2. SIMULATION MODEL DESCRIPTION
Fig. 1 Phase-screen model of air-sea hybrid optical link
An optical link connecting a UUV and a UAV comprises two sections: an underwater section and an aerial section,
as is illustrated in Fig. 1. Given the facts that oceanic turbulence is several magnitude stronger than atmospheric
turbulence, and that the air density decreases as the altitude increases, the air-sea channel is highly lopsided – the
majority of the turbulence effects happens near the underwater UUV. In other words, severe wavefront distortion only
lies near the uplink transmitter and the downlink receiver. A comparison of the instantaneous intensity pattern of a same
coherent Gaussian beam after propagating through an uplink and a downlink is shown in Fig. 2. It can be seen that in the
uplink the beam forms optical speckles and has longer correlation length, while in the downlink the wavefront is more
fragmented but less evolved.
Taking into account that laser beams attenuate within a short range in the sea water, we only consider up to 50 m
depth of sea water in the vertical direction. Moreover, recent field data gathered in the offshore areas of China reveal that
in cold seasons the vertical variations of oceanic parameters is almost negligible in the upper layer waters32, which is
why we will presume the oceanic turbulence to be homogeneous and depth-independent. Therefore, as indicated in Fig.
1, the oceanic turbulence is modeled by equally separated, statistically equivalent phase screens. The power spectrum
density (PSD) model of oceanic refractive index fluctuations developed by Nikishov33 is adopted here:
Proc. of SPIE Vol. 10770 1077003-2
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0.2
0.1
0
-0.1
-0.2
-0.3
(a)
o,°
-0.2 00.2
x (m)
0.2
0.1
0
-0.1
-0.2
-0.3 -0.2 00.2
x (m)
1 1/3 11/3 2/3
01
Φ() (4) 1 ( ) (, ),
sea n
κπCχε κ Cκη φ κ ω
−−−
⎡⎤
=+
⎣⎦
(1)
where the following denotations have been defined
2
2
22 4/3 2
0
0
exp( ) exp( ) (1 )exp( )
(, )= = ,
1(1)
(d d )
= , 2 , 8.284( ) 12.978( ) ,
(d d )
TS TS
T
S
nT S TS
ωθ AδAδω θ AδK
φκω θ
ωθ ω θ K
αTz
ω χ α χ β χ αβχ δ κη κη
βSz
−+−−+ −
+− +
=+− = +
，
among which κ is the spatial wave number, η is the Kolmogorov microscale, and ε is the rate of dissipation of turbulent
kinetic energy per unit mass of fluid ranging from 10−1 m2/s3 to 10−10 m2/s3. For constant gradients of mean temperature
and salinity, ω defines the ratio of temperature to salinity contributions to the spectrum, varying from −5 (corresponding
to temperature dominated turbulence) to 0 (corresponding to salinity dominated turbulence). C0 = 0.72 is the Obukhov-
Corrsin constant, C1 is a free parameter to be determined by comparison with experiment and its value is taken as 2.35.
KT is eddy thermal diffusivity and KS is diffusion of salt. AT = 1.683×10−2, AS = 1.9×10−4, ATS = 9.41×10−3. α = 2.6×
10−4 L/deg, β = 1.75×10−4 L/g. χT and χS represent the rate of dissipation of mean squared temperature and that of
salinity respectively and χTS denotes the correlation of χT and χS.
Fig. 2 Instantaneous intensity pattern of a vertical air-sea hybrid (a) uplink and (b) downlink.
The underwater section is 50 m and the aerial section is 2 km.
On the other hand, the altitude-dependent atmosphere density directly leads to a vertically varying atmospheric
turbulence profile, for which a well acknowledged model is the H-V5-7, also shown in Fig. 1 with the blue curve, where
the horizontal scale marks the turbulence strength. To better represent the unevenness of the H-V5-7 model13 and fully
utilize the limited computational power, nonuniformly arranged phase screens are used to represent the effects of
turbulent wavefront distortions. The partition is based on the path integral of the structure constant, and the atmospheric
turbulence PSD used here is the modified von Kármán spectrum:
2
2
2
2211/6
exp( / )
Φ(,) 0.033 () ,
()
l
air n
m
κκ
κhCh
κκ
−
=+ (2)
where 2()
n
Chis the atmospheric refractive index structure constant at altitude h, κl = 5.92/l0, κm = 5.92/L0, l0 and L0 being
the inner scale and the outer scale. With the PSDs given by Eq. (1) and (2), the turbulence phase screens generation
process is merely to randomize the PSD and then take the Fourier transform to get the spatial pattern34.
