# All-Optical and Microwave-Free Detection of Meissner Screening using
Nitrogen-Vacancy Centers in Diamond

D. Paone  Max Planck Institute for Solid State Research  3rd Institute of
Physics and Institute for Integrated Quantum Science and Technology IQST,
University Stuttgart  D. Pinto  Max Planck Institute for Solid State Research
Institut de Physique, École Polytechnique Fédérale de Lausanne  G. Kim  Max
Planck Institute for Solid State Research  L. Feng  Max Planck Institute for
Solid State Research  4th Institute of Physics and Research Center SCoPE,
University Stuttgart  M-J. Kim  Max Planck Institute for Solid State Research
4th Institute of Physics and Research Center SCoPE, University Stuttgart  R.
Stöhr  3rd Institute of Physics and Institute for Integrated Quantum Science
and Technology IQST, University Stuttgart  A. Singha  Max Planck Institute for
Solid State Research  S. Kaiser  Max Planck Institute for Solid State Research
4th Institute of Physics and Research Center SCoPE, University Stuttgart  G.
Logvenov  Max Planck Institute for Solid State Research  B. Keimer  Max Planck
Institute for Solid State Research  J. Wrachtrup  Max Planck Institute for
Solid State Research  3rd Institute of Physics and Institute for Integrated
Quantum Science and Technology IQST, University Stuttgart  K. Kern  Max Planck
Institute for Solid State Research  Institut de Physique, École Polytechnique
Fédérale de Lausanne

###### Abstract

Microscopic studies on thin film superconductors play an important role for
probing non-equilibrium phase transitions and revealing dynamics at the
nanoscale. However, magnetic sensors with nanometer scale spatial and
picosecond temporal resolution are essential for exploring these. Here, we
present an all-optical, microwave-free method, that utilizes the negatively
charged nitrogen-vacancy (NV) center in diamond as a non-invasive quantum
sensor and enables the spatial detection of the Meissner state in a
superconducting thin film. We place an NV implanted diamond membrane on a
$20\,\mathrm{nm}$ thick superconducting La2-xSrxCuO4 (LSCO) thin film with
$T_{c}$ of $34\,\mathrm{K}$. The strong B-field dependence of the NV
photoluminescence (PL) allows us to investigate the Meissner screening in LSCO
under an externally applied magnetic field of $4.2\,\mathrm{mT}$ in a non-
resonant manner. The magnetic field profile along the LSCO thin film can be
reproduced using Brandt’s analytical model, revealing a critical current
density $j_{c}$ of $1.4\cdot 10^{8}\,\mathrm{A/cm^{2}}$. Our work can be
potentially extended further with a combination of optical pump probe
spectroscopy, for the local detection of time-resolved dynamical phenomena in
nanomagnetic materials.

††preprint: AIP/123-QED

##  I Introduction

Microscopic phenomena revealing complex magnetic phases in two-dimensional
materials are catching the central attention in modern condensed-matter
physics Bandy . Prime examples are superconducting systems which are
accompanied by electronic phases Wu ; Bednorz ; Hazen , such as vortex
formation in the case of type II superconductors Essmann . Various approaches
are already established for studying superconductivity mainly based on
superconducting quantum interference devices (SQUIDs) Ceccarelli , magnetic
force microscopy (MFM) Hug , scanning tunneling microscopy (STM) Kot  and the
investigation of magneto-optical effects Goa . However, each of these
techniques suffer from drawbacks such as limited temperature and magnetic
field ranges, spatial resolution and complex sample preparation. A promising
alternative for surpassing these drawbacks is to employ negatively charged
nitrogen vacancy (NV) centers in diamond. In fact, the NV center in diamond is
a non-invasive nanoscale magnetic field sensor allowing measurements at both,
cryogenic as well as ambient conditions, with a magnetic field sensitivity of
$1\,\mathrm{pT/\sqrt{Hz}}$ for NV ensembles and $1\,\mathrm{\mu T/\sqrt{Hz}}$
in the case of single NV centers Degen . Applications of NV center sensing
have been shown in single molecular systems, investigated using nuclear
magnetic resonance (NMR) Staudacher  and electron spin resonance (ESR) Schlipf
; Pinto . In addition, magnetic properties of materials have been investigated
including spin waves Du , ferromagnetism Page ; Ferror  and superconductivity
Waxman ; Thiel ; Pelliccione ; Nusran ; Joshi ; Xu ; Rohner ; Sydney ;
SCreview  at the nanoscale with this approach. The fundamental sensing
principle of the NV center relies on the spin dependent photoluminescence (PL)
of the defect center Wrachtrup ; Donghun . Microwave excitations allow
coherent manipulation within different spin sublevels present in the ground
state. The resulting transition frequencies show a Zeeman effect, forming a
toolset for magnetic field sensing, known as optically detected magnetic
resonance (ODMR) technique. However, microwave excitations are usually linked
with heating effects, which could locally change properties of the
investigated sample Sydney .
Here, we introduce the magnetic field dependent fluorescence yield of an NV
center ensemble which allows a reliable and direct investigation of the
spatial modulation of superconductivity on a microscopic scale. Besides
calibrating the change in the NV emission intensity caused by an external
magnetic field with ODMR spectroscopy, our experiments rely solely on an all-
optical, non-resonant, microwave-free measurement scheme. We position an NV
implanted diamond membrane at the edge of a superconducting La2-xSrxCuO4
(LSCO) thin film. We collect the NV center fluorescence at different positions
on the superconductor at $4.2\,\mathrm{K}$ and under an external magnetic
field of $4.2\,\mathrm{mT}$ aligned along the $z$-direction. Normalization to
zero-field measurements provides us a fingerprint of the Meissner screening in
terms of the PL rate drop when the NV ensembles are in close proximity
($\approx 1\,\mathrm{\mu m}$) to the LSCO thin film. Combining this with an
analytical model, developed by E. H. Brandt Brandt , allows us to extract the
critical current density $j_{c}$. Furthermore, we provide a comparison of our
results with a complementary SQUID measurement.

Figure 1: (a) Sketch of the experimental setup. A confocal microscopy setup is
attached to a UHV-cryostat at $4.2\,\mathrm{K}$ and equipped with a 3D vector
magnet for applying external magnetic fields. The microwave circuit is only
used for resonant calibration purpose and is shown in light grey. The inset
depicts the sample geometry consisting of an NV diamond membrane attached onto
a superconducting LSCO thin film. Dimensions are not drawn to scale. (b)
Energy level scheme of the negatively charged NV center. The ground-state spin
levels can be pumped via a green laser to the excited state. The relaxation to
the ground-state leads to an emission of red photons, which are measured using
a confocal microscope. The NV center spin state can be driven between the
$m_{s}=|0\rangle$ and the $m_{s}=|-1\rangle$, $m_{s}=|+1\rangle$ states using
microwave excitations. The magnetic field experienced by the NVs can be
calculated using the Zeeman equation. (c) ODMR spectra of an NV ensemble in
the bare diamond membrane for different magnetic fields aligned in
z-direction, acquired at $4.2\,\mathrm{K}$ inside the UHV cryostat. The
spectra are vertically offset for clarity. (d) Effect of increasing the
external magnetic field on the observed NV fluorescence. The count rate drop
is collected for different magnetic fields aligned in z-direction, estimated
from the corresponding ODMR measurements. The red solid line indicates a
smoothing spline interpolation. The measurement has been performed at ambient
conditions in a separate confocal setup with a permanent magnet attached
closely to the diamond membrane.

