of 41
1
Orbital
Angular Momentu
m
-
based Spa
ce
Division
Multiplexing
for
High
-
capacity
Underwater
Optical
Communications
Yongxiong Ren
1
*,
Long Li
1
*
,
Zhe Wang
1
,
Seyedeh
Mahsa Kamali
2
, Ehsan Arbabi
2
,
Amir
Arbabi
2
,
Zhe Zhao
1
, Guodong Xie
1
,
Yinwen Cao
1
,
Nisar Ah
me
d
1
, Yan Yan
1
,
Cong Liu
1
, Asher J.
Willner
1
, Solyman Ashrafi
3
,
Moshe Tur
4
,
Andrei Faraon
2
, and Alan E. Willner
1
1
Department of Electrical Engineering, University of Southern California, Los Angel
es, CA
90089, USA.
2
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA
91125, USA
.
3
NxGen Partners, Dallas, TX75219, USA
.
4
School of Electrical Engineering, Tel Aviv University, Ramat Aviv 69978
,
I
srael
.
Corresponding email:
yongxior
@usc.edu
,
willner@usc.edu
*These authors c
ontributed equally to this work
Abstract:
To increase system capacity of underwater optical communications, we employ
the spatial domain to simultaneously transmit
multiple
orthogonal spatial beams, each
carrying an independent
data channel
. In this paper, we multiplex and
transmi
t four
green
orbi
tal angular momentum (OAM) beams through a single aperture. Moreover, we
investigate t
he
degrading effects
of
scattering/turbidity, water current, and thermal
gradient
-
induced turbulence
, and we find that thermal gradients cause the most distortions
and tu
rbidity causes the most loss
.
We show systems results using two different data
generation techniques, one at 1064 nm for 10
-
Gbit/s/beam and one at 5
20
nm for 1
-
2
Gbit/s/beam; we use both techniques since present
data
-
modulation technologies
are faster
for
in
frared (IR) than for
green
. F
or the higher
-
rate link, data is modulated in the IR, and
OAM imprinting is performed in the green
using a
specially
-
designed
metasurface phase
mask.
For the lower rates, a green laser diode is directly modulated. Finally, we
show that
inter
-
channel crosstalk induced by thermal gradients can be
mitigated using
multi
-
channel
equalisation processing.
There is growing interest in high
-
capacity underwater wireless communications in order to
support the significant increase in the
demand for data
, such as from sens
or networks, unmanned
vehicles
and submarines
1
-
5
. Tradit
ionally, acoustic waves have been used
for
underwater
communication
s, but this
technique
has quite limited bandwidth capacity
1,
2, 5
-
7
.
Alternatively,
optics
especially for the low
-
attenuation blue
-
green region
can enable higher
-
capacity
underwa
ter transmission links due to the much
higher carrier
-
wave frequency
8
-
1
5
.
In order to
increase the capacity of underwater communications,
a laudable goal would be to
sim
ultaneously
transmit multiple
independent
data channels
by using
the spatial domain
for multiplexing, i.e.,
space division multiplexing (SDM)
1
6
. If the beams are mutually orthogonal, the different beams
can
then
be efficiently (de
-
)multiplexed,
transmitted through a single transmitter/receiver
aperture pair, and co
-
propagate with little inherent crosstalk
.
An orthogonal spatial modal basis set that
might enable underwater SDM
is orbital angular
momentum (OAM) modes
1
7
. A light beam with a helical
wavefront carries an OAM
value
corresponding to
ℓℏ
per photon, where
is the reduced Planck
’s
constant and
is an unbounded
integer
that represents the number of 2
π
phase changes in the azimuthal direction
1
7,
1
8
.
The phase
front of an OAM beam twists alo
ng the propagation direction
and results in
a ring
-
shaped
intensity profile
with a central null
1
8
.
Previous reports have
explored the use of
OAM
3
multiplexing for high
-
capacity data transmission
through the atmosphere using 1.55
-
μ
m light
1
9
-
23
.
In general,
free
-
space systems may need to deal with atmospheric turbulence, which can disrupt
the beams’ phase
fronts and cause intermodal crosstalk
2
4
-
2
7
.
Much has been uncovered in free
-
space OAM systems in the
infrared (IR)
, yet little has been
reported for underwa
ter blue
-
green communicat
ions.