The air-sea scenario considered here is nearly impossible to derive analytical results for, whereas the WOS
numerical method provides a viable approach to study complex optical propagation problems like this. The basic
principle for WOS is the split-step propagations between separate phase screens, which can be written as
[]
2
11 1
exp( )
() ()exp ()exp , [1,m]
2
i i ii ii i i i
S
jkL m jk
UUjψdi
iλLm Lm
++ +
⎛⎞
=⋅−∈
⎜⎟
⎝⎠
∫
rrrrrr (3)
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where r is the transverse position vector, Ui(ri) is the optical field at the ith screen,，ψi(ri) is the wavefront distortion
induced by the turbulence within the ith interval, L is the path length, m is the number of phase screens. For the specific
implementation and the sampling constraints of WOS, the reader is referred to the literature34.
3. RESULTS AND DISCUSSIONS
As indicated above, the optical channel that is to be analyzed here is a two-section air-sea path, which is comprised
of a 25/50 m underwater path that is subjected to oceanic turbulence, and a vertical atmospheric path whose length is
variably 1km, 2 km and 5 km. The optical beams considered here are the RPCB and the GSM beams. The basic
properties of GSM are well known, while the self-focusing of RPCBs might still sounds peculiar to many. So we first
give an experimental demonstration of how a convex DoC modulation can induce self-focusing.
The optics setup is shown in Fig. 3. The output of a He-Ne laser is collimated, expanded and rendered into linear
polarization before illuminating a liquid crystal phase-only SLM (BNS SN8200). The SLM is loaded with a series of
random RPCB phase screens29 and consecutively switches at a frame rate of 60. Then, after passing a scaling 4f system
the modulated beam is captured by a CCD camera (Basler scA640-70gc）, which is shifted longitudinally so that the
distance evolution of the beam profile can be obtained.
Fig. 3 Experimental setup for verification of the RPCB self-focusing. P: linear polarizer, L1 & L2: secondary
expanding, HWP: half-wave plate, M: mirror, BS: beam splitter, L3 & L4: 4f system.
Figure 4 (a) is an example of the RPCB phase screen loaded to the SLM in which 2π wrapping has been applied
since the maximum phase stroke of the SLM is 2π. An instantaneous beam profile captured by the CCD from some
distance is shown in Fig.4 (b). The camera is carefully adjusted so that it does not saturate, and is shifted from the back
focal plane of the 4f system to 380 mm away (corresponding to a Fresnel number of ~10) along the optical axis. The
obtained on-axis intensity evolution is presented in Fig. 4 (c), where each data point is computed by averaging 500
frames of CCD output, and the corresponding results of the coherent source (shown in the inset) and the GSM beam are
also given for comparison. Different from the monotonically decreasing trend of the GSM and the coherent beam, the
on-axis intensity of RPCB first rises slightly and then takes a deep fall before reaching a primary peak and attenuating
afterwards. This is a clear evidence of the self-focusing of the RPCB, induced by the convex DoC modulation. Note that
the coherent source in this experiment is not an ideal Gaussian beam. Actually the convex DoC modulation caused self-
focusing is barely dependent on the source amplitude profile. It is also should be pointed out that the self-focusing peak
is lower than what is predicted by typical numerical simulation results29 (the trend is very much alike though), which
might be due to the transient imperfections of the SLM.
Next we show how the effects of self-focusing turn into improvements at the receiver end of an air-sea hybrid link.
As indicated above, the optical beam propagates in the vertical direction and the oceanic section is 50 meters long,
represented by 11 discrete phase screens. The oceanic turbulence parameters are set as: η = 2 mm, ε = 10−5 m2/s3, ω =
−2.5, χT = 10−8 K2/s. For the atmospheric section, three values of distance are considered, namely, 1 km, 2 km and 5 km.
The turbulence strength at the ground level is 2(0)
n
C= 5×10−14 m−2/3 and 21 discrete phase screens are used to import the
effects of the atmospheric turbulence. The coherent source is a Gaussian beam with characteristic width ω0 = 25 mm, the
diameter of the receiving aperture is 20 mm.