##  II Experimental Setup and Methods

All measurements are carried out using a confocal microscope connected to an
UHV-He bath cryostat operating at a base pressure of $3\cdot
10^{-10}\,\mathrm{mbar}$ at $4.2\,\mathrm{K}$ (Fig. 1(a)) Nolte . A green
$512\,\mathrm{nm}$ pulsed laser is used to excite the NV centers. The emitted
fluorescence is recorded with a photon detector device. The laser spot is
scanned over the sample, while recording the NV fluorescence, resulting in a
confocal image. Further details of this experimental setup and of an
additional setup used for NV characterization at ambient conditions can be
found in section 1 of the Supporting Information (SI). The pulsed microwave
source integrated with the setup allows us to perform magnetometry with NV
centers and ODMR measurements which require NV spin manipulations.
Magnetometry with NV centers relies on the energy-level scheme shown in Fig.
1(b). The ground electronic state of the NV center is a spin triplet. The
energy gap between the excited triplet state and the ground state corresponds
to a photon emission of $637\,\mathrm{nm}$. The NV center can be excited from
the ground state into the phonon side band using $\approx 512\,\mathrm{nm}$
green laser light. Subsequently, it relaxes to the ground state by emitting
photons in the range of 637-$750\,\mathrm{nm}$. The fluorescence is highly
spin state selective Wrachtrup . In particular, the fluorescence rate of the
$m_{s}=|-1\rangle,|+1\rangle$ states is lower than that of the
$m_{s}=|0\rangle$. In presence of an externally applied magnetic field, the
$|\pm 1\rangle$ states experience a Zeeman splitting. Subsequently, a resonant
microwave excitation enables the transition between the bright
$m_{s}=|0\rangle$ state and one of the less fluorescent dark $|\pm 1\rangle$
states, whenever the microwave frequency matches the induced energy splitting.
Therefore, in absence of an external magnetic field, the NV fluorescence shows
only a single resonance signifying the zero field splitting of
$D=2.87\,\mathrm{GHz}$. For a non zero magnetic field, this splits into two
resonances corresponding to the $|0\rangle\rightarrow|-1\rangle$ and
$|0\rangle\rightarrow|+1\rangle$ transitions. The unique combination of these
properties of the NV center, allows us to calibrate the magnetic field, by
observing field dependent ODMR spectra, as shown in Fig. 1(c). For all
measurements, the magnetic field is applied along the z direction
($\vec{B}=(0,0,B_{z})$), normal to the (100) surface. Therefore, all four
possible NV orientations experience the same Zeeman splitting $\Delta f$
Nusran  given by $\Delta f=\frac{2\gamma B_{z}}{\sqrt{3}}$. $\gamma$ is the
gyromagnetic ratio, which is $28\,\mathrm{MHz/mT}$ for the NV electronic spin.
The observed frequency splitting is proportional to the applied magnetic field
following this equation. However, this method requires the application of a
resonant microwave driving frequency. Microwave applications are often
accompanied by local heating effects, which could cause undesired changes in
the properties of the investigated system, especially in case of a
superconducting sample.
This can be circumvented by utilizing a non-resonant measurement scheme
without microwave excitations. The fluorescence yield detected from the NV
center strongly depends on the applied off-axis magnetic field. In particular,
it decreases with increasing the $B_{z}$-field. This can be explained by the
spin mixing of the sublevels when the magnetic field is misaligned with
respect to the NV axis. The mixing of the spin sublevels leads to an
inefficient spin-dependent PL rate by enhancing the probablity of the non-
radiative inter system crossing to the metastable state. The resulting PL drop
can be used for a qualitative investigation of the magnetic fields Tetienne .
Fig. 1(d) shows this behavior of the NV emission for different magnetic fields
$B_{z}$ at ambient conditions. A significant decrease of the detected PL up to
$25\,\mathrm{\%}$ is observed for the highest applied magnetic field of
$22.5\,\mathrm{mT}$ along the $z$-direction. This approach still relies on
ODMR spectra for the quantitative calibration of the magnetic fields on the NV
axis. However, besides this the direct all-optical record of the NV emission
relies on a non-resonant, microwave-free method. Measurements of field
variations and qualitative observations of magnetic properties, which are
often required for supercondcting systems, are still viable using the direct
emission of the NV centers. Therefore, the magnetic field dependent PL can be
a sensitive tool for detecting non-equilibrium phase transitions and dynamical
phenomena with a high spatial resolution.

Figure 2: (a) Real part of the mutual inductance versus the temperature. The
mutual inductance is measured as the magnetic interaction between two coils.
Within these, the LSCO sample is positioned and the temperature is swept from
$300\,\mathrm{K}$ to $5\,\mathrm{K}$. The inset shows a significant drop of
the inductance at $34\,\mathrm{K}$ indicating a critical temperature of
$T_{c}=34\,\mathrm{K}$. (b) Hysteresis curve measured with a superconducting
quantum interference device (SQUID) at $4\,\mathrm{K}$. The magnetic moment is
investigated as a function of the applied magnetic field ranging from
$-7\,\mathrm{T}$ to $7\,\mathrm{T}$. The inset shows the behavior of the
magnetic moment for weak magnetic fields between 0 and $5\,\mathrm{mT}$. The
inflection point of the curve indicates the first critical field $H_{c1}$,
being at around $2\,\mathrm{mT}$.

##  III Results and Discussion

###  III.1 Investigated LSCO Sample

In order to demonstrate this, we characterized the Meissner screening caused
by a type II cuprate superconducting LSCO sample. LSCO is among the most
studied high $T_{c}$ superconductors in recent years Logvenov ; Gilardi .
Furthermore, it has attracted much interest since Cooper pair formation,
diamagnetism Li  and vortex mechanisms Iguchi  have been measured above
$T_{c}$. Therefore, LSCO is not only an ideal sample to benchmark our
technique with existing quantities and models, but also forms a system with
interesting superconducting properties which could be investigated with our
method in future experiments. The studied sample consists of a single
crystalline LSCO thin film epitaxially grown on a (001) LaSrAlO4 (LSAO)
substrate Gideok  and exhibits a critical temperature of
$T_{c}=34\,\mathrm{K}$ which is depicted in the mutual inductance measurement
shown in Fig 2(a). The mutual inductance has been measured by placing the LSCO
sample within two pick-up coils (see section 7 of the SI). By applying a weak
magnetic field through one of the coils, the magnetic interaction through the
superconducting sample can be investigated. We also recorded the magnetic
moment $m$ as a function of the magnetic field at 4 K for gaining more
information about the magnetic phase diagram including the lower critical
field $H_{c1}$ (see Fig. 2(b)). This indicates a first magnetic penetration at
about $2\,\mathrm{mT}$, where magnetic fluxes start to enter the
superconducting sample.