Indeed, t
he underwate
r environment
presents several different
challenges for
a high
-
speed OAM link
2
8
, 2
9
. For example, the OAM
beam itself and the data it carries can be significantly degraded due to various widely
-
varying
effects, such as
dynamic
scattering/turbidity, water current
s
,
and temperature gradients
12
-
15,
30
-
34
.
Although these issues are challengi
ng for non
-
OAM
,
single beam underwater links, the problem
may escalate for systems using phase front
-
sensitive OAM beams
25
,
33
-
34
.
Recent reports have shown a 4.8
-
Gbit/s underwater link
using a Gaussian beam
by directly
modulating a
1.2
-
GHz bandwidth 450
-
n
m
laser diode
with
orthogonal
-
frequency
-
divisio
n
-
multiplexing (OFDM) data
11
. Moreover
, it has been
shown recently
that
a
blue
OAM beam can
propagate through 3
-
metre of water, which includes a scattering solution
2
8
. However,
little
has
been
reported
on the
performance of OAM
-
multiplexed underwater data transmission or its
degradation due to underwater effects.
In this paper, we
explore OAM multiplexing for high
-
speed underwater communications, and we
transmit four multiplexed green OAM beams
through
1.2
-
metr
e
of
water
35
.
Furthermore, we
investigate the impact of v
arious underwater conditions
(e.g.,
scattering/turbidity, current
,
and
thermal
gradients
) on beam quality and
system performance
, finding that thermal gradients can
produce significant beam
-
quality d
egradation (e.g., modal distortion and beam wander).
Importantly, we show systems results using two different approaches for data modulation, one at
4
10
-
Gbit/s/beam in the infrared (IR) and one at 1
-
Gbit/s/beam in the green); we show both
approaches since d
ata modulation technologies are currently faster in the IR
5
,
36
. For the IR
approach,
we
modulate a 1064
-
nm beam at 10
-
Gbit/s/beam and frequency double it into the
green by using a periodically poled lithium n
iobate (PPLN)
nonlinear crystal, and a speciall
y
designed integrated dielectric metasurface phase mask
37
imprints the OAM on the beam; note
that this 40
-
Gbit/s aggregate capacity is ~8 times higher than the previously reported result using
a conventional Gaussian beam
11
. For the green approach, we
directly modulate the 532
-
nm laser
diode. Finally, in order to take advantage of the multiple beams traversing the same medium, w
e
demonstrate that inter
-
channel crosstalk induced by
thermal gradients
can be mitigated using
a
multi
-
channel
equalisation dig
ital signal processing
(DSP)
algorithm
at
the receiver
38
.
Results
Figure 1 illustrates a prospective application scenario of using OAM multiplexing for high
-
speed
underwater data
transmission. We explore such a scenario under laboratory conditions to help
determine the challenges of OAM
-
based SDM underwater communications.
OAM beam
propagation
through various water conditions
We first investigate the
influence of underwater propag
ation on green OAM beams
.
In general, a
light beam
propagating through water may suffer
degradation
from various
effects
, including
scattering
/turbidity
,
current
s
, and turbulence.
W
e
emulate these
underwater
conditions
in
a 1.2
-
met
re
-
long rectangular tank
(with 17 cm
in width and 30 cm in height
)
filled with tap water
.
Specifically,
underwater s
cattering
/turbidity
is produced with suspensions of Al(OH)
3
and
Mg(OH)
2
, which
are obtained by adding a commercial antacid pr
eparation (Maalox
®
)
8
,
1
2
,
1
4
.
C
irculation pumps
pointing perpendicular to the propagation direction
are evenly placed
along
5
the link path
in
side
the water tank
to produce
a
water current.
Additionally
,
thermal gradient
-
induced
water turbulence
is
created
by
introducing temperature
inhom
ogeneity
along the optical
link
, which is accomplished via mixing
room temperature
and
heated
water
.
The me
asured
power
loss induced by
traversing
the tank and
the
1.2 metre
s
of
tap
water
is around
2.5
dB,
which is mainly caused by the reflect
ion
s
at the
tank’s glass interfaces
,
with
the power
loss
incurred by
the
water
itself
being
negligible.
