# Reconfigurable and Real-Time Nyquist OTDM Demultiplexing in Silicon
Photonics

Arijit Misra, Karanveer Singh, Janosch Meier, Christian Kress, Tobias Schwabe,
Stefan Preußler, J. Christoph Scheytt, and Thomas Schneider This work was
supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under grant numbers - 322402243, 403154102, 424608109, 424608271,
424607946, 424608191, and in part by the German Federal Ministry of Education
and Research (BMBF) under funding code 13N14879.A. Misra, K. Singh, J. Meier,
S. Preußler and T. Schneider are with the THz Photonics Group, Technische
Universität Braunschweig, Schleinitzstraße 22, 38106 Braunschweig, Germany
(Coressponding author: Arijit Misra, e-mail: arijit.misra@ihf.tu-bs.de).C.
Kress, T. Schwabe, and J. C. Scheytt are with the Paderborn University, System
and Circuit Technology, Heinz Nixdorf Institute, Fürstenalle 11, 33098,
Paderborn, Germany.

###### Abstract

We demonstrate for the first time, to the best of our knowledge,
reconfigurable and real-time orthogonal time-domain demultiplexing of coherent
multilevel Nyquist signals in silicon photonics. No external pulse source is
needed and frequency-time coherence is used to sample the incoming Nyquist
OTDM signal with orthogonal sinc-shaped Nyquist pulse sequences using Mach-
Zehnder modulators. All the parameters such as bandwidth and channel selection
are completely tunable in the electrical domain. The feasibility of this
scheme is demonstrated through a demultiplexing experiment over the entire
C-band (1530 nm - 1550 nm), employing 24 Gbaud Nyquist QAM signals due to
experimental constraints on the transmitter side. However, the silicon Mach-
Zehnder modulator with a 3-dB bandwidth of only 16 GHz can demultiplex Nyquist
pulses of 90 GHz optical bandwidth suggesting a possibility to reach symbol
rates up to 90 GBd in an integrated Nyquist transceiver.

###### Index Terms:

Silicon photonics, Nyquist pulses, OTDM, multiplexing, demultiplexing, optical
sampling, optical frequency comb.

##  I Introduction

Surging data traffic in high-speed communication, the internet-of-things and
datacenters demand a further scaling of multiplexing and transmission
techniques, along with upgraded transceiver designs capable of handling higher
modulation formats adaptively and flexibly on a power efficient, small
footprint, and economical platform like silicon photonics. Along with the
efforts in parallel transmission using multiplexing in space, wavelength and
polarization the enhancement of single carrier line rates is also essential in
this regard [1, 2]. Time-domain multiplexing (TDM) facilitates single carrier
line rate enhancement in a wavelength division multiplexing (WDM) system
without increasing the optoelectronic bandwidth of available transceiver
components [3].

Sinc-shaped Nyquist pulse based orthogonal-TDM (OTDM) offers the most
efficient way of time-domain multiplexing owing to the zero inter-symbol-
interference (ISI) between such pulses, low peak-to-average power ratio
(PAPR), and tolerance to linear and nonlinear impairments in high data rate
channels [4, 5, 6, 7, 8, 9, 10]. This allows several time-domain channels to
be multiplexed, if the data is modulated on such pulses and then interleaved
with a specific time delay dictated by the orthogonality condition [4, 6].
Such a sinc-shaped Nyquist pulse sequence based transceiver is signal-format-
transparent with the capability of transmitting versatile data formats on a
single carrier [11]. Additionally, for a multi-carrier or WDM system, the need
for any guardband can be precluded due to the rectangular shape of the
singular wavelength channels [11]. So, a WDM system based on sinc-shaped
Nyquist pulses can exploit the available channel bandwidth for data
transmission in the maximum possible way.