Figure 3: (a) Schematic and scanning electron microscope image (SEM) of the
investigated system showing an NV implanted diamond membrane glued at the edge
of a thin film superondcuting LSCO. Due to the Meissner effect, an applied
magnetic field gets expelled by the LSCO thin film. An enhancement of the
magnetic flux density occurs at the edges of the superconducting sample. The
dimensions are not drawn to scale. (b) Normalized confocal images indicating
the NV fluorescence behavior inside ($y<a$) and outside ($y>a$) of the
superconductor at $4.2\,\mathrm{K}$. The normalized fluorescence count rate
drop is determined by averaging the PL counts from the central $2\,\mathrm{\mu
m}$ x $2\,\mathrm{\mu m}$ area, highlighted as white box. We observe almost a
two-fold decrease in the PL drop inside the sample, indicating the Meissner
screening of the LSCO thin film. All data are normalized with respect to
images measured at $B=0$. The confocal scans are obtained with a resolution of
$100$ x $100$ pixels, where each pixel has been recorded for
$0.01\,\mathrm{s}$. (c) Effect of Meissner screening verified by using ODMR
spectra for $y>a$ and $y<a$ at $4.2\,\mathrm{K}$. For $y>a$ (blue curve), the
ODMR splitting is about 2 times larger compared to the case of $y<a$ (red
curve).

###  III.2 Detection of Meissner State with the NV Center PL Drop

To study the spatial distribution of the Meissner screening caused by the LSCO
thin film at $4.2\,\mathrm{K}$, we positioned our diamond membrane across the
edge of the LSCO sample (see Fig. 3(a)). This particular geometry allows us to
characterize the effect of an external magnetic field on the LSCO thin film
$(y<a)$, as well as background measurement without having LSCO on top $(y>a)$.
Note that all PL measurements are normalized with respect to a corresponding
zero field confocal scan for estimating the effective fluorescence rate drop.
Fig. 3(b) shows a confocal scan of the NV ensemble obtained from regions $y<a$
(left panel) and $y>a$ (right panel) respectively, for an applied field of
$4.2\,\mathrm{mT}$. It is evident that the zero-field normalized confocal scan
obtained from $y>a$ is significantly brighter compared to the case of $y<a$.
We choose the central area (depicted as white square) of the confocal images
for evaluation, since the center of the image shows the least distortion (see
section 2 of the SI). For $y<a$, the normalization with respect to a zero
field measurement reveals an average fluorescence drop of $2.5\,\mathrm{\%}$
in the central area. In contrast, for $y>a$ the fluorescence count rate drop
amounts to $5.4\,\mathrm{\%}$. The $2.9\,\mathrm{\%}$ increase in the
fluorescence count rate drop can be explained by the presence of the LSCO thin
film. The superconducting phase in the LSCO thin film causes a Meissner
expulsion Takeda  leading to varying magnetic fields experienced over the
whole diamond membrane. NV centers in the area of $y<a$ experience a reduced
magnetic field strength and therefore show a significantly decreased PL drop
compared to the $y>a$ region. For $y>a$, which is outside the superconductor,
no Meissner screening is present. Therefore, the NV center ensemble measures
the unscreened applied field of $4.2\,\mathrm{mT}$ resulting in a higher
fluorescence drop. Note that, the confocal scans have been obtained by a fixed
laser power of $0.688\,\mathrm{\mu W}$, measured in front of the UHV chamber
glass with a powermeter. With such low laserpower we can ensure, that the
laser spot is not changing the superconducting properties of our sample Sydney
.
In order to quantify the strength of the magnetic field that penetrates
through the LSCO thin film, we first verify the Meissner effect using a
resonant process, i.e. ODMR spectroscopy. We obtained ODMR spectra on the NV
ensembles for both regions, $y<a$ and $y>a$. The corresponding spectra are
depicted in Fig. 3(c). The red curve on the left panel shows the resonance
peaks of the NV ensemble inside the LSCO thin film with a frequency splitting
of $\Delta f=60\,\mathrm{MHz}$. This corresponds to a $z$-aligned magnetic
field of $\approx 1.8\,\mathrm{mT}$. In contrast, the blue curve (Fig. 3(c),
right panel), which represents the ODMR spectrum of the NV ensemble for $y>a$,
exhibits a splitting $\Delta f$ of $\approx 140\,\mathrm{MHz}$ corresponding
to a magnetic field strength of $\approx 4.2\,\mathrm{mT}$ along the
$z$-direction. This is in an excellent agreement with the fact, that the NV
ensemble in $y>a$ does not experience any Meissner screening. Therefore, the
magnetic field strength calculated from the ODMR spectrum matches the applied,
unscreened magnetic field value. Consequently, these results corroborate a
magnetic field screening of $\approx 56\,\mathrm{\%}$. Note that, the magnetic
field in the region of $y<a$ is not vanishing. This can be attributed to the
relatively large NV to superconductor distance ($\approx 1\,\mathrm{\mu m}$)
(see section 6 of the SI). Also the formation of magnetic vortices in type II
superconductors could result in a non vanishing magnetic field in the LSCO
sample Gilardi .

Figure 4: (a) Spatial variation in the PL drop measured by laser raster scan
at $4.2\,\mathrm{K}$ with (blue dots) and without (red dots) superconducting
sample (left panel). At each position, the PL drop of the NV ensemble is
recorded. Estimates of the magnetic fields (right panel) come from a
calibration with ODMR spectra. In presence of the LSCO thin film, for $y>a$,
the external magnetic field asymptotically reaches $4.2\,\mathrm{mT}$, while
for $y<a$ it is strongly screened due to the superconducting properties of
LSCO. The sharp increase of the magnetic field at the edge indicates high
magnetic flux densities. Such a spatial dependence is not observed in absence
of the LSCO thin film. Each data point corresponds to the normalized averaged
PL drop at the center of the confocal scan of about $4\,\mathrm{\mu m^{2}}$.
(b) Fitting of the experimental data by using Brandt’s model. The solid lines
represent the fit. Both fit functions (inside and outside) reveal a critical
current density $j_{c}$ of $1.4\cdot 10^{8}\,\mathrm{A/cm^{2}}$.

This approach can be extended further to gain insights about the Meissner
screening and for characterizing the LSCO thin film to a greater detail. This
is achieved by raster sweeping the laser focal spot over the diamond membrane
along the $y$ direction. The corresponding spatial variation of the PL drop
under an applied magnetic field of $B_{z}=4.2\,\mathrm{mT}$ is shown in Fig.
4(a) (left panel). Again, each confocal scan and corresponding fluorescence
rate is normalized to a zero field measurement for evaluating the relative
fluorescence drop. Two distinct regimes characterized by different degrees of
PL drops, are observed for $y<a$ and $y>a$ respectively. Inside the
superconductor, we measure a relatively homogeneous PL drop of about
$2\,\mathrm{\%}$, which slowly increases towards the boundary, i.e. $y=a$.
Note that, the conversion from PL drop to an effective magnetic field is
achieved using the calibration data presented in Fig. 1(d). The latter reveals
a magnetic field strength ranging between $1.8\,\mathrm{mT}$ and
$2.1\,\mathrm{mT}$, as plotted on the right panel of Fig. 4(a). In contrast,
an increased PL drop of $\approx 5.1\,\mathrm{\%}$ is observed at locations
which are far away from the LSCO thin film. This corresponds to a magnetic
field strength of $\approx 4\,\mathrm{mT}$ which is in good agreement with the
applied magnetic field. In addition, we have also observed a significant and
sharp increase in the PL drop at the boundary, i.e., $y=a$, implying an
equivalent increase of the effective magnetic flux density, which penetrates
through the LSCO thin film. While the majority of the LSCO thin film expels
the magnetic field, near the boundaries the field is enhanced to almost
$16\,\mathrm{mT}$. The magnetic field flux is screened to the edge of the LSCO
sample due to the diamagnetic properties of the superconducting compound. This
leads to an enhanced magnetic flux density at the boundary of the
superconducting LSCO sample. Note that, in absence of the LSCO sample, such a
spatial dependence of the PL drop is not observed in the bare NV membrane (red
dots in Fig. 4(a)).