Figure
2
(
a
)
shows the intensity profiles of
the
individually transmi
t
ted and
received
Gaussian
(
=0)
and
OAM
beams
(
=+1 and +3) at 520 nm
under various conditions:
(i) with
only tap
water
(a1
-
a3)
,
(ii) with water current (a4
-
a6), (iii) with
the
Maalox solution (a7
-
a9)
, and (iv) with
a
thermal gradient
(a
10
-
a
12
)
.
The OAM beam with either
=+1 or +3 is generated by shining
the
Gaussian
beam
onto a
spatial light modulator
(SLM
)
loaded with a helical phase pattern of
=+1
or
=+3
.
The water
current
in
Fig
s.
2(a4
-
a6)
is
created using three circulation pumps
,
each with
a flow rate of
26.8 litters per min
.
The Maalox solution added into the water tank
containing
30
litters
of water is
1.
5
-
millilitre
of
0.5%
diluted Maalox
, and t
he water
after adding
the
Maalox
is
circulated
by pumps
for 1 minute
to obtain a uniform scattering suspension
(
see Fig. S1(a
-
b)
in
Supplementary Section 1
for the case of
a
nonuniform suspension whe
n
there is
no added
circulation
)
.
The
room temperature
and heated water
that are mixed for turbulence emulation
have a temperature difference of
0.
2
o
C
; such an approach has been used previ
ously to emulate
thermal gradients in water
33
,
3
4
.
We see that t
he
ring
-
shaped
intensity
profiles
of
the
OAM beams tend to
be
maintain
ed
after
propagating through
tap
water
, and are slightly distorted by
the
water current. When
a
1.
5
-
millilitre
Maalox solution is added into
still
water,
there is
a
small,
time
-
varying
change in
the
intens
ity profiles
that
might
be a result of
the natural dynamic diffusive
movement of
6
Al(OH)
3
/
Mg(OH)
2
particles in the water.
When the particles become evenly distribu
ted in the
water after
1
-
minute
circulation
from one pump
,
the distortions of
the
OAM intensity profiles
tend to be
small
(
Fig
s
.
2(
a7
-
a9)
)
. However,
a
n additional
power loss of
4
.
5
dB
to the link
is
measured
.
We expect a larger power loss for a higher concentration of scattering particles.
Figures 2(a10
-
a12)
depict
snapshots of intensity profiles
under
thermal
gradient
-
induced
turbulence
, showing significant distortions in
the
beam profiles
.
We believe
that
this is
mainly
due to
the
high
er
-
order wavefront
aberrations
that can result
from the
refractive index
inhomogeneity
induced by
the water
thermal gradient.
Moreover, the
thermal gradient introduces
a
dynamic beam
wander
at the receiver, as
depicted
in
Fig
.
2
(b
)
.
T
he maximal displacement of
the received beams is estimated to be ~
1
mm
, which is expected to increase under a larger
thermal gradient
(
as shown in
Supplementary
Fig. S1(c)
)
.
For comparison,
the statistic for the
beam wander
due to water current is also shown.
The
beam
wander
combined with other high
er
-
order wavefront
aberrations
c
ould cause the spreading of the transmitted OAM
beam power into
neighbouring modes
, resulting in significant performance degradation (
Supplementary
Fig.
S1(d))
.
Figure
2
(
c
) shows
the
OAM power spectrum
for beam
=+3
under
the above underwater
conditions
.
The crosstalk values onto adjacent modes increase by 0.5 and >7 dB with
current
and
turbulence
,
respectively.
Figure
2
(
d
) presents
the
power transfer between OAM
modes
=±1
and
±3
under water
current
.
It is estimated that the total crosstalk for each mode is
below
-
10.3 dB if
all four beams are simultaneously transmitted
.
Given the above measurements, it seems that the thermal
gradie
nt
-
induced turbulence has a
larger impact on beam quality than scattering or current, yet the Maalox
-
induced scattering
(if
uniformly distributed)
may
introduce significant link loss.
7
System performance measurements of four OAM multiplexed underwater
links
In this section, we present the system performance measurements when simultaneously
transmitting four OAM beams.
Two OAM multiplexed underwater links each using a d
ifferent
source data generation
technique are demonstrated
.
The first link transmits a
1
-
Gbit/s signal at
520 nm on each beam using the direct modulation of a laser diode, resulting in a capacity of 4
Gbit/s.
