Simulation and verification of pulsed laser beam
propagation underwater using Markov chains [Invited]
Tianhua Zhou (周田华)*, Jian Ma (马 剑), Tingting Lu (陆婷婷), Guyu Hu (胡谷雨),
Tingwei Fan (范婷威), Xiaopeng Zhu (竹孝鹏), Xiaolei Zhu (朱小磊),
and Weibiao Chen (陈卫标)
Key Laboratory of Space Laser Communication and Detection Technology, Shanghai Institute of Optics
and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
*Corresponding author: siomzth@siom.ac.cn
Received July 2, 2019; accepted August 22, 2019; posted online September 5, 2019
One fast simulation method using Markov chains was introduced to simulate angular, energy, and temporal
characteristics of pulsed laser beam propagation underwater. Angular dispersion of photons with a different
number of collisions was calculated based on scattering function and the state transition matrix of Markov
chains. Temporal distribution and energy on the receiving plane were obtained, respectively, by use of a novel
successive layering model and receiving ratio. The validity of this method was verified by comparing it with the
Monte Carlo ray tracing (MCRT) method. The simulation results were close to those obtained by MCRT but
were less time consuming and had smoother curves.
OCIS codes: 010.3310, 010.4458.
doi: 10.3788/COL201917.100003.
The underwater optical wireless communication (UOWC)
system makes use of the blue–green wavelength of the vis-
ible spectrum and provides higher data rates than the tra-
ditional acoustic communication system with significantly
lower power consumption over moderate distances
[1]
.
However, the communication performance of the UOWC
system depends on the inherent optical properties of
water. As water is a kind of multiple scattering medium
with intense absorption, when a pulsed laser beam prop-
agates underwater, absorption and scattering will cause
angular and temporal spreading, as well as energy attenu-
ation. The temporal spreading, resulting from angular
dispersion, limits the reachable data rate, and the energy
attenuation limits the range and distance of communica-
tion. Thus, for a UOWC system, it is im portant and
necessary to study the performance of a pulsed laser
beam through an underwater optical channel. So far,
the Monte Carlo ray tracing (MCRT) method
[2–8]
has been
widely used to simulate pulsed laser beam propagation
underwater. MCRT is simple to understand and easy to
program. Especially, MCRT has been proved to be a re-
liable method and be in good agreement with experimen-
tal results
[9–12]
. However, the MCRT method needs a long
execution time, and the precision is limited by the number
of simulated photons.
In this Letter, we firstly introduce Markov chains into
the simulation of pulsed laser beam propagation under-
water. Using the state transition matrix, angular distribu-
tion of photon packets after collision can be easily
obtained, as it is only related to the state before the colli-
sion
[13]
. In addition, according to the distribution of the
number of collisions and the proposed concept of receiving
ratio, we can quickly obtain the energy on the receiving
plane. As the state transition matrix can only be used
to describe memoryless procedures, but the total propaga-
tion delay of one photon packet after multiple scattering is
related to the whole propagation path, it is difficult to
directly use Markov chains to simulate the temporal dis-
tribution of laser pulses on the receiving plane. So, we pro-
pose a novel successive layering model to make the
Markov chains available for the simulation of temporal
distribution of laser pulses. Compared with the MCRT
method, the angular distribution after collisions, the en-
ergy, and the temporal distribution on the receiving plane
simulated by Markov chains have similar results with a
higher calculation rate by about two orders of magnitude
and a smoother curve. The main reason is that, differ ent
from brute-force tracing used in MCRT, Markov chains
are based on matrix operation.
The parameters, which relate to pulsed laser beam prop-
erties after underwater propagation, mainly include ab-
sorption coefficient a, scattering coefficient b, attenuation
coefficient c ðc ¼ a þ bÞ, albedo
¯
ω ð
¯
ω ¼ b∕cÞ, and asym-
metric parameter g. References [
14–16] systematically
introduced the influences of those parameters and pro-
vided a set of data for reference. When a photon undergoes
scattering underwater, the Mie theory is available to
describe the probability distribution of the scattering
angle, provided that the s ize distribution of scattering
particles underwater is known. In simulation, the Henyey–
Greenstein (HG) scattering function
[17]
and Fournier–
Forand scattering function
[18]
have been widely adopted
for consistency with experimental data. In this Letter,
we select the HG scattering function for its simpler form.
The HG scattering function is given by
PðθÞ¼
1-g
2
2πð1-2g cos θ þ g
2
Þ
3∕2
; (1)
COL 17(10), 100003(2019) CHINESE OPTICS LETTERS October 2019
1671-7694/2019/100003(5) 100003-1 © 2019 Chinese Optics Letters