###  III.3 Application of Brandt’s Model

The magnetic field profile in a superconducting thin film can be analytically
evaluated by Brandt’s modelBrandt . The spatial dependence along the
$y$-direction, of the magnetic field applied perpendicular to the
superconducting thin film is:

$\displaystyle
H(y)=\begin{cases}\frac{J_{c}}{\pi}\operatorname{arctanh}\frac{\sqrt{\left(y^{2}-b^{2}\right)}}{c|y|}&y<a\\\
\\\
\frac{J_{c}}{\pi}\operatorname{arctanh}\frac{c|y|}{\sqrt{\left(y^{2}-b^{2}\right)}}&y>a\end{cases}$
(1)

$J_{c}$ stands for the critical sheet current in units of $\mathrm{A/m}$ and
the parameters $b$ and $c$ can be represented as

$\displaystyle b$ $\displaystyle=a/\cosh{\frac{\pi H_{a}}{J_{c}}}$
$\displaystyle c$ $\displaystyle=\tanh{\frac{\pi H_{a}}{J_{c}}},$

where $a$ corresponds to the halfed sample length. The parameter $b$ can be
interpreted as a lateral penetration depth of the externally applied magnetic
field $H_{a}$, indicating how far $H_{a}$ penetrates from the sides into the
sample. We fit our experimental data using this model in order to quantify the
critical current density $j_{c}=J_{c}/d$, in which the flux lines start to
move under the action of Lorentz force. Note that, similar to the observation
in Fig. 3, the magnetic field is not vanishing inside the superconductor.
Therefore, we restrict our fit within the limit where the magnetic field is
reduced to $18\%$ of the maximum observed field. This model agrees very well
with our data for both $y<a$ (Fig. 4(b), left panel) and for $y>a$ (Fig. 4(b),
right panel). The corresponding fitting paramaters for fixed values of
$H_{a}=4.2\,\mathrm{mT}$ and $a=5000\,\mathrm{\mu m}$ are, $b=4709\pm
2.2\,\mathrm{\mu m}$, $c=0.335\pm 0.0059$ and $J_{c}=27997\pm
2249\,\mathrm{A/m}$. Knowing $J_{c}$ and the sample thickness
$d=20\,\mathrm{nm}$ we have extracted the critical current density as
$j_{c}=1.4\cdot 10^{8}\,\mathrm{A/cm^{2}}$. This value is in very good
agreement with recently reported values for LSCO nanowires Lit  indicating the
NV fluorescence drop as reliable quantity for characterizing thin film
superconductors. Also note, that the corresponding $j_{c}$ value agrees very
well with a calculation based on our SQUID measurement in Fig. 2. The magnetic
moment $m$ can be obtained using Brandt’s analytical model and the
corresponding $J_{c}$ with Brandt

$\displaystyle m=J_{c}a^{3}\tanh{\frac{\pi H_{a}}{J_{c}}}.$ (2)

resulting into a magnetic moment of $m\approx 0.012\,\mathrm{emu}$. This is
comparable with our SQUID measurement in Fig. 2(b), in which the magnetic
moment ranges from $0.0075\,\mathrm{emu}$ to $0.0052\,\mathrm{emu}$. The
slight mismatch in $m$ can be explained by the performed calibration
measurement. The PL drop to magnetic field strength conversion in Fig. 1(d)
assumes a magnetic field applied in z-direction ($B_{z}$). This is a fair
assumption for the region $y<a$ and $y>a$ (far inside and outside of the
superconductor). However, in close proximity of the LSCO edge ($y=a$) the
magnetic field is forced to curl around the edge of the superconductor.
Therefore, it is expected, that the off-axis component of the magnetic field
is not pointing only in the z-direction. Instead, a strong in-plane component
has to be assumed. This fact can explain the overestimation of $j_{c}$.

##  IV Conclusion

In conclusion, we have presented a microwave-free NV center based method for
characterizing relative magnetic field changes. In order to demonstrate this,
we investigated a superconducting LSCO thin film. So far, the NV center has
mainly been used as magnetic field sensor in a resonant measurement scheme
utilizing microwave excitations. Here we extend its application by employing
the magnetic field dependent PL of an NV center ensemble in a microwave-free
manner providing a direct manifestation of the Meissner screening in our LSCO
sample. To the best of our knowledge, this is the first demonstration of NV
center magnetometry on a superconducting sample that does not require resonant
microwave pulse schemes, apart from calibrating the absolute magnetic field.
The PL calibration can either over-or underestimate the magnetic field
strength to a certain extent. However, this is not important for measurements
relying on relative strength changes of the magnetic field such as in the case
of the Meissner state in superconductors. The presented method enables a fast
and precise measurement of such relative magnetic changes excluding heating
effects on the sample. Furthermore, the magnetic field dependent NV emission
used in this work can be extended further by combining optical pump probe
spectroscopy, thereby enabling access to dynamical systems with fast
timescales. With the NV center as nanoscale magnetic field sensor, this opens
up a promising avenue for exploring a multitude of problems in condensed-
matter physics such as non-equilibrium collective phenomena including the
vortex formation and motion in type II superconductors.

## Acknowledgments

We acknowledge financial support for this work provided by the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No. 742610), EU via project ASTERIQS,
Max Planck Society and DFG via FOR 2724.

## Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## References

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# Pilot-Based Key Distribution and Encryption for Secure Coherent Passive
Optical Networks

Haide Wang, Ji Zhou, Qingxin Lu, Jianrui Zeng, Yongqing Liao, Weiping Liu,
Changyuan Yu, and Zhaohui Li Manuscript received; revised. This work was
supported in part by the National Natural Science Foundation of China under
Grant 62371207 and Grant 62005102 and in part by the Hong Kong Scholars
Program under Grant XJ2021018. (Corresponding author: Ji Zhou.)Haide Wang, Ji
Zhou, Qingxin Lu, Jianrui Zeng, and Weiping Liu are with the Department of
Electronic Engineering, College of Information Science and Technology, Jinan
University, Guangzhou 510632, China (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>wpl@jnu.edu.cn).Yongqing Liao is with the China Mobile Internet Co., Ltd,
Guangzhou 510640, China (email: 13802885078@139.com).Changyuan Yu is with the
Department of Electronic and Information Engineering, The Hong Kong
Polytechnic University, Hong Kong (email: changyuan.yu@polyu.edu.hk).Zhaohui
Li is with the Guangdong Provincial Key Laboratory of Optoelectronic
Information Processing Chips and Systems, Sun Yat-sen University, Guangzhou
510275, China, and also with the Southern Marine Science and Engineering
Guangdong Laboratory (Zhuhai), Zhuhai 519000, China (e-mail:
lzhh88@mail.sysu.edu.cn).

