# Self-Adaptive Integrated Photonic Receiver for Turbulence Compensation in
Free Space Optical Links

Andres Ivan Martinez  Dipartimento di Elettronica, Informazione e
Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci, 32, Milano,
20133, Italy  Gabriele Cavicchioli  Dipartimento di Elettronica, Informazione
e Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci, 32, Milano,
20133, Italy  Seyedmohammad Seyedinnavadeh  Dipartimento di Elettronica,
Informazione e Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci,
32, Milano, 20133, Italy  Francesco Zanetto  Dipartimento di Elettronica,
Informazione e Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci,
32, Milano, 20133, Italy  Marco Sampietro  Dipartimento di Elettronica,
Informazione e Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci,
32, Milano, 20133, Italy  Alessandro D’Acierno  Huawei Technologies Italia
Srl, Centro Direzionale Milano 2 SNC, 20054 Segrate, Italy  Francesco
Morichetti  Dipartimento di Elettronica, Informazione e Bioingegneria,
Politecnico di Milano, P.za Leonardo da Vinci, 32, Milano, 20133, Italy
Andrea Melloni  Dipartimento di Elettronica, Informazione e Bioingegneria,
Politecnico di Milano, P.za Leonardo da Vinci, 32, Milano, 20133, Italy
<EMAIL_ADDRESS>
###### Abstract

In Free Space Optical (FSO) communication systems, atmospheric turbulence
distorts the propagating beams, causing a random fading in the received power.
This perturbation can be compensated using a multi-aperture receiver that
samples the distorted wavefront on different points and adds the various
signals coherently. In this work, we report on an adaptive optical receiver
that compensates in real time for scintillation in FSO links. The optical
front-end of the receiver is entirely integrated in a silicon photonic chip
hosting a 2D Optical Antenna Array and a self-adaptive analog Programmable
Optical Processor made of a mesh of tunable Mach-Zehnder interferometers. The
photonic chip acts as an adaptive interface to couple turbulent FSO beams to
single-mode guided optics, enabling energy and cost-effective operation,
scalability to systems with a larger number of apertures, modulation-format
and data-protocol transparency, and pluggability with commercial fiber optics
transceivers. Experimental results demonstrate the effectiveness of the
proposed receiver with optical signals at a data rate of 10 Gbit/s transmitted
in indoor FSO links where different turbulent conditions, even stronger than
those expected in outdoor links of hundreds of meters, are reproduced.

###### keywords:

Silicon Photonics, Free Space Optical Communications, Atmospheric turbulence,
Adaptive integrated optics

## Introduction

Free Space Optical (FSO) communication systems operating in the near [1, 2] ,
mid [3, 4], and even long infrared wavelengths [5] have received increasing
interest in recent years. With respect to radiofrequency wireless, FSO systems
are suitable for ultrahigh data rates, offer unlicensed frequency spectrum,
and require low power consumption[6]; compared to optical fiber
communications, FSO avoids the need for cabling, thus reducing installation
time and costs [7, 8]. These properties set FSO systems as the leading
candidates to implement earth-space satellite communications [9], cellular
radio network backhaul [10], security [11], LiDAR and ISAC (Integrated Sensing
And Communication) systems [12, 13], and even fiber backup paths [14].
However, FSO performance is typically impaired and limited by adverse
atmospheric phenomena such as air turbulence, temperature gradients, fog and
rain, dust, and pollution, which induce beam distortion and wander, in
addition to beam deviation, extra attenuation, and link misalignments [15].
Currently, solutions have been proposed to compensate for the optical beam
divergence, keep the alignment, and compensate for attenuation, but turbulence
effects remain mostly unsolved [2].

Atmospheric turbulence introduces a random phase and amplitude perturbation to
the propagating optical beams [16]. This effect can induce a deep signal
fading at the photodetector [17], known as scintillation. In addition to the
use of large area photodetectors, having the drawback of an inherent narrow
bandwidth and limiting the maximum data rate of the link, in the literature,
three different approaches are commonly used to compensate for scintillation:
adaptive optics [18], modal diversity receivers [19], and spatial diversity
receivers [8]. In the first approach, deformable mirrors adapt to the incoming
beam wavefront to correct the phase front, mitigating the scintillation.
However, the complexity of their control algorithm limits the bandwidth,
making them unsuitable to adequately compensate for the scintillation [20].
The second approach exploits the fact that a scintillated beam can be seen as
the linear combination of various spatial modes [19]; here, a mode
demultiplexer is used to decompose the beam in its fundamental modes, and then
each mode is mapped to a single mode fiber (SMF). By coherently combining
these signals, it is possible to recover the spatial coherence of the beam.
Although this approach allows a complete beam reconstruction, it requires a
mode demultiplexer and SMFs with length difference in the order of a small
fraction of the bit duration, i.e., tens of $\mu$m for 10-100 Gbps signals.
Finally, spatial diversity exploits multi-aperture receivers that sample the
incoming beam in different positions of the arriving beam front and then
recombine the signals coherently. This combination can be done in the
electrical domain [21], limited by the processing speed of electronics, or in
the optical domain [8], with some limits on the scalability.