For
the second
link
, each beam carries a 10
-
Gbit/s signal generated using frequency
doubling of a data signal at 1064 nm, achieving a
significantly
higher capacity of 40 Gbit/s.
4
-
Gbit/s
data
link using directly modulated laser diodes
:
Two 1
-
Gbit/s
on
-
off
-
keyed (
OOK
)
signal beams at 520 nm are generated by directly modulating each of the
two 520
-
nm
green
laser
diodes
. The two modulated
green light beams
are
converted into
two different
OAM beam
s
with
=+1
and
+3
by
adding different spiral phase
pattern
s
using
SLMs
.
The
generated
OAM beams
are
coaxially
combined and then split into two identical copies
. Another two beams with
opposite
values
of
-
1
and
-
3
can
then
be
obtained by reflecting one of the copies three times.
We note that this beam copy is relatively
delayed
with respect to the original one in free
-
space
for data sequence correlation.
Subsequently, t
he resulting four beams are spatially multiplexed
and then
propagate
d
through
the
above
-
mentioned water conditions.
At the receiver, each of the
four OAM channels is sequentially demultiplexed
using another SLM and
detected using a high
-
sensitivity
silicon
avalanche photodiode
(APD) with
1
-
GHz bandwidth
.
The detected signal is
amplified,
filtered
and
sent to a 1
-
Gbit/s receiver for bit
-
error rate (BER) measurements
(
see
Supplementary Section
2
for implementation details
)
.
Figure
3(a)
depicts the eye diagrams of the 1
-
Gbit/s OOK signal for OAM channel
=+3
under
various conditions when
the
other channels
(
=
-
3,
-
1, and +1
)
are turned off
or
on
.
The inter
-
channel crosstalk effects can be clearly observed in
Fig
s.
3(a4
-
a6).
In the pres
ence of
a
thermal
8
gradient,
the eye diagram
of channel
=+
3
is time
-
varying
d
ue to
fluctuations in
the
received
power
and crosstalk
, and is not shown here
.
Figure 3(b) shows measured
BER
s
as a function of
received power
for all four channels with and without water.
The BER curve for the back
-
to
-
back
(B2B)
1
-
Gbit/s signal
is also provided as a benchmark
.
We observe that
tap
water introduces
power penalties of less than
2
.
9
dB
at the forward error correction (FEC) limit of
3.8
×
10
-
3
for all
channels. Figure
3
(
c
)
present
s
BER
curves
for OAM channels
=+1
and
+3
under various
conditions
.
Power penalties are measured to be 2.
2
, 2.
3
,
and
2.
7
dB
in the cases of
tap
water,
Maalox
-
induced scattering
and
current
, respectively.
D
ue to
the effects of
thermal gradient
-
induced
turbulence
,
the
BERs are all above
the
FEC limit
,
exhibiting
a
severe error
-
floor
phenomenon, and power penalties are above 1
2
dB for all channels.
40
-
Gbit/s
OAM
link using
PPLN
-
based frequency doubling
:
Due to water absorption,
underwater optical communication links
generally
use blue
-
green light. However, data
modulation technologies in this spectral region tend to have much lower bandwidths (e.g.,
around 1 GHz) than are available for IR light (e.g., bey
ond 10 GHz)
9
,
3
6
.
An important goal
would be the achievement of higher data rates for each underwater OAM channel. Therefore,
modulating data in the IR
region
at
a
much higher speed and then wavelength converting it into
the blue
-
green region for subseque
nt OAM generation and underwater transmission might enable
significantly higher system capacities. Specifically, whereas we
previously
described data rates
on each OAM beam of 1 Gbit/s, we show here the ability to transmit 10 Gbit/s on each beam
using freq
uency doubling
(
see Supplementary Section
3
for implementation details
)
.
A 10
-
Gbit/s OOK signal at 1064
nm
is generated using
a
l
ithium
n
iobate modulator
and then
amplified
with a high power y
tterbium
-
d
oped fibre
a
mplifier
(YDFA). The 1064
-
nm light
after
9
amplification
is
sent to a frequency
-
doubling
module
that consists of a PPLN crystal and a
temperature
stabilized
crystal oven
for frequency doubling
.