###### Abstract

The security issues of passive optical networks (PONs) have always been a
concern due to broadcast transmission. Physical-layer security enhancement for
the coherent PON should be as significant as improving transmission
performance. In this paper, we propose the advanced encryption standard (AES)
algorithm and geometric constellation shaping four-level pulse amplitude
modulation (GCS-PAM4) pilot-based key distribution for secure coherent PON.
The first bit of the GCS-PAM4 pilot is used for the hardware-efficient carrier
phase recovery (CPR), while the second bit is utilized for key distribution
without occupying the additional overhead. The key bits are encoded by the
polar code to ensure error-free distribution. Frequent key updates are
permitted for every codeword to improve the security of coherent PON. The
experimental results of the 200-Gbps secure coherent PON using digital
subcarrier multiplexing with 16-ary quadrature amplitude modulation show that
the GCS-PAM4 pilot-based key distribution could be error-free at upstream
transmission without occupying the additional overhead and the eavesdropping
would be prevented by AES algorithm at downstream transmission. Moreover,
there is almost no performance penalty on the CPR using the GCS-PAM4 pilot
compared to the binary phase shift keying pilot.

###### Index Terms:

Coherent passive optical networks, physical-layer security, advanced
encryption standard, pilot-based key distribution, geometric constellation
shaping.

##  I Introduction

Recently, since the standards of 50G passive optical networks (PONs) have been
finalized by the International Telecommunication Union, the research on the
100G and beyond PONs has been a hot topic [1, 2, 3]. Among the solutions,
coherent optical technologies with digital subcarrier multiplexing (DSCM) for
the beyond 100G PON show competitiveness [4, 5, 6]. Coherent PON using DSCM
can combine the time-division multiple access (TDMA) with frequency-division
multiple access (FDMA) to provide more end users with higher data rates by the
time- and frequency division multiple access (TFDMA). Since physical-layer
security issues have always been a concern for the existing PONs at broadcast
downstream (DS) transmission, the future coherent PON with higher data rates
and more end users will face more severe security issues, especially
eavesdropping [7]. Thus, adequate attention should be paid to the physical-
layer security enhancement as the transmission performance for coherent PON.

Encryption of cryptography for digital data is the most commonly used means
that enhance physical-layer security to combat eavesdropping. Advanced
encryption standard (AES) algorithm has been adopted in the standards of the
10G symmetrical PON (XGS-PON) and the 50G-PON [8, 9]. The data encryption
standard and deoxyribonucleic acid algorithms were also demonstrated for
physical-layer security enhancement [10, 11, 12]. Various physical-layer
encryption schemes based on digital chaos have also been investigated [13, 14,
15]. However, these new encryption schemes rely on static and pre-shared keys
while the key distribution is not solved. Besides encryption, optical
steganography based on optical chaos is also used to enhance the physical-
layer security of optical communication systems [16]. However, high-speed
optical chaos communication faces the challenges of chaos synchronization
relying on transceivers with complicated structures, which would be cost-
prohibitive for PONs.

Quantum computers pose great challenges to the security enhancement based on
classical cryptography, while post-quantum cryptography has made progress in
identifying mathematical operations that quantum algorithms cannot
significantly speed up [17, 18]. However, post-quantum cryptography faces the
challenge of realizing cryptographic usability and flexibility, while
maintaining a high level of confidence [19]. Frequent key updates are another
way to enhance the security of PON. Even if a key is compromised, the impact
is limited to a short period by frequent key updates. Combined with post-
quantum cryptography authentication, quantum key distribution can offer
extreme security and show promise for future potential [20, 21]. However,
quantum key distribution with a relatively low rate is not yet suitable for
cost-sensitive PONs with large-scale deployment [22].

In the previous generation of PONs, keys of the AES algorithm were generated
by optical network units (ONUs) and distributed to the optical line terminal
(OLT) at the unicast upstream (US) transmission. However, there is at most one
frame sublayer header for the key distribution every 125-$\mu$s burst frame.
Moreover, the payload and the control messages share the same forward error
correction (FEC) codeword, which leads to a decline in the net rate and
frequent key updates are not permitted. Therefore, a low-overhead key
distribution scheme is required for more frequent key updates to enhance the
security of PON. The redundancy of overhead, such as phase and synchronization
header was used for key distribution in orthogonal frequency division
multiplexing-PON [23, 24, 25]. However, FEC coding schemes for error-free
redundancy-based key distribution have not been further studied yet. In this
paper, we propose the AES algorithm and the geometric constellation shaping
four-level pulse amplitude modulation (GCS-PAM4) pilot-based key distribution
for the secure coherent PON using DSCM. The main contributions of this paper
are as follows:

  * •

The GCS-PAM4 pilot is designed for both carrier phase recovery (CPR) and key
distribution of the AES algorithm without additional overhead and the penalty
on CPR.

  * •

Key for the AES algorithm is encoded by a polar code and carried by the GCS-
PAM4 pilot, which enables error-free and frequent key updates for every
codeword.

The rest of the paper is organized as follows. In Section II, the principle of
the secure coherent PON is presented. The experimental setups of the secure
coherent PON using DSCM are demonstrated in Section III. The experimental
results and discussions are given in Section IV. Finally, the paper is
concluded in Section V.

Figure 1: (a) Structure of the data frame with periodically inserted pilot for
CPR and key distribution. (b) Diagram of hardware-efficient CPR and key
distribution algorithm. (c) The constellation of the GCS-PAM4 pilot with an
amplitude coefficient $a$ for CPR and key distribution.

##  II Principle of the secure coherent PON

In this section, the principles of the encryption of cryptography, GCS pilot-
based CPR and key distribution, and FEC coding for the secure coherent PON are
introduced.

###  II-A Encryption of cryptography for secure coherent PON

Cryptography is the core of security technologies, including encryption,
decryption, key distribution, and so on. AES algorithm is one of the most
famous symmetric encryption algorithms of cryptography, which was proposed in
2006 [26]. AES algorithm supports the key of 128, 192, and 256 bits for both
encryption and decryption, while the AES-128 and AES-256 have been employed by
the XGS-PON and 50G-PON to enhance the physical-layer security, respectively.
Therefore, the AES algorithm can be also used in the future coherent PON to
enhance the physical-layer security. When a more advanced encryption algorithm
is proposed, it can be a candidate encryption scheme for the coherent PON.
However, with the advent of quantum computing for brute force attacks, the key
for encryption and decryption should be updated more frequently in the
coherent PON. Thus, frequent key updates should be achieved without occupying
additional overhead.