In this work, we present a multi-aperture self-adaptive FSO receiver
integrated into a single silicon photonic chip. The receiver, realized in a
commercial silicon photonics platform, includes a 2D Optical Antenna Array
(OAA) that samples the incoming beam and is connected with a Programmable
Optical Processor (POP) made of a mesh of tunable Mach-Zehnder interferometers
(MZIs). The POP self-adapts in real-time and coherently combines the sampled
optical signals to a single-mode fiber, thus minimizing the fading of the
received signal. Experimental results demonstrate the effectiveness of the
approach with intensity-modulated optical signals at a data rate of 10 Gbit/s.

## Results

### Design criteria for multi–aperture integrated photonic FSO receiver

In this section, we illustrate the approach we used to design the OAA front-
end of the FSO-integrated photonic receiver. To this end, we performed
numerical simulations to understand the effects of turbulence-induced
scintillation on Gaussian beams and extract the spatial coherence parameter
that is required to design the multi-aperture OAA and the POP.

#### Turbulence effects on free space Gaussian beams

Figure 1: Effects of turbulence on a Gaussian beam. Beam with $w_{0}=1$ mm and
$\lambda=1550$ nm propagated for 800 m for low (1${}^{\text{st}}$ row),
moderate (2${}^{\text{nd}}$ row), and strong (3${}^{\text{rd}}$ row)
turbulence regime. The $1^{\text{st}}$ column corresponds to the beam power
density, the $2^{\text{nd}}$ to the phase front, and the $3^{\text{rd}}$ to
the spatial coherence. The dashed circles correspond to the theoretical Fried
parameter $r_{0}$.

Figure 1 shows the effects of the turbulence on a Gaussian beam with an
initial waist $w_{0}=1$ mm and wavelength $\lambda=1550$ nm propagated for
$L=800$ m under weak ($C_{n}^{2}=10^{-15}[\text{m}^{-2/3}]$), moderate
($C_{n}^{2}=10^{-14}[\text{m}^{-2/3}]$), and very strong
($C_{n}^{2}=10^{-13}[\text{m}^{-2/3}]$) turbulence strength (details on the
numerical model are given in the Methods). The beam divergence is 1 mrad full
width, and the final diameter of the beam is 80 cm. The first column (a) shows
the spatial power density distribution on the front of the received beam. For
weak turbulence (a1), the intensity profile is similar to a pure Gaussian
beam. As the turbulence increases, the scintillation increases (a2), and for
very strong turbulence (a3), the beam assumes a speckle-like aspect. This
characteristic is measured in literature with the Rytov variance [15] that,
for the three considered cases, is equal to 0.013, 0.132, and 1.322.

The scintillation also affects the phase front of the beam, as shown in column
(b). In (b1), the phase changes smoothly across the wave-front, remaining
always within $2\pi$ [rad]. In (b2), the perturbation increases more than
$2\pi$ [rad], and therefore, jumps in the phase profile are observed. In (b3),
the phase is heavily distorted, presenting frequent phase jumps. The Fried
parameter $r_{0}$, or atmospheric coherence width, defines the diameter of a
circular area over which the RMS wavefront aberration equals 1 radian [22].
The colormaps in Fig. 1c show the spatial coherence of the beam; the dotted
circles indicate the theoretically expected coherent area $r_{0}$, equal to
35, 8.9 and 2.2 cm for the three considered cases. The lower the turbulence
(c1), the larger the spatial coherence of the beam $r_{0}$, which reduces
rapidly with the accumulated scintillation. These amplitude and phase patterns
of the received beam evolve with the time scale of atmospheric turbulence,
which is in the order of a few hundred Hz [17].

Figure 2: Single-aperture receiver. a, Scheme of the single-aperture receiver
that focuses a portion of the incoming beam on a single-mode fiber or PD. b-c,
Simulated time trace (b) and PDF (c) of the optical power coupled to the PD
for a large and small aperture $d_{R}$ with respect to $r_{0}$. d-f, Simulated
mean received power (d), standard deviation (e), and three-sigma limit (f) of
a single aperture receiver with a single-mode detector as a function of the
aperture diameter $d_{R}$ for $C_{n}^{2}=10^{-13}$ (yellow), $10^{-14}$
(blue), $10^{-15}$ (red), and without turbulence (purple). $\overline{P_{rx}}$
and $\sigma_{rx}$ have been calculated as the average of 100 simulations.

#### Single-aperture receiver

A single aperture receiver is considered here, and the main limitations are
discussed, setting the motivations for multi-aperture receivers in FSO
applications. The main purpose of the receiver is to couple as much power as
possible from the incoming beam and provide an output power not affected by
time-varying fading due to beam scintillation. We consider the system sketched
in Fig. 2a as a reference single-aperture receiver: a generic input optical
aperture with a diameter $d_{R}$ is coupled to some optics (lens or
telescope), which focuses the collected portion of the incoming beam to an
output aperture with spot size $d_{D}$. Such output aperture can be a small-
area photodetector (PD), an optical fiber, or a waveguide. Ideally, $d_{R}$
should be as large as possible. At the same time, $d_{D}$ has to be small in
the case of single-mode fibers or high-speed integrated PDs. The smaller the
active area, the lower the PD’s junction capacitance and, in turn, the
resistor-capacitor (RC) time constant [23]. In contrast, the distorted
intensity and phase of the beam are inherently associated with a multimode
nature, thus reducing the minimum achievable size of the focused beam on
$d_{D}$. In other words, the loss of spatial coherence of the scintillated
beam limits the size at which it can be concentrated using an optical system,
that is, the ratio $d_{R}/d_{D}$ is limited by the étandue constraint [24].
The PD size can be set as a trade-off between coupling efficiency and
bandwidth. Still, in any case, the performance of the system in the presence
of scintillated beams is severely limited, making it difficult to achieve data
rates above 1 Gbit/s over distances of a few hundred meters.