There has been abundant exploration on sinc-shaped Nyquist pulse synthesis and
multiplexing techniques over the years. However, the reception techniques are
limited to a few. Demultiplexing of sinc-shaped orthogonal time-domain
multiplexed channels requires either the sampling with much higher sampling
rates and narrower time gates, or a sinc-shaped orthogonal time-domain gate
that extracts the concerned time-domain channel without interference. The
first method is realized by very high-bandwidth digital signal processing
(DSP) [12], or by polarization-sensitive nonlinear optical sampling of
synchronous control pulse trains of much higher bandwidth in a nonlinear
optical loop mirror (NOLM) [13, 4, 14, 8, 9]. For the sinc-shaped orthogonal
time-domain gate, linear optical sampling in a coherent receiver using Nyquist
pulse sequences as the local oscillator (LO) [15, 16, 17], optical Fourier
transform (OFT) [18], and optical parametric amplification [19] have been
utilized. However, these receiver configurations suffer from significant
drawbacks such as complex system architectures for nonlinear optical
interactions, static configuration due to scarcity of reconfigurable external
sampling pulse sources in terms of central wavelength and pulse width, need
for sampling pulses with bandwidth much higher than the signal bandwidth, or
intensive electronics and computational hardware requirements in terms of
bandwidth for the DSP.

In contrast, time-frequency coherence based all-optical sinc-shaped pulse
sequence sampling by a Mach-Zehnder Modulator (MZM) provides a much easier
solution with the existing state-of-the-art components [20, 21, 22, 23, 24].
The method utilizes spectral convolution by creating equal, phase-locked
spectral replicas of the incoming signal to achieve a full-field sampling in
the time-domain. It neither requires any reconfigurable Nyquist pulse sources
operating at different spectral bands, nor any optical filters or tunable
delay lines. Channel selection is achieved merely by phase shifts in the
electrical driving signals to the modulator.

Besides simplicity, this method is also agile by virtue of multi-wavelength
operation with fully controllable operational bandwidth. A high bandwidth
Nyquist OTDM signal can be demultiplexed into $N$ low bandwidth signal
channels. The bandwidth of the receiver electronics can be as low as $1/(2N)$
times the overall single carrier symbol rate. Additionally, it is possible to
demultiplex higher order quadrature amplitude modulated (QAM) channels in a
real-time and dynamic manner with a single MZM [11].

Based on the convenient setup and the basic integrability of the optical and
electronic components, this sampling technique is apt for realization using
integrated photonics platforms like silicon photonics, indium phosphite, or
lithium niobate on insulator. Many commercial foundries offer silicon MZMs,
germanium photodetectors, and other standard photonic devices as part of their
process design kits [25, 26]. In addition, silicon leverages matured
semiconductor processing technology for electronic integration along with
photonics. So far, a few non-orthogonal optical time-domain multiplexing or
serializer circuits based on Gaussian pulses have been reported in silicon
photonics [27, 28]. Recently, sinc-shaped Nyquist pulse sequence generation
with various silicon based MZM structures have been demonstrated [29, 21, 30,
31], and their quality has been analyzed in detail [32]. However, the
demonstration of time-domain demultiplexing in any integrated platform is yet
to be reported.

In this article, we present for the first time, to the best of our knowledge,
the experimental demonstration of orthogonal time-domain demultiplexing in
silicon photonics. High capacity Nyquist QAM signals have been demultiplexed
to three lower capacity channels in real-time by linear sinc-shaped Nyquist
pulse sequence sampling using electronic-photonic co-integrated dual-drive
silicon MZMs with high modulation efficiency (external $V_{\pi}$ = 420 mV),
low power consumption, and high DC extinction ratio (40 dB). 16QAM and QPSK
modulation formats have been received after up to 30 km single-mode fiber
transmission at multiple wavelengths over the C-band of optical
telecommunication. Investigations on sinc-shaped pulse sequence generation of
different bandwidths and repetition rates have also been presented with a
demonstrated capability of synthesizing sinc-shaped Nyquist pulse sequences of
90 GHz bandwidth. The experimental results suggest potential silicon coherent
transceivers with single carrier symbol rates of 90 GBd.