###  II-B GCS-PAM4 pilot-based CPR and key distribution

Since the digital signal processing (DSP) for coherent PON should be hardware-
efficient, the pilot-based CPR is proposed to replace the blind CPR [27, 28,
29]. In the data frame, pilots $p$ are inserted periodically into every
$(K-1)$ payload for CPR as shown in Fig. 1(a). The pilot-based CPR and key
distribution algorithm is shown in Fig. 1(b), which estimates the phase noise
between the $n$-th and the $(n+1)$-th pilot as

$\psi_{\text{Pilot}}(n)=\arg\left[e(n)\right]-\arg\left[p(n)\right]$ (1)

where $\boldsymbol{e}$ is the received pilot and $\boldsymbol{p}$ is the
transmitted pilot. $\operatorname{arg}(\cdot)$ is the angle of a complex. The
residual phase noise is estimated as

$\psi_{\text{Res}}(j)=\frac{1}{2Q+1}\sum_{l=j-Q}^{j+Q}\left\\{\arg\left[q(l)\right]-\arg\left[\hat{q}(l)\right]\right\\}$
(2)

where $q(l)$ denotes the equalized signal after the $\psi_{\text{Pilot}}(n)$
phase recovery and $\hat{q}(l)$ is $q(l)$ after hard decision (HD). $Q$ is the
half-length of the average window. Only the phase of the pilot is pre-shared
and used for CPR. Therefore, each ONU can share the secure keys with OLT at
the unicast US transmission, which is carried by the amplitude of the pilot
and recovered after CPR and hard decision.

The constellation of the GCS-PAM4 pilot for both CPR and key distribution is
shown in Fig. 1(c). The proposed GCS-PAM4 pilot is chosen from the set
$\\{-3d\times(1+1j),-ad\times(1+1j),ad\times(1+1j),3d\times(1+1j)\\}$, where
$d$ denotes the unit Euclidean distance and the range of the amplitude
coefficient is $0<a\leq 3$. When $a$ is $1$, the pilot becomes the uniformly
distributed PAM4, while it becomes binary phase shift keying (BPSK) if $a$ is
$3$. When the Gray coding is used, the de-mapped bits of the GCS-PAM4 pilot
are $\\{(0,0),(0,1),(1,1),(1,0)\\}$. The first bit represents the phase
information for CPR, while the amplitude information represented by the second
bit can be used as the control channel for key distribution. The signal-to-
noise ratio (SNR) penalty caused by phase noise on 16-ary quadrature amplitude
modulation (16QAM) at the 20% soft-decision (SD) FEC limit (i.e., 2.4$\times
10^{-2}$) versus the amplitude coefficient $a$ of the GCS-PAM4 pilot for CPR
is shown in Fig. 2. The linewidth of the laser is set to 100 kHz, 500 kHz, and
1 MHz. As the amplitude coefficient $a$ increases, the phase noise of the
laser is estimated more accurately and the SNR penalty is lower.

$\displaystyle P_{b,2}=$ $\displaystyle\frac{1}{2\sqrt{\pi
N_{0}}}\left[\int_{kd}^{\infty}e^{-\frac{(x-ad)^{2}}{N_{0}}}dx+\int_{-\infty}^{-kd}e^{-\frac{(x-ad)^{2}}{N_{0}}}dx+\int_{-kd}^{kd}e^{-\frac{(x-3d)^{2}}{N_{0}}}dx\right]$
(6) $\displaystyle=$
$\displaystyle\frac{1}{4}\left[2\operatorname{erfc}\left(\frac{3-a}{2\sqrt{N_{0}}}d\right)+\operatorname{erfc}\left(\frac{3+3a}{2\sqrt{N_{0}}}d\right)-\operatorname{erfc}\left(\frac{9+a}{2\sqrt{N_{0}}}d\right)\right]$
Figure 2: SNR penalty caused by phase noise on 16QAM at the 20% SD-FEC limit
versus the amplitude coefficient $a$ of GCS-PAM4 pilot for CPR.

The theoretical bit-error ratio (BER) of the first bit in the proposed GCS-
PAM4 pilot can be calculated as

$\displaystyle P_{b,1}$ $\displaystyle=\frac{1}{2\sqrt{\pi
N_{0}}}\left[\int_{0}^{\infty}e^{-\frac{(x-ad)^{2}}{N_{0}}}dx+\int_{0}^{\infty}e^{-\frac{(x-3d)^{2}}{N_{0}}}dx\right]$
(3)
$\displaystyle=\frac{1}{4}\left[\operatorname{erfc}\left(\frac{ad}{\sqrt{N_{0}}}\right)+\operatorname{erfc}\left(\frac{3d}{\sqrt{N_{0}}}\right)\right]$

where $N_{0}$ denotes the power spectral density of the noise. The
complementary error function is defined as

$\operatorname{erfc}(x)=\frac{2}{\sqrt{\pi}}\int_{x}^{\infty}e^{-z^{2}}dz.$
(4)

$d/\sqrt{N_{0}}$ can be expressed as

$\frac{d}{\sqrt{N_{0}}}=\sqrt{\frac{SNR}{2\times(3^{2}+a^{2})}}.$ (5)

The theoretical BER of the second bit in the proposed GCS-PAM4 can be
calculated by Eq. (6) as shown at the top of this page, where $k=(3+a)/2$ is
the normalized decision threshold for the second bit. To achieve a similar CPR
performance of the BPSK pilot, the amplitude coefficient $a$ of GCS-PAM4
should be as close to $3$. However, as $a$ increases, the BER of the first bit
for CPR becomes smaller, while the BER of the second bit for key distribution
becomes larger. Therefore, the amplitude coefficient $a$ should be optimized
to trade off the performance of CPR and key distribution.

Figure 3: BER versus SNR of the uncoded 16QAM, uncoded key bits,
$(17280,14592)$-LDPC encoded 16QAM, $(512,256)$-polar encoded key bits, and
the theoretical BER of the uncoded key bits given by Eq. (6).

###  II-C Coding schemes for data and control channels

Frequent key updates should be permitted for every FEC codeword to improve the
security of coherent PON. Therefore, it requires a relatively long FEC
codeword for the data channel and a relatively short FEC codeword for the
control channel as shown in Fig. 1(a). The $(17280,14592)$-low-density parity-
check (LDPC) code was adopted as the default FEC in 50G-PON [30], which can
also be adopted in coherent PON before a more proper coding scheme is
proposed. Since the GCS-PAM4 pilot is much shorter than the payload, an FEC
code with a short codeword length can be used for the control channel.
Referring to the coding schemes standardized by the 3rd generation partnership
project (3GPP) for fifth-generation new radio in the enhanced mobile broadband
scenarios, the LDPC code can be used for the data channel, while the polar
code can be employed for the control channel of coherent PON to realize the
error-free key distribution [31, 32].

Only the second bit of the GCS-PAM4 pilot is used as the control channel to
carry the key bit and encoded by polar code. Fig.3 shows the BER versus SNR of
the uncoded 16QAM payload, uncoded key bits, $(17280,14592)$-LDPC encoded
16QAM, $(512,256)$-polar encoded key bits in simulation and the theoretical
BER of the uncoded key bits given by Eq. (6). The amplitude coefficient $a$ is
set to 1.7 to make a trade-off between the CPR performance and the code rate
of the polar code. When the GCS-PAM4 pilot with an $a$ of 1.7 is used for CPR,
the SNR penalty is no more than 0.1 dB compared to the BPSK pilot. BER of
$(17280,14592)$-LDPC encoded 16QAM and $(512,256)$-polar encoded key bits are
fitted to reach $10^{-15}$. The key bits in the control channel can reach the
BER of $10^{-15}$ in a slightly lower SNR than the data channel.