As a result
, a 532
-
nm
green light
carryi
ng a 1
0
-
Gbit/s data
stream
is generated,
w
here
its power depend
s
upon both
the oven
temperature and
the
input pump power
.
The generated green light acts as
a
light source, being
converted into OAM beams
using
specially
-
designed
efficient
dielectric metasurface
phase
masks
3
7
,
39
.
Each phase mask
is composed of a large number of square cross
-
section nano
-
posts
that locally modify
light
's
phase with subwavelength spatial resolution.
Phase masks of
=
±
1
and
=
±
3 each having a
blazed grating
‘fork’
phase pattern
(i.e.,
combination of the
spiral
phase structure of the desired OAM mode
and a linear phase ramp
18
)
are
designed, fabricated,
and characterized
(
see Supplementary Section
4
)
.
Employing
a
setup similar to the one
described
in the previous section
, the four OAM beams
with
=
±1 or ±3
are spatially combined and propagate through
the
underwater channel. At the
receiver,
each of the
four
OAM data channels is
sequentially demultiplexed using
a
metasurface
phase mask
with an inverse spiral phase
pattern
. The beam
of the desired channel
is s
patially
filtered after demultiplexing
,
detected using a high
-
bandwidth APD
(3
-
dB cut
-
off frequency of 9
GHz)
and sent
to
a 10
-
Gbit/s receiver for BER measurements
.
Figure
4
(a)
depicts the eye diagrams
of
the
1
0
-
Gbit/s OOK signal
for
OAM channel
=+3
when
the other channels are turned o
ff
and o
n
.
The total crosstalk from
all the
other channels are
-
11.2,
-
10.
7
,
-
11.0 dB for the cases of
tap
water,
current
, and Maalox scattering, respectively.
Because
of this,
the quality of
the
eye diagrams degrades w
hen other channels are turned on.
Figure
4
(
b
)
show
s
measured BER curves
for OAM channels
=+1 and +3
in the cases of
tap
water and
current
with and without crosstalk from
the
other channels.
The
B2B
BER curve
of the 10
-
Gbit/s
signal
is also provided
.
The power penalties are observed to be less than
2
.
2
dB
for all cases
10
when all channels are on
.
Mitigation of thermal gradient
-
induced crosstalk
using
multi
-
channel
equalisation
P
revious section
s
found various OAM beam d
egradations and consequent data
-
channel crosstalk
based on underwater effects. In this section, w
e
address the data degradation problem and
show
the mitigation of inter
-
channel crosstalk
due to
thermal gradient
-
induced turbulence
. We empl
o
y
a
constant modulus algorithm
(
C
MA)
-
based
multi
-
channel equalisation in the receiver DSP
to
reduce channel
crosstalk effects
and thus recover the transmitted data stream
s
40
-
4
2
. This approach
has been previously employed i
n few
-
mode and multi
-
mode fibre
-
based mode division
multiplexed systems to mitigat
e the mode coupling effects
among
multiple spatial modes
4
3
,
4
4
.
In
general,
it is required that all the transmitted channels are simultaneously detected
to enable
multi
-
channel equalisation processing
. Due to receiver hardware limitations,
we
only
show
crosstalk mitigation between two OAM channels.
With a
similar
system approach, t
wo OAM
beams
with
=+1 and +3
are
generated using
metasurface phase masks,
spatially combined using a beam splitter and
transmitted
through
water with a thermal gradient of
0
.2
o
C
.
Each OAM beam carries a 10
-
Gbit/s OOK signal
generated by doubling the frequency of a modulated 1064
-
nm signal using a PPLN nonlinear
crystal.
After demultiplexing and detection,
the two OAM channels
are
simultaneously received,
converted into Gauss
ian
-
like beam
s
and detected by
two
9
-
GHz bandwidth APD
s
. The two
signals are
then
amplified, sampled by a real
-
time scope and recorded for offline DSP.
A
2×2
CMA
equalisation algorithm is implemented in the DSP
to recover two data OAM channels with
=+1 and
=+3
.
For a
2
CMA
equalis
ation,
t
he
equalis
er includes
four
adaptive finite
-
impulse
-
response (FIR) filters
each with a tap number of
11
,
the coefficients of which can be
11
adaptively updated until convergence based on
the
CMA algorithm
(see Supplementary Section
5
)
.