To better understand the effect of beam scintillation on the optical power
$P_{rx}$ detected by the single-mode receiver, Fig. 2b shows the time traces
of $P_{rx}$ for two apertures larger (80 cm, blue) and smaller (4 cm, red)
than $r_{0}$ (8.9 cm). Throughout the paper, the effects of a misalignment of
the receiver are neglected. The average detected power with the large aperture
is higher, but it suffers from an intense fading caused by the multimodality
of the beam. In contrast, with the small aperture, $P_{rx}$ is much less
affected by the scintillation, even if its mean value is lower. Fig. 2c shows
the probability density functions of $P_{rx}$ for the two considered
apertures.

Figure 2d shows a simulation of the relative mean received power
$\overline{P_{rx}}$ as a function of the input aperture size $d_{R}$ for no
turbulence (purple), weak $C_{n}^{2}=10^{-15}[\text{m}^{-2/3}]$ (red),
moderate $C_{n}^{2}=10^{-14}[\text{m}^{-2/3}]$ (blue), and strong
$C_{n}^{2}=10^{-13}[\text{m}^{-2/3}]$ (yellow) turbulence strength. The
corresponding values of $r_{0}$ are marked as a reference. Figure 2e shows the
corresponding standard deviation $\sigma_{rx}$ of $P_{rx}$, i.e., the fading.
Generally, the stronger the turbulence, the lower the mean received power and
the higher the fading. As long as $d_{R}<r_{0}$, the received power increases
with the size of the aperture, is almost independent of the turbulence
strength, and has a $\sigma_{rx}$ that slightly reduces with $d_{R}$. The
received power reaches a maximum for $d_{R}$ slightly higher than $r_{0}$,
meaning that there is no significant gain in increasing the aperture size
further. Instead, the standard deviation $\sigma_{rx}$ increases rapidly for
apertures approximately larger than $r_{0}/3$ and above $r_{0}$ reaches values
that can be very detrimental for high data rate optical communication systems.
As a result, the scintillation limits the maximum diameter of the aperture.
See Supplementary Information sec. 1.1 for details.

As in any communication system, also in FSO it is important to guarantee a low
probability that the received power drops below a given sensitivity threshold,
say -25 dB, to avoid out-of-service of the link. Figure 2f shows the quantity
$\overline{P_{rx}}-3\sigma_{rx}$. It is evident that apertures comparable with
$r_{0}$, despite a lower mean $\overline{P_{rx}}$, guarantee the largest
probability to remain above the sensitivity threshold, at least for moderate
turbulence, and are therefore the best choice. The aperture size should be
selected for the maximum turbulence $C_{n}^{2}$ that has to be compensated
because $\overline{P_{rx}}-3\sigma_{rx}$ improves with the reduction of the
turbulence.

#### Multi-aperture receiver

A small aperture guarantees a received power that is almost scintillation
insensitive, and it is suitable for high bit rates but has the drawback of
coupling just a small portion of the incoming power. A possible solution to
achieve higher received power, with minor fading and large bandwidth, is to
sample the received beam using several small apertures (see Fig. 3a) and then
combine the samples by adding their power. In our approach, the received beam
is sampled by an Optical Antenna Array that is integrated directly into the
photonic chip. Pairs of samples are coherently combined using balanced
tuneable MZIs, which are cascaded to form a binary-tree mesh as shown in Fig.
3b. The MZI mesh implements a Programmable Optical Processor (POP) that can be
adapted and reconfigured in real time to follow the time-varying scintillation
of the received beam. To this end, each MZI has an analog electronic feedback
loop that controls the two phase shifters based on the power read by the on-
chip integrated slow photodetectors [25]. Different topologies of MZI meshes
have been proposed in the literature, with a single output that can be
connected to an optical fiber, a PD, or a standard receiver. Remarkably, the
POP configuration and tracking time have to match the bandwidth of the
scintillation and not that of the signal data rate. A comprehensive
description of the working principle of the POP is reported in [26, 27, 28].
The circuit schematic is shown in Fig. 3b with an 8 apertures OAA that samples
the incoming beam and the POP that sums the samples coherently. This
architecture is easily scalable to a more significant number of optical
antennas without increasing the control complexity.

Figure 3: Multi-aperture receiver structure. a, Optical Antenna Array
distribution for $M=2$, 5, 9, 16. b, Schematic of the Programmable Optical
Processor connected to the OAA. c-e, Mean received power (c), standard
deviation (d), and three-sigma limit (e) as a function of the number of
apertures for different separation distance $d_{S}=5$, 11 and 30 cm, and the
three considered turbulences $C_{n}^{2}=10^{-13}$, $10^{-14}$, and $10^{-15}$
$[\text{m}^{-2/3}]$. $d_{R}=4.5$ cm. $\overline{P_{rx}}$ is calculated by
summing coherently the contributions of the $M$ apertures. $\overline{P_{rx}}$
and $\sigma_{rx}$ have been calculated as the average of 100 simulations.