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1.2
(b)
(c)
0.8
's.
RPCB
GSM
Coherent
0 50 100 150 200 250 300 350 400
Z (mm)
0.6
C0.4
To
5 0.2
cn
(a) RPCB
- - - - - - GSM
oo
10
8
ca
z6
4
2
0.5 1
o0.5 1
0.8
c 0.6
o
0.4
C
c.7)
(f) 0.2
oo
8
6a-o 4zci) 2
0.5 1
(e)
oo0.5 1
1.5
5 0.5
o
5
ca
o
z
-5o
o0.5 1
(f)
0.5
/6
1
Fig. 4 The RPCB self-focusing experiment. (a) a realization of the RPCB phase screen, (b) an example of the intensity
pattern obtained by the CCD camera, (c) normalized on-axis intensity evolution of RPCB, GSM and coherent beams.
The results of the uplink are presented in Fig. 5. The horizontal coordinates β indicates the overall coherence state
of the beam, and β = 0 corresponds to fully coherent while β = 0 corresponds to a uniformly correlated GSM beam
whose source coherence length is lc0 = 2 mm. It is clearly seen that in the uplink GSM has smaller scintillation in all
cases and its SNR is also higher than the RPCB. By comparison, in the downlink, as shown in Fig. 6, RPCB can provide
2 dB SNR gain in the 1 km aerial path case and 1 dB in the 2 km case. For the 50 m underwater + 5 km aerial path case,
the GSM and the RPCB are no difference, since it is the coherent beam that becomes the optimal option. Also note that
under exactly the same parameters for the beam and the path, uplink suffers more severe fluctuations than the downlink.
Fig. 5 Scintillation and SNR versus coherence state β in the uplink comprised of 50 m underwater path and
(a, d) 1 km aerial path, (b, e) 2 km aerial path and (c, f) 5 km aerial path
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0.08
0.06
o
c'T 0.04
U) 0.02
20
a15
-o
co 10
5
(a) RPCB
.GSM
0.5 1
O0.5
/6
1
oo
Co=+E.o
0.1
0.05
O
O
(b) o.2
"72t)
0.15
0.1
0.05
Oo
RPCB
GSM (C) RPCB
GSM
0.5
/6
10.5
/6
1
20
15
-o 10
z5
(e)
0.5
/6
1
15
10
-o 5
z
O
-5 O
RPCB
GSM
0.5
/6
1
The reason why the uplink and the downlink show very different aspects is mainly due to the distribution of the
turbulence along the optical path, as we have discussed earlier. Although the details of the mechanism of how
nonuniformly correlated beams interact with turbulence eddies is still unclear, we speculate that the initial oscillations of
the RPCBs29 might be very susceptible to turbulent perturbations, and perhaps that’s why the effectiveness of the RPCB
is only noticeable in the downlink where stronger turbulence lies far away from the source.
Fig. 6 Scintillation and SNR versus coherence state β in the downlink comprised of 50 m underwater path and
(a, d) 1 km aerial path, (b, e) 2 km aerial path and (c, f) 5 km aerial path
4. SUMMARY
In this paper, we investigated the turbulent propagation of radial partially coherent beams as well as Gaussian
Schell-model beams in the scenario of an air-sea hybrid link. We are interested in the performance of the RPCB because
in horizontal terrestrial links it has proved to be able to provide some extra gain in the receiver SNR over the
conventional GSM beam. It is worth mentioning that in the context of partially coherent beams, it takes the same efforts
to generate either GSM beams or RPCBs. Before digging into the link performance, we first verified in the lab that the
RPCB, or more specifically, the convex DoC modulation, can really induce self-focusing, which is believed to be the
cause of the noteworthy properties of the RPCB. Then, by numerical simulation we studied the propagation of the RPCB
in air-sea hybrid links in comparison with the GSM beam. It is found that RPCB does not provide any benefit in the
uplink, whereas in the downlink, 1~2 dB SNR gain will be obtained through the use of RPCB. In future we will perform
propagation simulation of partially coherent beams in artificially designed turbulent environments, and hopefully more
details of the interaction between partial coherence and the turbulence will be revealed.
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