The obtained FIR filter coefficients are used to
equalis
e the crosstalk
between the
two OAM
channels.
Figure
5
(
a
)
depicts
the
received
power and crosstalk of OAM channel
s
=+1 and +3
measured
every
2
seconds under the effects of
thermal gradient
-
induced turbulence
.
T
he received power
and crosstalk fluctuate by up to
4.5
and
1
2.5
dB
, respectively.
The corresponding BERs
for the
two OAM
channels during the same time period
are shown in Fig.
5
(
b
)
.
Withou
t
CMA
equalis
ation,
the measured
BERs fluctuate significantly between 1
.7
×10
-
2
and
7.4
×10
-
6
,
and
dramatically decrease
,
reach
ing
below the FEC limit of
3.8×10
-
3
after
2
CMA
equalis
ation
.
We note that only a length of 2
,0
00
,000
symbols
is
recorded for each data sequence due to
the
limited memory of
the
real
-
time scope
,
and therefore
the minimum BERs
that can be measured
are around
5×10
-
7
.
To further illustrate the improvement,
Fig
.
5
(c)
shows the measured BERs
averaged over
1
minute
as a f
unction of
received power
for channels
=+1 and +3
.
Due to inter
-
channel crosstalk, the measured BER curves
without
2
×
2
equalization
also have
BER
error floor
s
.
T
he power penalties
at the FEC limit
, compared to the B2B case, fall below 2.
0
dB for
the two
channels
after equali
s
ation
.
Discussion
The
experiments
described in this paper explore the potential of using OAM
-
based
SDM
to
increase the transmission capacity of underwater optical communications, and several issues lend
themselves to further exploration.
In general, the use of OAM multiplexing would likely require a more precise alignment between
the transmitter and receiver compared to a single
-
channel underwater optical link. This is due to
12
the fact
that orthogonality
among OAM channels
relies on a commo
n optical axis
, and any
misalignment may result in
inter
-
channel crosstalk
4
5
.
Given the beam wander that is introduced
by thermal gradients, the above problem is exacerbated and will likely require an accurate
pointing and tracking system.
Additionally, gi
ven that small thermal gradients can produce system degradation, we assume that
this problem could become more severe for longer links for which different types of water may
exist. M
eanwhile
, this problem may depend on the transmission direction, such tha
t a vertical
link may experience a different thermal gradient than a horizontal link. Furthermore, a
channel
equalisation algorithm
was utilised to help mitigate the thermal gradient
-
induced crosstalk.
However, it might be necessary under harsher and wide
-
ranging underwater conditions to
explore the use of multiple
mitigation
techniques, including adaptive optics
compensation
and
advanced channel coding
4
6
-
48
. We emphasise that other effects, such as
spatial dispersion and
object obstructions
,
are not consi
dered yet
might cause beam spreading and link outage
4
9
, 50
.
We investigated t
he effects of underwater propagation on OAM
-
multiplexed
data transmission
and the mitigation of inter
-
channel crosstalk over a
s
hort link of metre
-
length scale
. However, we
believe our results could
potentially be expanded to longer distances and scaled to a larger
number of
OAM channel
s through careful system design
4
5
and
the use of
proper mitigation
approaches for channel
degradation
effects
.
We envision that
the underwater transmission
capacity of 40 Gbit/s achieved in this paper could be
further extended into sub
-
Tbit/s
by
including ot
her techniques, such as
advanced modulation formats
(e.g.,
quadrature
-
amplitude
-
modulation and OFDM
) and wavelength division multiplexing.
Method
s
Summary
13
Generation and detection of
data
-
carrying
green
OAM beams
.
Two different data
-
modulation approaches
are employed to generate high
-
speed green light signals
:
1
-
Gbit/s
signal
generation
at green using internal modulation
By
directly modulating the
driving current of a 520 nm laser dio
de, a 1
-
Gbit/s signal at 520 nm is produced.
Due to the
bandwidth limitation of the internal modulation of the laser diode, the
maximal
data rate of the
gre
en beam
i
s
1
Gbit/s.
The generated signal is then launch
ed
onto a programmable SLM with a
specific helical phase pattern to create an OAM beam with either
=+1 or +3
. Multiple
generated OAM beams are then multiplexed using a beam splitter
-
based combiner a
nd the
resulting beams propagate through the underwater channel. The received signal after
demultiplexing is detected using a
high sensitivity Si APD with a 3
-
dB bandwidth of 1
-
GHz.