The main design parameters of the multi-aperture receiver are the number of
apertures $M$ of the OAA, the size of the apertures $d_{R}$, and the distance
$d_{S}$ between them. In the following numerical analysis, the size $d_{D}$ is
assumed to be suitable for the coupling with single-mode waveguides, and the
POP is assumed to work properly, i.e., the output power is the sum of the
power received by all the apertures. To determine the optimal values for $M$
and $d_{S}$, we fixed $d_{R}=4.5$ cm (from Fig. 2) as a good compromise
between a high $P_{rx}$ and low $\sigma_{rx}$ for $C_{n}^{2}\geq 10^{-13}$
(see Supplementary Information sec. 1.2 for details).

Figure 3c shows the mean power $\overline{P_{rx}}$ (overall power received by
the OAA) vs. the number of apertures $M$ for the three values of $C_{n}^{2}$
and three separations of adjacent apertures $d_{S}=5$, 11, and 30 cm. The
arrangement of the apertures of the OAA is shown in Fig. 3a. As expected, the
power $\overline{P_{rx}}$ increases with the number of apertures and saturates
when the OAA size is comparable to or larger than the beam width.
$\overline{P_{rx}}$ is weakly dependent on the separation distance unless the
size of the OAA is larger than that of the beam. The great advantage of using
a multi-aperture receiver is that the coherent combination of the $M$ signals
reduces the $\sigma_{rx}$ of the output power, especially if the contributions
are uncorrelated, that is, when $d_{S}>r_{0}$ because the single fluctuations
tend to compensate. Instead, there is no diversity gain when the apertures are
within the same coherence area ($d_{S}<r_{0}$). In any case, the reduction of
the fading improves with $M$, as shown in Fig. 3d.

As a result of this numerical analysis, the OAA has to cover the most
significant portion of the beam with a sufficiently large number of apertures
with individual size and mutual distance comparable with the smaller $r_{0}$
to be compensated. Fig. 3e shows that the quantity
$\overline{P_{rx}}-3\sigma_{rx}$ increases with these choices and guarantees
the largest probability of remaining above the sensitivity threshold (-25 dB),
indicated by the gray horizontal line. It is worth noting that a multi-
aperture receiver with $M\geq 9$ satisfies the minimum sensitivity request of
-25 dB also with the strongest considered turbulence, with a significant
advantage with respect to the single aperture results shown in Fig. 2f.

### Integrated FSO photonic receiver

t!]

Figure 4: Integrated silicon photonics FSO receiver. a-e, Photograph of the
fabricated PIC (a), the inner ring of the OAA (b), a single Mach-Zehnder
interferometer (c), integrated Ge photodiodes for feedback control (d), and
the chip assembled on a PCB with control electronic and fiber transposer (e).

An integrated photonic FSO receiver has been realized according to the design
criteria described in the previous section [28]. The receiver operates in the
C-band, and it has been fabricated on a standard 220-nm silicon photonic
platform by the commercial foundry AMF in an active MPW run. The total
footprint is 1.3 mm $\times$ 3.2 mm (including the electrical pads) and
comprises three sections: a 2D OAA, a POP, and an array of Ge PDs. A
photograph of the chip is shown in Fig. 4a. The OAA is composed of 16 surface
grating couplers (GCs). Each GC is 48 $\mu$m-long and 23 $\mu$m-wide, with a
24 $\mu$m-long taper. The radiated field of each GC has an elevation angle of
12°, an azimuth angle of 0°, and a full-width divergence of 5.6° $\times$
9.8°. The GCs of the OAA are distributed as follows: a central GC, an inner
ring of 60 $\mu$m radius with 7 GCs, and an outer ring of 180 $\mu$m radius
with 8 GCs. A photograph of the inner ring is shown in Fig. 4b. The distances
between the GCs have been optimized to match the coherence radius of the beam
in the maximum turbulence conditions ($d_{S}\approx r_{0}$). Note that here,
the considered value for $r_{0}$ is after the demagnification of the
collimating optics used to couple the FSO beam (see "Experimental results").

The POP has a 16×1 binary-tree mesh architecture with thermally tuneable MZIs
(see Fig. 4a,c). Each MZI has two actuators (TiN thermal phase shifters), a
trench between the arms to reduce the thermal crosstalk, and an integrated Ge
PD (see Fig. 4d and Fig. 3b), placed in one of the output ports, that provides
a feedback signal to the control loop. The POP is connected through wire
bonding to a custom electronic board that minimizes the signal read by the PDs
(see Fig. 4e). In this way, the two optical signals at the input of each MZI
are coherently recombined and routed towards a common waveguide (not connected
to a PD) [26]. The control system uses a dithering technique applied to the
phase shifters and a lock-in readout of the integrated PDs, which allows the
control of the MZIs with no ambiguity on the direction of tuning (see Methods)
[25]. In this way, every single actuator can be controlled independently, and
all the MZIs can be tuned in parallel, speeding up the setting up of the POP
and the tracking of incoming beam scintillation. Finally, the coherently
recombined signal is coupled using a single-mode fiber array glued on the
chip.

