Effects of underwater turbulence on laser
beam propagation and coupling into
single-mode optical fiber
Frank Hanson* and Mark Lasher
Space and Naval Warfare Systems Center Pacific, San Diego, California 92152, USA
*Corresponding author: hansonfe@spawar.navy.mil
Received 18 November 2009; revised 29 April 2010; accepted 6 May 2010;
posted 7 May 2010 (Doc. ID 120206); published 31 May 2010
We characterize and compare the effects of turbulence on underwater laser propagation with theory.
Measurements of the coupling efficiency of the focused beam into a single-mode fiber are reported.
A simple tip-tilt control system, based on the position of the image centroid in the focal plane, was shown
tomaintain good coupling efficiency for a beam radius equal to the transverse coherence length, r
0
. These
results are relevant to high bandwidth communication technology that requires good spatial mode
quality. ? 2010 Optical Society of America
OCIS codes: 010.4450, 010.4455, 010.7060, 060.2605.
1. Introduction
Optical communication in the ocean canprovidemuch
higher data rates than are available with acoustic
techniques, and it can be useful for certain military
and scientific applications that involve sending large
quantities of data [1,2]. However, the underwater en-
vironment presents challenges for propagation of la-
ser beams. In clean ocean water, the extinction due to
absorption and scattering probably limit the useful
range to ∼100 m in the blue-green spectral window
[3]. Forward scattering also leads to pulse broadening
due to multipath effects and limits the intrinsic
bandwidth of themedium as the receiver field of view
(FOV) increases [4]. Present communications sys-
tems are typically designed to maximize signal and,
therefore, employ large area sensitive photomulti-
plier tube (PMT) detectors and collect light over a
significantFOV.Blue-green sensitivePMTs that com-
bine bandwidth up to a few 100 MHz and detector
areas of several square cm are useful for many appli-
cations; however, they have limitations. They are
generally suited to low duty-cycle signals, such as
pulse-position-modulation (PPM)waveforms because
themaximumaverage anode current is limited to pre-
vent saturation and tube degradation. However, for a
given receiver bandwidth, simple on–off-key wave-
forms provide a higher data rate than PPM wave-
forms. PMT receivers are also very sensitive to solar
background light and narrowband and wide FOV
filters are typically required.
Underwater communication systems that can
operate at much higher data rates (>10
9
bits per sec-
ond) would require different receiver technology. For
example, very high bandwidth InGaAs detectors
have been developed for the telecom industry, and it
is appealing to consider nonlinear frequency conver-
sion approaches for wavelength translation from the
visible to infrared in order to make use of them. Such
techniques have benefited by developments in engi-
neered nonlinear materials, such as periodically
poled and waveguide structures in crystals [5] and
microstructured silica fibers [6]. However, high effi-
ciency requires a high spatial coherence of the optical
field at the receiver in order to have a good overlap of
the blue-green “signal” field with the pump field(s).
This can be especially difficult for laser beam propa-
gation underwater, due to levels of turbulence that
can be much higher than typically found in the
0003-6935/10/163224-07$15.00/0
? 2010 Optical Society of America
3224 APPLIED OPTICS / Vol. 49, No. 16 / 1 June 2010