1
0
-
Gbit/s
signal
generation
at green using PPLN
-
based frequency doubling
Generally, the
modulation bandwidth of both internal and external modulations for green light is limited to GHz
4, 7
. To overcome this, the frequency doubling of a data
-
carrying 1064
-
nm signal
is
thus
used to
produce
a
high
-
speed green light signal. Specif
ically,
we perform high
-
speed data m
odulation
using a 1064
-
nm
l
ithium
n
iobate modulator
and use a PPLN
-
based frequency
-
doubling module
to convert the carrier wavelength from 1064 nm to
532
nm
.
Consequently, a green light signal at
532 nm is generated, which is then split into multiple copies and converted into OAM beams
using
transmissive
metasurface
phase masks
.
At the receiver, a
Si APD with a 3
-
dB bandwidth
of 9
-
GHz
but a lower sensitivity tha
n the detector used for the 520
-
nm si
gnal detection
is
employed for signal detection.
Crosstalk mitigation using
multi
-
channel
equalisation
.
T
he multiplexed OAM beams
may
be
distorted
due to
underwater propagation
, causing
the
power spreading of each transmitted OAM
mode onto neighbo
u
ring
modes
. Consequently, each OAM channel experiences interferences
14
from the
other
channel
s, resulting in a non
-
diagonal channel matrix
.
T
heoretically
,
t
o
recover the
data streams,
the received signals of all OAM channels could then be multiplied with the inve
rse
channel matrix.
In our experiment, w
e use
a
2×2
CMA adaptive
channel
equalis
ation
in the
receiver
to reduce the
effects of
interference
s
and recover the two data channels. In general, the
dimension of the
equalisation
processing is determined by the
total number of OAM ch
annels.
The
CMA
-
based
equalis
ation utilises
a
n
FIR filter
-
based
linear
equalis
er for each channel
.
The
FIR
-
CMA
equalis
er contains
four
FIR filters, the coefficients of which can be adaptively updated
until convergence based on
the
CMA
.
The obtained FIR filter coefficients are used to
equalis
e
the crosstalk
between
two OAM channels.
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Acknowledgements
We acknowledge
James M
.
Krause,
Michael J.
Luddy, and Jack H. Winters
for valuable help and
fruitful discussions.
S.M.K.
i
s supported by
Light
-
Material Interactions in Energy Conversion
Energy Frontier Research Center funded by the US Department of Energy, Office of Science,
Office of Basic Energ
y Sciences
.
E.A. and A.A.
are
supported by Samsung Electronics.
D
evice
nanofabrication
wa
s performed at the Kavli Nanoscience Institute at
California Institute of
Technology
.
This
work is supported by
the
National Science Foundation
and NxGen Partners.
Author contributions
Y.
R
.
, L.L.,
and A.W. developed the concept and designed the experiments.
Y.
R
.
, L.L.,
Z.Z., G.X.,
Z.W., N.A., Y.Y., C.L., and A.J.W carried out the measurements and analysed the data. L.L.,
Y
.
C
.
,
and
Y.R.
designed and
implemented
the mu
ltiple
-
input
-
multiple
-
output
equalisation
algorithm.
S. M. K., E. A., A. A., and A. F.
designed, fabricated, and characterized
the
metasurface OAM generator phase masks. S.A.,
M.T
.
,
A.
F.
,
and A.W. provided technical support.
The project
was
conceived and s
upervised by A.W.
.
The authors declare no competing financial interests. Correspondence and requests for materials
should be addressed to A.W. (willner@usc.edu).
21
Figure
1
Figure 1 |
Prosp
ective application scenario for
a
high
-
capacity
underwater
optical
communications link
with
OAM
-
based space division multiplexing
.
Key modules including
light source, signal
modulation
, OAM generation/
multiplexing
,
OAM demultiplexing/detection
and
receiver
signal processing are shown.
RX Aperture
OAM
Demux
Signal Detection
Signal Processing
Receiver
Scattering
Currents
Turbulence
TX Aperture
OAM Gen. &
Mux
Light Source
Transmitter
Signal Modulation
OAM 4
OAM 3
OAM 2
OAM 1
OAM Multiplexing