### Experimental results

To validate the mitigation of turbulence-induced scintillation performed by
the integrated photonic receiver, we built an indoor experimental setup
emulating realistic conditions of an outdoor FSO link.

Figure 5: Static turbulence-induced scintillation compensation. a-b, Schematic
(a) and photo of the experimental setup (b) used for the emulation of
turbulence-induced scintillation on FSO beams. c, Image of the optical beam
(c1) without and (c2) with the distortion introduced by the SLM phase screen.
d, Optical power of the FSO beam at the output port of the integrated receiver
for different phase screens when the adaptive control is idle (orange) and
active (blue).

As a first demonstration, we used a spatial light modulator (SLM) to introduce
controllable static perturbations of the FSO beam. The schematic and the photo
of the setup are shown in Fig. 5a,b, respectively (details on the setup are
given in the Methods). Panel (c1) shows the beam shape acquired with a near-
infrared (IR) camera when the SLM acts as a mirror, while (c2) shows how the
phase screen generated by the SLM distorts the beam. Figure 5d shows the
optical power received at the output port of the POP for different PSs
introduced by the SLM (the PSs used are shown in Supplementary Fig. S4). When
the control is idle (orange), the average received power is -10.1 dBm with a
standard deviation $\sigma_{rx}$ = 5.0 dB. In this case, the signals sampled
by the 16 GCs of the OPA combine randomly (constructively or destructively)
depending on the local phase in the sampling points of the beam front of the
incoming scintillated beam. On the other hand, when the control is active
(blue), the POP compensates for the relative phase differences between the
samples, maximizing the output power. In this way, the average power increases
by 8.7 dB (to -1.4 dBm), and the fading standard deviation reduces to 0.8 dB.
The residual fading in the output power is due to the wander effect that
deviates the beam’s trajectory and cannot be compensated by the adaptive
receiver.

To test the receiver in time-varying conditions and verify the speed of the
adaptive control, a dynamic test was performed by replacing the SLM with a
heat gun (see Methods). Figure 6a shows the received optical power $P_{rx}$
acquired for 50 sec in two different conditions. When the POP is off (orange),
the main paths across the MZI mesh are the ones passing through the cross
ports of the MZIs. Therefore, the $P_{rx}$ is not optimized, presenting a low
mean power $\overline{P_{rx}}=-17.5$ dBm and a large standard deviation
$\sigma_{rx}=1.3$ dB. When the control loop is active (blue), the average
received power at the output port is -11.3 dBm with a standard deviation of
only 0.3 dB. The residual minor fading is due to the fill factor of the OAA.
In fact, the geometrical loss caused by the spacing between the GCs depends on
the pattern of the incoming distorted beam, and the total power sampled by the
OAA depends on it. This issue can be mitigated by increasing the fill factor
of the OAA, for instance by integrating arrays of microlenses on top of the
GCs (see Discussion).

Figure 6: Real-time turbulence compensation with 5 Gbit/s signal. a-c,
Received optical power $P_{rx}$ (a), power spectral density (b), and
probability density function (c) of the received optical power when the POP is
in its native state (orange) and when the adaptive control is active (blue).
d-f, Eye diagrams of the received 5 Gbit/s OOK signal in the absence (d) and
in the presence of turbulence when the adaptive control is off (e) and active
(f).

The spectral power density of the output signal is shown in Fig. 6b. The
components associated with the artificial turbulence induced by the heat gun
(orange) extend up to a frequency range of about 500 Hz, which is in line with
the expected spectrum of real atmospheric turbulence (300 Hz) [17]. Results
show that the real-time adaptation of the POP reduces these components by more
than 7 dB up to 400 Hz (blue), which is sufficient to compensate for natural
turbulence. Despite the residual fading of the received power with the control
ON, the probability density function (PDF) of $P_{rx}$ (see Fig. 6c) shows a
narrow distribution with most of the power concentrated around -11.3 dBm.
Instead, when the control loop is not operative, the $P_{rx}$ PDF has its
maximum around -17 dBm and spreads through several dB (from -24 to -14.5 dBm).
Fig. 6d shows the received eye diagram for a 5 Gbit/s signal without
turbulence. In the presence of turbulence with $C_{n}^{2}\approx 10^{-15}$,
Fig. 6e shows the closed-eye diagram when the POP is in its native state.
Instead, when the control loop is active (Fig. 6f), the eye remains open in
error-free conditions, proving the effective mitigation of scintillation
effects.

Figure 7: Real-time turbulence compensation with 10 Gbit/s signal. a-c,
Optical power (a), probability density function (b), and cumulative density
function (c) of the received optical signal when the control is active (blue),
idle (orange), and in the absence of turbulence (yellow). d-f Corresponding
eye diagrams of the received 10 Gbit/s OOK.