##  III Experimental setups of secure coherent PON

In this section, the experimental setups of the 200-Gbps secure coherent PON
using DSCM are introduced. The GCS-PAM4 pilot-based key distribution and the
AES algorithm are demonstrated at the US and DS transmissions to enhance the
security of coherent PON, respectively.

Figure 4: (a) Experimental setups of the secure coherent PON using
4-SCs$\times$8-Gbaud/SC DSCM with the GCS-PAM4 pilot-based key distribution at
the unicast US transmission. (b) The optical spectrum of CDM output signal and
the US signal at Point 1. (c) Experimental setups of the secure coherent PON
using 4-SCs$\times$8-Gbaud/SC DSCM with AES-256 algorithm at the broadcast DS
transmission. (d) The optical spectrum of the DS signal at Point 1 and Point
2.

###  III-A GCS pilot-based key distribution at US transmission

The experimental setups of the 200-Gbps secure coherent PON using
4-subcarriers (SCs)$\times$8-Gbaud/SC DSCM with GCS pilot-based key
distribution at the unicast US transmission are shown in Fig. 4(a). There were
two ONUs and each ONU was allocated two subcarriers. The keys for the AES
algorithm of each ONU were generated and encoded by the $(512,256)$-polar
code, which uses an 11-bit cyclic redundancy check (CRC) encoding. The encoded
key bits were mapped into the GCS-PAM4 pilot as the second bits, while the
first bits for the CPR were pre-shared. Then the DSCM signal was generated as
follows. The bit sequences of each ONU were first encoded by
$(17280,14592)$-LDPC and mapped into 16QAM. The training sequence for the
coherent DSP was added [28]. The pilots were inserted periodically into every
31 $(K-1)$ payloads. After the pulse shaping using a square root-raised cosine
(RRC) filter with a 0.1 roll-off factor, frequency shift, and subcarrier
multiplexing, each ONU generated a 2-SCs$\times$8-Gbaud/SC DSCM signal.

The digital signal was converted to the analog signal by a 90-GSa/s digital-
to-analog converter (DAC). The transmitted signal at each SC is 8 Gbaud. Each
subcarrier contains 8640 16QAM payloads, 416-symbol training sequences, and
279 GCS-PAM4 pilots. Thus, the line rate of the secure coherent PON at US
transmission is 256 Gbps (4-SCs$\times$8-Gbaud/SC$\times$4
bits/symbol/polarization$\times$2 polarizations), while the net rate is
$\sim$200.08 Gbps ($8640/9335\times 14592/17280\times$256 Gbps). The signal
was amplified and modulated on the optical carriers @ $\sim$1549.85 nm for ONU
1 and $\sim$1550 nm for ONU 2 by a coherent driver modulator (CDM) with an
output optical power of about $-12.08$ dBm. An Erbium-doped fiber amplifier
(EDFA) was used as the booster amplifier with a launched optical power (LOP)
of about $8$ dBm. EDFA should be replaced by a semiconductor optical amplifier
for commercial deployment. Then the optical signals of two ONUs were coupled
by a 50:50 optical coupler (OC). The optical spectrum of CDM output and the US
signal at Point 1 with attenuation is shown in Fig. 4(b). The optical signal
was launched into a 20 km standard single-mode fiber (SSMF).

Figure 5: (a) Pre-FEC BER of the secure coherent PON using different pilots
for CPR. (b) Pre-FEC BER of the ONU 1 and ONU 2 using the GCS-PAM4 pilot.
Constellations of the (c) BPSK, (d) GCS-PAM4, and (e) PAM4 pilots.

A variable optical attenuator (VOA) was used to adjust the received optical
power (ROP) at the OLT. An external cavity laser (ECL) with a linewidth less
than 100 kHz was used as the local oscillator (LO). The LO output power is
$\sim$11.7 dBm and the wavelength is $\sim$1549.93 nm. The optical signal was
mixed with the LO in an integrated coherent receiver (ICR) and converted to an
analog signal. Then the signal was digitized by a 90-GSa/s analog-to-digital
(ADC). The burst DSCM signal was recovered by the coherent DSP, including
frame detection, frequency offset estimation (FOE), frequency shift, match
filtering, timing recovery (TR), synchronization, multiple-input multiple-
output (MIMO) equalizer, and the pilot-based CPR with a half-length $Q$ of 11.
The 16QAM payload was de-mapped and LDPC decoded using the sum-product
algorithm. Finally, the GCS-PAM4 pilot was recovered and the key bits were
polar decoded using the CRC-aided successive cancellation list algorithm to
realize the key distribution.

###  III-B AES algorithm at DS transmission

The experimental setups of the secure coherent PON using
4-SCs$\times$8-Gbaud/SC DSCM with AES-encryption at the broadcast DS
transmission are shown in Fig. 4(c). The new keys from the US transmission for
the AES algorithm were first updated. The bit sequence at OLT was encrypted by
the AES-256 algorithm using the new keys of each ONU. After LDPC encoding, the
bit sequence was mapped into 16QAM. Training sequence and pilot for CPR were
also added for coherent DSP. Then a 4-SCs$\times$8-Gbaud/SC DSCM signal
without guard interval was generated, including the power optimization, the
pulse shaping using an RRC filter with a 0.1 roll-off factor, frequency shift,
and subcarrier multiplexing.

Each subcarrier contains 8640 16QAM payloads, 480-symbol training sequences,
and 279 pilots. Thus, the line rate of the secure coherent PON at DS
transmission is 256 Gbps (4-SCs$\times$8-Gbaud/SC$\times$4
bits/symbol/polarization$\times$2 polarizations), while the net rate is
$\sim$198.72 Gbps ($8640/9399\times 14592/17280\times$256 Gbps). The DSCM
signal was converted to an analog signal by the 90-GSa/s DAC and modulated at
an optical carrier @ $\sim$1539.98 nm by a CDM with about $-12.93$ dBm output
power. An EDFA was used as the boost amplifier at OLT for DS transmission. The
LOP was optimized to $\sim$8 dBm by adjusting the gain of the EDFA. The
optical spectrum of the signal at Point 1 and Point 2 is shown in Fig. 4(d).
Finally, the optical signal was launched into a 20 km SSMF.

A VOA was used to adjust the ROP at ONU. A tunable ECL with a linewidth of
less than 100 kHz and $\sim$11.7 dBm output power was used as LO. The optical
signal was converted to an analog signal by an ICR. The subcarriers of
interest were selected by LO wavelength tuning and transferred into the
baseband signal by coherent detection without using the optical filter. Then
the analog signal was digitized by a 90-GSa/s ADC. The DSCM subcarriers of
interest were recovered, including FOE, frequency shift, match filtering, TR,
synchronization, MIMO equalizer, and pilot-based CPR. After the 16QAM payload
was de-mapped and LDPC decoding, the AES decryption was implemented with the
updated keys, which were generated by the ONU.