##  II MZM based Nyquist time-domain demultiplexing

The basic principle behind the integrated orthogonal time-domain
demultiplexing system is the multiplication between the received modulated
Nyquist signal of bandwidth $B$ and an unmodulated sinc-shaped Nyquist pulse
sequence with the same bandwidth in each of the $N$ parallel receiver
branches. This multiplication reduces the data rate of the incoming signal by
the factor $N$. This is shown for $N=3$ for the incoming signal Fig.1 (a) and
(b) with the red, green and blue dots. By the multiplication with a sinc-pulse
sequence with the right time shift, as the red one in Fig.1 (c), only the red
points (or data signals) will be extracted. In a second and third branch the
green and blue points can be extracted at the same time. As result the
detector and signal processing electronics in each branch just require a
bandwidth of $B/(2N)$.

For all of the optical demultiplexing techniques reported so far, external
pulse sources are required [13, 4, 14, 8, 9, 15, 16, 17]. For the method
presented here, however, the incoming signal spectrum is convolved with a
flat, equispaced, phase-locked optical frequency comb. In the time-domain,
this results in the desired multiplication of the signal with a sinc-shaped
Nyquist pulse sequence [20, 21]. The multiplication occurs for the full-field,
thereby achieving coherent sampling [22, 23].

The operation principle for a demultiplexer with $N$ branches is presented in
the upper part of Fig. 1. A Nyquist signal of optical bandwidth $B$ is
demultiplexed in parallel in $N$ odd numbers of branches with MZMs, each
driven with $n=(N-1)/2$ equispaced, phase-locked radio frequencies ($RF_{n}$).
In each modulator, the input signal undergoes a sinc-sequence sampling, or a
spectral convolution with an $N$-line, flat, rectangular, phase-locked optical
frequency comb. Similar to ideal sinc pulses, sinc-sequences are orthogonal.
The sampling instances are controlled precisely by the RF phase shifts between
the inputs to the modulator. Hence the orthogonality can be controlled
entirely in the RF domain. Moreover, the frequency of the highest RF tone and
the RF bandwidth of the modulator has to be just $B/3$ for a three branch
system. Even a modulator bandwidth of $B/5$ is possible, as we will show in
the results section.

Figure 1: Basic configuration of orthogonal time-domain demultiplexing using
MZMs and sinc-shaped Nyquist pulse sequences. In the upper part a complete
generalized system is shown, while the lower part presents the signal
processing steps for one of the branches, if the MZM is driven with one
sinusoidal radio frequency. The black lines correspond to optical and the blue
to electrical connections. MZM: Mach-Zehnder modulator, RFG: radio frequency
generator, LPF: electrical lowpass filter, CD: coherent detector.

After the orthogonal time-domain sampling with the correct input phase shifts,
the signals in each branch are detected by a detection system with a baseband
bandwidth of $B/(2N)$. Thereby, the Nyquist signal with an optical bandwidth
$B$ is demultiplexed into $N$ electrical Nyquist signals with a bandwidth of
$B/(2N)$.

In the following paragraphs, we present a mathematical description of this
process. An optical Nyquist signal can be created by modulating an electrical
Nyquist-shaped data signal on a continuous wave (CW) optical carrier [33].
However, it can also be generated all-optically via modulation and time-domain
multiplexing of spectrally shaped mode-locked laser pulses [4] or Nyquist
pulse-sequences synthesized by one or more cascaded modulators [6, 34, 11].
Therefore, we shall show how regardless of the origin, the high-bandwidth
Nyquist channel can be demultiplexed to several low-bandwidth signals using
this method.

In general, a Nyquist signal can be seen as the infinite sum of time-shifted
ideal sinc-pulses weighted with the data symbols. Such a signal $s(t)$ (see
Fig. 1(a)) will have a rectangular bandwidth of $B$ in the optical domain. An
identical Nyquist signal $s(t)$ can be created as the sum of $N$ time-shifted
sinc-shaped pulse sequences, weighted with $N$ data streams of lower symbol
rates. Figure 1(b) shows this for a sinc-sequence with two zero-crossings
between the peaks, corresponding to a 3-line comb. In the frequency domain,
such a sinc-sequence is a flat, three-line frequency comb of bandwidth $B$ [6,
21, 22]. This three-line sinc-sequence can be used to transmit three
multiplexed Nyquist channels with a symbol rate of $B/3$ for each channel, and
thus an aggregated symbol rate of $B$ in the optical bandwidth $B$. So,
regardless if ideal sinc pulses or sinc-sequences are considered, the
resultant time-domain signals are identical.