atmosphere, because the density is orders of magni-
tude higher and, consequently, the dependence of
the refractive index on temperature is much greater.
In the blue-green region, dn=dT∼−8 × 10
−5
ðK
−1
Þ [7]
in water compared with∼−1 × 10
−6
ðK
−1
Þ in air [8].
Some previous work has shown that temporal [9,10]
and spatial [11] coherence is degraded by scattering
due to particulates in the water path; however, it is
not clear that these results were not affected by
turbulence, especially because some agitation was
required to keep the suspension of particulates uni-
form. For coherent interactions, it is probably reason-
able to conclude that the scattered portion of the
laser beam would not be useful, and, therefore, it
is important to understand the effects of turbulence
on the unscattered or ballistic portion of the beam. In
clear ocean water, the total 1=e extinction range due
to absorption and scattering can be a few meters [3],
and, therefore, significant beam intensity can persist
for tens of meters. There has been little work pub-
lished on the effects of underwater turbulence on la-
ser beam propagation. One study demonstrated that
low-order adaptive optics (tip-tilt plus a 17-element
deformable mirror) could improve the focusing or
Strehl ratio of a beam that passed through turbu-
lence created by a transverse temperature gradient
across the path [12]. In that work, the size of the
beam was not given and the strength of turbulence
was not determined. In this work we have investi-
gated the effects of turbulence on coherent laser pro-
pagation in more detail. Our results explicitly show
the importance of beam size relative to the trans-
verse coherence length. We also have measured the
coupling efficiency of the focused beam into a single-
mode optical fiber (SMF) and show that a simple
tip-tilt feedback control system can maintain good
coupling efficiency when the beam radius is equal
to the transverse coherence length, r
0
.
2. Propagation Theory
The experiments described below involve the focused
images of collimated Gaussian or nearly flat-top la-
ser beams that have been propagated through 2 m of
turbulent water. In this section we will apply the the-
ory developed by Yura and Hanson for optical beams
propagating through complex optical systems de-
scribed by a general ABCDmatrix [13]. In particular,
propagation through random inhomogeneous media
is treated using the Rytov approximation in the weak
fluctuation regime. It will be useful to review some
results derived for a general spectrum of refractive
index fluctuations and then give expressions for fo-
cused images using the Kolmogorov spectrum scaled
with the familiar refractive index structure constant
C
n
2
. This theory is normally applied to atmospheric
propagation, and in Appendix A, we consider how the
results might be affected for underwater propagation
subject to fluctuations of temperature and salinity.
Using Eqs. (102)–(112) in Ref. [13] and assuming
cylindrical symmetry, the intensity IðpÞ in the focal
plane is given by an integration in the source plane
IðpÞ¼
k
2
B
2
Z
drrJ
0
ðkpr=BÞKðrÞ exp½−D
w
ðrÞ=2
; ð1Þ
where k ¼ 2pi=λ, B is the appropriate ray-transfer
matrix element and J
0
is the Bessel function of
the first kind. KðrÞ is given by an integration of the
incident field U
i
ðrÞ in the plane perpendicular to
propagation
KðrÞ¼
Z
d
2
RU
i
ðRþ r=2ÞU
i

ðR − r=2Þ; ð2Þ
and D
w
ðrÞ is the wave structure function given by an
integration over spatial frequencies of the power
spectrum of refractive index fluctuations Φ
n
ðκ; zÞ
along the propagation path from 0 to L:
D
w
ðrÞ¼8pik
2
Z
L
0
dz
Z
dκκΦ
n
ðκ; zÞ½1 − J
0
ðκrbðzÞ=BÞ
;
ð3Þ
where bðzÞ is the ray matrix element for backward
propagation from a point p in the image plane to a
point a distance z toward the source plane and B ¼
bðLÞ is the overall matrix element for a backward
propagated ray. In this geometry, for z between the
lens and the source plane, B ¼ bðzÞ¼f , the focal
length of the lens. If the incident optical field is Gaus-
sian, U
i
ðrÞ¼U
0
expð−r
2
=ω
B
2
Þ, Eqs. (1)and(2) give
IðpÞ¼
k
2
2pif
2
Z
drrJ
0
ðkpr=f Þ expð−r
2
=2ω
B
2
Þ
× expð−D
w
ðrÞ=2Þ: ð4Þ
If we consider an isotropic Kolmogorov spectrum
Φ
n
ðκÞ¼0:033C
n
2
κ
−11=3
based on the refractive index
structure constant C
n
2
, the integration in Eq. (3)
gives D
w
ðrÞ¼2ðr=r
0
Þ
5=3
, where r
0
¼½1:46k
2
R
L
0
dzC
n
2
ðzÞ

−3=5
is the transverse coherence length. It can
been shown [13] that if D
w
ðrÞ is approximated as
∼2ðr=r
0
Þ
2
, the integration in Eq. (4) can be per-
formed, giving IðpÞ ∝ expð−2p
2
=ω
2
Þ, where the spot
size ω in the focal plane is
ω
2
¼ 4f
2
=k
2
ω
B
2
þ 8f
2
=k
2
r
0
2
: ð5Þ
The first term on the right is the diffraction-limited
value ω
DL
2
, and the second term accounts for the in-
crease in spot size due to turbulence. The broadening
of the spot relative to the diffraction limit becomes
more significant as the radius of the collimated beam
ω
B
increases relative to r
0
:
ω
2
=ω
DL
2
¼ 1þ 2ω
B
2
=r
0
2
: ð6Þ
It is useful to consider this expression for the spot
size in the analysis of the experimental results, even
though approximations have been made. In particu-
lar, the finite geometry of the water pipe and the
1 June 2010 / Vol. 49, No. 16 / APPLIED OPTICS 3225