Figure 6: Post-FEC BER of the 16QAM payload and the key bit at (a) one-ONU and
(b) two-ONU scenarios. Inset is the normalized GCS-PAM4 pilot at Tx and Rx.

##  IV Experimental results and discussions

The pre-FEC BER of the secure coherent PON using different pilots for CPR at
US transmission is shown in Fig. 5(a). Figs. 5(c-e) show the normalized
constellations of the BPSK, GCS-PAM4, and PAM4 pilots at the transmitter (Tx)
and receiver (Rx) with an ROP of $-28$ dBm, respectively. At the Tx, the power
of PAM2, GCS-PAM4, and PAM4 pilots was normalized to be consistent with that
of the payload. The dashed black lines are the decision thresholds of the
first bits for CPR. Compared to the BPSK pilot for CPR, there is a $\sim$0.3
dB penalty on the receiver sensitivity at the 20% SD-FEC limit when the PAM4
pilot is used for CPR. When the proposed GCS-PAM4 pilot is used for CPR, there
is almost no penalty on the receiver sensitivity at the 20% SD-FEC limit.
Therefore, the proposed GCS-PAM4 pilot is effective for hardware-efficient CPR
in the secure coherent PON. The pre-FEC BER of ONU 1 and ONU 2 using the GCS-
PAM4 pilot is shown in Fig. 5(b). Scenarios that only ONU1 or ONU2 works alone
and ONU1 and ONU2 work together were evaluated. The BER performance of the two
ONUs is almost the same. When two ONUs work together, the signal bandwidth is
doubled and the total power of the signal is 3 dB higher than that of the
single ONU signal. The BER of the 16QAM payload is lower than the 20% SD-FEC
limit when the ROP is no less than $-28$ dBm and $-25$ dBm at one-ONU and two-
ONU scenarios, respectively. It can be estimated that a 3 dB higher ROP is
needed when the number of ONUs using FDMA is doubled and some penalties are
caused by the out-of-the-band noise, while the system performance is slightly
affected by burst detection when the ONUs use TDMA.

Figure 7: Electrical spectrum of the (a) transmitted DSCM signal, the received
(b) SC 1, (c) SC 2, (d) SC 3, and (e) SC 4 in the coherent PON at DS
transmission. The dashed lines represent the received signal and the solid
lines represent the selected SC by wavelength tuning.

The post-FEC BER of the 16QAM payload and the key bit for the AES algorithm at
(a) one-ONU and (b) two-ONU scenarios are shown in Fig. 6. When the ROP is no
less than $-28$ dBm and $-25$ dBm for the one-ONU and two-ONU scenarios, the
16QAM payload is error-free after the LDPC decoding. The power budget of the
coherent PON using 4-SCs$\times$8-Gbaud/SC DSCM at US transmission is $\sim$33
dB (i.e., $+8$ dBm minus $-25$ dBm). The post-FEC BER of the 16QAM payload can
match the pre-FEC BER in Fig. 5(b). Inset is the normalized GCS-PAM4 pilot at
the Tx and Rx with ROPs of $-28$ dBm and $-25$ dBm, respectively. The dashed
black lines represent the decision thresholds of the second bits for key
distribution. Although the key bits with inadequate length become error-free
at all the measured ROP after the polar code decoding, according to the
simulation results, key bits should be error-free at an ROP of no less than
around $-28$ dBm and $-25$ dBm, respectively. Thus, the GCS-PAM4 pilot is also
effective for key distribution without additional overhead. The payload within
one LDPC codeword is inserted by 279 pilots at each polarization to allow
frequent key updates for every FEC codeword, which improves physical-layer
security. Moreover, the proposed algorithm can be also applied to other
encryption algorithms with the need for key distribution.

Figure 8: Post-FEC BER performance of (a) SC 1, (b) SC 2, (c) SC 3, and (d) SC
4 in the secure coherent PON using DSCM at DS transmission without or with key
for AES decryption.

The electrical spectrum of the (a) transmitted DSCM signal, the received (b)
SC 1, (c) SC 2, (d) SC 3, and (e) SC 4 in the coherent PON at DS transmission
is shown in Fig. 7. To maintain the similar BER performance of all SCs, more
power was loaded to the SCs at a higher frequency, while those at a lower
frequency were loaded with less power to compensate for the limited bandwidth
of the transceiver. The dashed lines represent the received signal and the
solid lines represent the selected SC. Each SC of the DSCM signal can be
transferred to the baseband signal by tuning the wavelength of LO. Therefore,
the coherent optical technologies and the DSCM for TFDMA allow the low-
bandwidth transceivers at the ONUs. However, eavesdropping would still occur
in the coherent PON using DSCM and it is not easily discovered by OLT. For
example, illegal ONUs can eavesdrop on the broadcast DS signal of other ONUs
at the same SCs or different SCs by wavelength tuning. Therefore, the
physical-layer security enhancement is crucial for the future coherent PON
using DSCM, which will also face severe security issues, especially
eavesdropping at the broadcast DS transmission.

The post-FEC BER performance of each subcarrier in the secure coherent PON
using DSCM at DS transmission without or with key is shown in Fig. 8. When the
ROP is no higher than $-26$ dBm, the signal after LDPC decoding and the AES
decryption with the correct key is still not error-free because the pre-FEC
BER can not reach the 20% SD-FEC limit. When the ROP is no less than $-25$
dBm, the signal of these four SCs after AES decryption with the correct key
becomes error-free. Since the power of the subcarriers is adjusted to balance
the SNR, the BER performance of these four subcarriers is similar. The power
budget of the coherent PON at DS transmission is $\sim 33$ dB (i.e., $+8$ dBm
minus $-25$ dBm). However, despite the increase in the ROP, the post-FEC BER
of the four SCs is still $\sim$0.5 when the correct key of the AES decryption
is unavailable for illegal ONUs. Therefore, the physical-layer security of the
coherent PON is enhanced by the proposed scheme based on the AES algorithm
with frequent key updates using the GCS-PAM4 pilot. It is worth mentioning
that the eventual timing processing is asymmetry in the DS and US transmission
due to pilot mapping for CPR and key generation/data encryption.

##  V Conclusion

In this paper, we propose the AES algorithm and GCS-PAM4 pilot-based key
distribution for secure coherent PON. At the unicast US transmission, the
first bit of the proposed GCS-PAM4 pilot is used for the hardware-efficient
CPR and the second bit is encoded by the polar code and utilized for error-
free key distribution without additional overhead. Frequent key updates are
permitted for every codeword to improve the security of coherent PON at the
broadcast DS transmission. Experimental results of the 200-Gbps secure
coherent PON using DSCM demonstrated that the polar code and GCS-PAM4 pilot
enable the error-free key distribution without additional overhead at US
transmission, while the AES-256 algorithm has prevented eavesdropping at DS
transmission. Furthermore, the proposed GCS-PAM4 pilot exhibits comparable CPR
performance to the BPSK pilot with the best CPR performance. In conclusion,
the proposed physical-layer security enhancement scheme shows potential in the
application to future coherent PON.

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