If $N$ Nyquist signals of symbol rate $B/N$ are modulated on sinc-sequences of
bandwidth $B$ having $N-1$ zero crossings between two consecutive pulse peaks
and multiplexed orthogonally in time, then the resultant signal of symbol rate
$B$ can be written as,

$\centering
s(t)=\sum_{l=1}^{N}s_{l}\left(t\right)\cdot\operatorname{sq}_{N,B}\left(t-\frac{l-1}{B}\right),\@add@centering$
(1)

with $l=1,2,...,N$, and $N$ as an odd number.

Here, following the Nyquist-Shannon sampling theorem, one of the $N$ different
Nyquist data streams with a symbol rate $B/N$ can be expressed as,

$\centering
s_{l}(t)=\sum_{k=-\infty}^{\infty}s_{l}\left(\frac{kN}{B}+\frac{l-1}{B}\right)\cdot\operatorname{sinc}\left(\frac{B}{N}t-\frac{l-1}{N}-k\right)\@add@centering$
(2)

Moreover, the sinc-shaped pulse sequence in Eq. (1) can be defined as the sum
of time-shifted ideal sinc-pulses as,

$\centering\operatorname{sq}_{N,B}(t)=\sum_{k=-\infty}^{\infty}\operatorname{sinc}(Bt-
kN).\@add@centering$ (3)

Due to orthogonality of the sinc-sequences, the signal $s(t)$ has an overall
symbol rate of $B$ and following the definition in Eq. (1), a baseband
bandwidth of $B/2$. Accordingly, it can be identified as a Nyquist signal and
therefore, following the Nyquist-Shannon sampling theorem, it can be expressed
as the sum of ideal time-shifted sinc-pulses, weighted with the data symbols:

$\centering
s(t)=\sum_{k=-\infty}^{\infty}s\left(\frac{k}{B}\right)\cdot\operatorname{sinc}\left(Bt-k\right).\@add@centering$
(4)

The operation of orthogonal demultiplexing of $s(t)$ into several low
bandwidth Nyquist signals can be seen as a two-step process. First the
incoming signal is sampled with sinc-sequences and second it is filtered or
detected with low bandwidth. The sampled signal in one of the branches as
shown by the red curve in Fig. 1(c) can be mathematically expressed as,

$\centering\tilde{s_{l}}(t)=s(t)\cdot\operatorname{sq}_{N,B}\left(t-\frac{l-1}{B}\right).\@add@centering$
(5)

The sinc-sequence sampled signal can be filtered in the optical domain by an
optical bandpass filter of bandwidth $B/N$ to create an optical analog signal
for further all-optical signal processing purposes. However, baseband analog
or digital filtering can also be done after demodulation with a low-pass
filter of bandwidth $B/(2N)$. Alternatively, a detection system of that
bandwidth can be used. The output signal after filtering is given by [11],

$\displaystyle\left[\mathscr{F}^{-1}_{f}\left(\left[\mathscr{F}_{t}\left(\tilde{s_{l}}(t)\right)\right](f)\cdot\sqcap_{B/N}(f)\right)\right](t)$
(6)
$\displaystyle=\frac{1}{N}\sum_{k=-\infty}^{\infty}s_{l}\left(\frac{kN}{B}+\frac{l-1}{B}\right)\cdot\operatorname{sinc}\left(\frac{B}{N}t-\frac{l-1}{N}-k\right)$
$\displaystyle=\frac{1}{N}s_{l}(t).$

Here, the low bandwidth detection system or the low pass filter is defined as
a rectangular function $\sqcap_{\frac{B}{N}}(f)$ equal to 1 for $\lvert
f\rvert<\frac{B}{2N}$, $0.5$ for $\lvert f\rvert=\frac{B}{2N}$, and 0,
elsewhere.