Figure 7 displays the results for a 10 Gbit/s signal. In panel (a), the POP is
initially optimized to maximize the coupled power for an incoming beam not
affected by turbulence (yellow). Then, the POP is kept in such a fixed state
(meaning that all the phase shifters are held in that state), but the heat gun
is switched on (orange); finally, the adaptive control is enabled (blue) to
track the evolution of the incoming beam distorted by the effect of the heat
gun. In this experiment, since the POP was already optimized to maximize the
coupling with the undistorted beam, the mean $P_{rx}$ in the idle case with
turbulence (-1.1 dBm) is close to that of the active case (-0.3 dBm). Yet,
$\sigma_{rx}$ is clearly different in the two cases, which show almost the
same values as the ones observed in Figure 6a, being 1.1dB for the idle state
and 0.3dB for the compensated one, as shown in Fig. 7a. The cumulative density
function CDF is reported in panel (c), showing that the outage probability is
always higher for the idle case. The CDF in the absence of turbulence is also
reported in yellow as a reference. Finally, the eye diagrams for the reference
perturbed and compensated cases are displayed in Fig. 7d-f, respectively. The
eye in the presence of scintillation is closed and shows a time-varying
fluctuation (e). Instead, the eye with the POP that cancels the turbulence is
well open and indistinguishable from the reference one.

## Discussion

In conclusion, we demonstrated the effectiveness of an integrated adaptive
receiver based on a 2D optical antenna array and a programmable optical
processor to compensate for the scintillation effects in a turbulent FSO link.
Design rules regarding the number, size, and distance between the optical
antennas of the OAA are discussed. Results show an effective reduction of
intensity fading for turbulent conditions that are even stronger than those
expected in a natural environment. Experiments at 10 Gbit/s show the recovery
of signal quality even in the presence of strong turbulence. In the current
device, the power coupling efficiency is limited by the geometrical loss of
the OAA, which is due to the separation of the GCs of the array that results
in a fill factor of 4.3% and a coupling loss of 13.6 dB. To improve the
coupling efficiency, an array of microlenses can be integrated on top of the
OOA. To this end, 3D printing techniques, such as two-photon polymerization
(TPP), can be used to build custom-designed free-form optical elements
directly on top of the photonic chip, thus facilitating optical alignment and
reducing assembly and packaging costs [29].

The beam contributions sampled by the OAA could also be added in the
electrical domain. In this case, each optical aperture of the OAA has to be
coupled to a fast PD, followed by a wide-band transimpedance amplifier and a
receiver suitable for the specific signal data rate. The different electric
signals can be combined by a multiple-input electronic digital signal
processor, which has to operate at a bit-time scale. This solution, widely
used in RF wireless spatial-diversity systems, becomes hardly practical,
energy-intensive, very expensive when the data rate is raised at more than a
few Gb/s, and sets strict constraints on the maximum number of apertures.
Moreover, signal processing in the electrical domain is data- and protocol-
dependent and unsuitable for simultaneous operation on multiple data channels
transmitted in wavelength division multiplexed (WDM) optical systems. In our
approach, the coherent combination of the signals in the optical domain
employing an analog POP enables energy and cost-effective operation,
scalability to a system with a larger number of apertures, modulation format
transparency, extension to WDM and coherent optical signals, and pluggability
with commercial fiber optics transceivers. From this point of view, the
proposed multi-aperture receiver acts as an optical front-end interface to
couple FSO beams (which are inherently multimode in the presence of
turbulence) to single-mode guided optics. Once FSO signals are coupled to
single-mode guiding structures (i.e., their spatial coherence is restored),
they can be processed on a chip by using the portfolio of standard silicon
photonics devices, and they can be efficiently coupled to fiber optics devices
or even re-transmitted into free space link.

The proposed device concept can be ported to other wavelength ranges that are
being explored for FSO communications, such as the mid infrared [4] and the
long wavelength infrared [5], provided that suitable photonic integrated
plaftorms enabling the realization of complex adaptive photonic integrated
circuits are available. Moreover, the all-optical analog processing performed
by our chip is expected to find applications also in quantum-communication FSO
links, for instance, in terrestrial and space-to-earth quantum-key
distribution systems [30]. Finally, future works will also target the use of
the POP-assisted OAA at the transmitter side of an FSO link to steer and
optimally shape the optical beam to compensate for both turbulence and beam
wander.

## Methods

Numerical simulation of turbulence-induced scintillation. The effects of
atmospheric turbulence on arbitrary propagating beams are numerically
evaluated by using a conventional split-step method [31] that considers
sections of free space propagation regions (where only beam divergence occurs)
alternated to phase screens (PSs). The PSs are generated using turbulence
models, such as Kolmogorov, Von Karman, or modified Von Karman [15], and the
required number of PSs depends on the turbulence regime and on the accumulated
scintillation along the path [32]. In this work, we considered a reference
link distance of 800 m and turbulence regimes characterized by a refractive
index parameter $C_{n}^{2}$ varying from $10^{-15}$ to
$10^{-13}[\text{m}^{-2/3}]$. In a weak turbulence regime, the scintillation
index equals about 0.1, and a single PS is sufficient. Instead, for the
strongest turbulence regime considered, up to three PS should be used to
guarantee the validity and accuracy of the split-step method.

Control electronics. The control strategy for the automated self-configuration
of the POP exploits local feedback loops to monitor and stabilize each MZI
individually [26]. To this end, dithering signals are applied to the thermo-
optic phase shifters, thereby identifying deviations from the optimal bias
point and maximizing the optical power detected at the PDs integrated at each
MZI’s output port[25]. The PDs have a sensitivity of -40 dBm, thus enabling
the control system to initiate automated configuration from arbitrary initial
conditions of the POP and for any field pattern of the optical beam impinging
on the OAA. Monitoring each MZI with a dedicated PD enables using a single
dithering frequency for many actuators, allowing a wider control bandwidth.
Alternatively, a single PD at the output port of the POP could be used, though
this requires more complex electronics to read different pairs or dithering
frequencies applied to the MZIs phase shifters [33]. The electrical bandwidth
of the electronic feedback controller (hosting 16 parallel lock-in chains to
manage the 30 thermal phase shifters of the POP) is 2 kHz and enables a
stabilization time of approximately 0.5 ms per MZI. The digital control
electronics operate at 12 bits, ensuring a control voltage accuracy of about 1
mV under worst conditions (5V), corresponding to a phase shift uncertainty of
approximately 1 mrad. In order to provide scalability to integrated POP-
assisted receivers with more apertures, control electronics can be integrated
into a multi-channel custom-designed CMOS application-specific integrated
circuit (ASIC) that can automatically stabilize and reconfigure the MZI
mesh.[34]

Experimental setup. With reference to Fig. 5a, a free-space Gaussian beam at a
wavelength of 1550 nm is transmitted by a fiber-coupled optical collimator
with a diameter of 3 mm. Controllable turbulence is intentionally introduced
in the free-space link by using a spatial light modulator (SLM), which
distorts the phase front of the beam by introducing a phase screen (PS) in the
propagation path of the beam. Synthetic PSs were numerically generated to
emulate a turbulence strength equivalent to several hundred meters of
propagation with $C_{n}^{2}$ in the range $10^{-13}$ to
$10^{-15}[\text{m}^{-2/3}]$ and then loaded in the SLM. A beam splitter was
used to deviate a portion of the optical power to a near-infrared (IR) camera
to capture the effects of the SLM on the beam. A 45°-tilted dielectric mirror
and a 2-inch biconcave lens were used to couple the incoming beam to the OPA.
For dynamic tests, the SLM was replaced by a heat gun, and a beam expander was
inserted at the transmitter side after the collimator. The beam expander
generates a beam with a diameter of around 5 cm, and the heat gun is used to
emulate the turbulence. By observing the beam scintillation of the IR camera,
we estimated an effective refractive index perturbation up to $C_{n}^{2}$ of
the order of $10^{-12}[\text{m}^{-2/3}]$. The spectral components of the
generated turbulence are shown in Supplementary Fig. S5. Due to the large size
of the beam compared to the short length of the link (4 m), wander effects on
the beam are negligible, and intensity fading is only due to scintillation.
System-level measurements were performed by intensity modulating the
transmitted beam at a data rate of 5 and 10 Gbit/s on-off keying (OOK) non-
return-to-zero (NRZ). The wavelength for the 5 Gbit/s experiment was 1545 nm,
whereas for the 10 Gbit/s was 1550 nm.

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## Acknowledgments

The research has been carried out in the framework of the Huawei-Politecnico
di Milano Joint Research Lab. Part of this work was carried out at Polifab
(https://www.polifab.polimi.it), Politecnico di Milano, Milan, Italy. The
Authors thank Photonpath srl (https://www.photon-path.com) for the chip-to-
fiber transposer assembly.

## Author contributions statement

A.I.M. and G.C. developed the FSO simulator and performed the numerical
analysis. S.S. designed the layout of the PIC. A.I.M. and S.S. designed and
set up the experiment. A.I.M. carried out the experiments. A.I.M., A.M., and
F.M. analyzed the results. F.Z. and M.S. supported the realization of the
electronic control system. A. D. provided the industrial vision. A.M. and F.M.
supervised the project. A.I.M., A.M., and F.M. wrote the manuscript. All the
authors contributed to the revision of the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

Correspondence and requests for materials should be addressed to A.M.

##  1 Supplementary Information

###  1.1 Single-aperture receiver

Figure S1 displays the results for a simulation considering a Gaussian beam at
the transmitter side with a beam waist $w_{0}=1$ mm that propagates for a
distance $L=800$ m. The single mode receiver is modeled as a Gaussian beam
with $w_{0}=d_{R}/2$. The total power coupled to the receiver $P_{rx}$ is
calculated based on the coupling coefficient $\eta$ as:

$\eta=\frac{|\int
E^{*}_{rx}E_{tx}\,dA|^{2}}{\int|E_{tx}|^{2}\,dA\int|E_{rx}|^{2}\,dA}$ (1)
$P_{rx}=10\log_{10}(\eta)[\text{dB}]$ (2)

where $E_{rx}$ and $E_{tx}$ are the complex electric fields of the receiver
and transmitted beam at the receiver plane. Panel (a) shows a simulation of
the relative mean received power as a function of $d_{R}$ for no turbulence
(purple), weak turbulence strength $C_{n}^{2}=10^{-15}[\text{m}^{-2/3}]$
(orange), moderate $C_{n}^{2}=10^{-14}[\text{m}^{-2/3}]$ (blue), and strong
$C_{n}^{2}=10^{-13}[\text{m}^{-2/3}]$ (yellow). The corresponding values of
$r_{0}$ are reported as reference.

Figure S1: Single aperture receiver simulation. a-c, Simulated mean received
power (a), standard deviation (b), one-sigma (c1), three-sigma (c2), and five-
sigma (c3) limit of a single aperture receiver with single mode detector as a
function of the aperture diameter $d_{R}$ for $C_{n}^{2}=10^{-13}$ (blue),
$10^{-14}$ (orange), $10^{-15}$ (yellow) $[\text{m}^{-2/3}]$, and without
turbulence (purple).

A beam with an initial waist $w_{0}=1$ mm and wavelength $\lambda=1550$ nm has
a Rayleigh length $z_{R}$:

$z_{R}=\frac{\pi w_{0}^{2}}{\lambda}=2.0268[\text{m}]$ (3)

then, at $L=800$ m, the transmitted beam has a radius $w(z)$:

$w(z=800)=w_{0}\sqrt{1+(\frac{z}{z_{R}})^{2}}=39.5[\text{cm}].$ (4)

Therefore, a receiver with $d_{R}=2w(z=800)=79$ cm will couple all the
incoming power ($P_{rx}=0$ dB) in the absence of turbulence, as seen in the
purple line. Figure S1b shows the corresponding standard deviation of
$P_{rx}$, i.e., the fading. As a general rule, the stronger the turbulence,
the lower the mean received power and the higher the fading. In an FSO
communication system, it is important to guarantee a low probability that the
received power decreases below a given sensitivity threshold, say -18 dB, as
an example. Figures S1c show the (c1) one-sigma, (c2) three-sigma, and (c3)
five-sigma limit.

###  1.2 Multi-aperture

In section 3, we fixed $d_{R}=4.5$ cm as a good compromise between a high
$P_{rx}$ and low standard deviation $\sigma_{rx}$ for $C_{n}^{2}\geq
10^{-13}$. The motivations behind this decision are displayed in Fig. S2. In
these graphs, we plot the (a1-3) mean received power and (b1-3) standard
deviation as a function of the separation distance $d_{S}$ for an aperture
size $d_{R}=2$ (blue), 4.5 (orange), and 18 (yellow) cm; a number of antennas
$M=1$ (dashed line), 2 (circles), 5 (diamonds), and 16 (squares); and a
turbulence parameter $C_{n}^{2}=10^{-15}$ (column 1), $10^{-14}$ (column 2),
and $10^{-13}$ (column 3) $[\text{m}^{-2/3}]$. As can be seen, the largest
aperture couples more power for medium scintillation but underperforms for
strong scintillation. In fact, the OAA with $M=16$ and $d_{R}=4.5$ cm is the
one that couples more power for $C_{n}^{2}=10^{-13}$ $[\text{m}^{-2/3}]$.
Also, as in the case of a single aperture, the $\sigma_{rx}$ increases as the
aperture size does; therefore, a large antenna is not recommended. When
comparing $d_{R}=2$ and $d_{R}=4.5$ cm, the latest is the best choice given
the higher $P_{rx}$ and equal or lower $\sigma_{rx}$.

Figure S2: Multi-aperture receiver simulation for different aperture sizes.
Each column corresponds to one of the considered turbulences:
$C_{n}^{2}=10^{-15}$, $10^{-14}$, and $10^{-13}$ $[\text{m}^{-2/3}]$. a-b,
Mean received power (a) and standard deviation (b) as a function of the
separation distance $d_{S}$ for an aperture size $d_{R}=2$ (blue), 4.5
(orange), and 18 (yellow) cm. The number of antennas is $M=1$ (dashed line), 2
(circles), 5 (diamonds), and 16 (squares). $P_{R}$ is calculated by summing
coherently the contributions of the $M$ apertures.

Figure S3 shows the same results as Fig. 3, that is, (a) mean received power,
(b) standard deviation, and (c) three-sigma but not as a function of the
number of antennas, but the separation distance $d_{S}$. The larger the
separation, the antennas move away from the centroid of the beam, and the
lower the power coupled to the receiver. The $\sigma_{rx}$ is almost constant
for all $d_{s}$, except when it is too large, which starts to increase.

Figure S3: Multi-aperture receiver simulation for different aperture
separations. a-b, Mean received power (a), standard deviation (b), and three-
sigma (c) as a function of the separation distance $d_{S}$ for a number $M=1$
(dashed line), 2 (circles), 5 (diamonds), and 16 (squares) of apertures and
the three considered turbulences $C_{n}^{2}=10^{-13}$ (yellow), $10^{-14}$
(orange), and $10^{-15}$ (blue) $[\text{m}^{-2/3}]$. $d_{R}=4.5$ cm. $P_{R}$
is calculated by summing coherently the contributions of the $M$ apertures.

##  2 Supplementary Figures

Figure S4: Phase screens used to emulate the turbulence with the SLM. See Fig.
5d. The red spot in the first PS, illustrates the size of the beam. Figure S5:
Emulated turbulence spectrum. FFT of the time trace acquired with a 3 mm
collimator for 3 distances of the thermal gun from the transmitter $d_{tx}=1$,
2, and 3 m. The closer the gun is to the transmitter, the stronger the
turbulence.