Therefore, if the incoming signal is split into $N$ branches, the
demultiplexing can be carried out in parallel and real-time with MZMs placed
in each branch. The sinc-sequences have to be time-shifted by $1/B$ relative
to one another. This corresponds to a relative phase shift of $2\pi/N$ between
the driving RF signals. In the simplest case, if the MZM is driven with one RF
tone, this results in three low-bandwidth signals at the output, corresponding
to $l$=1,2, and 3. The red sampling points $\tilde{s_{l}}(t)$ in Fig. 1(b))
were achieved with the red sinc-pulse sequence for sampling as shown in Fig.
1(d). The sampling points in between can be achieved with two sinc pulse
sequences phase shifted by $120^{\circ}$ and $240^{\circ}$, as shown with the
blue and green dots in Fig. 1(a) and 1(b).

##  III Experiment and Results

In this section, the proof of concept experimental details, characterization
of the si-MZM, and data transmission results are presented. First, the
performance of the silicon photonic MZM as a Nyquist time-domain demultiplexer
has been investigated over the entire C-band (1530 nm - 1560 nm). Later the
generation of Nyquist pulses of different pulse widths and repetition rates is
investigated to assess the capacity of a single carrier Nyquist transceiver
based on the presented MZM. We did not create one high symbol rate Nyquist
signal for the experiments. Instead, three low symbol rate signals were
multiplexed with sinc-sequences to create one high-capacity Nyquist channel.
Afterward, we demultiplexed each of them separately by the silicon photonic
MZM. Following the theory section, this is equivalent to the demultiplexing of
one single, high data rate Nyquist signal.

###  III-A Experimental setup and device

Figure 2: Schematic illustration of the experimental setup. A single carrier
from an integrated tunable laser assembly (ITLA) is modulated with three
different data channels and then orthogonally multiplexed using sinc-shaped
pulse sequences to create a high-capacity Nyquist channel. After transmission
through single mode fiber (SMF), the channels are demultiplexed by the Si-MZM
before detection by a coherent detector. EDFA: Er-doped fiber amplifier, DSP:
digital signal processing.

For the experimental demonstration, a setup as illustrated in Fig. 2 was
adopted. A wavelength-tunable CW laser was modulated with three different data
streams and orthogonally multiplexed with sinc-shaped Nyquist pulse sequences
in the time-domain. After transmission through standard single mode fiber
(SMF), the multiplexed signal was subjected to the silicon electronic-photonic
co-integrated Mach-Zehnder modulator. After 20 m SMF transmission, a coherent
detector detected the demultiplexed signals with another continuous wave laser
used as the local oscillator. The 20 m SMF was necessary since the integrated
device measurement setup was placed in another laboratory room than the
asynchronous detector. We used post-detection digital low-pass filtering in
the baseband to mimic a low-bandwidth detection system. A coherent modulation
analyzer (Tektronix-OM1106) performed the required digital signal processing
(DSP) of the recorded waveforms in a real-time oscilloscope (Tektronix
DPO73304) for the visualization of symbol constellations and the measurement
of other performance metrics like $Q$-factor and error vector magnitude (EVM).
Forward error correction, pre-distortion, and nonlinearity compensation were
not applied in the experiment. 1% of the output power after the chip was
subjected to an optical spectrum analyzer (OSA, Yokogawa AQ6370) for spectral
measurements. The limited sampling rate of the used arbitrary waveform
generators for data signal generation prohibited the possibility of reaching
higher single carrier optical bandwidths beyond 24 GHz for the sinc-sequence
multiplexed channels. As the transmitter was limiting the symbol rate to
$B=24$ GBd, the RF input to the modulator was 8 GHz ($B/3$), and the receiver
was restricted in the baseband to 4 GHz ($B/6$) via low pass digital
filtering. EDFAs along with BPFs were used to amplify the optical signals when
required. Polarization diversity was not employed in the proof of concept
experiment.

Figure 3:  (a) Block diagram of the fabricated MZM with a pre-amplifier and a
distributed driver that applies complementary signal inputs to the segmented
phase shifters in the two arms. (b) Chip picture: Bond wires connect chip pads
to printed circuit board lines for DC connections. The driving signal to the
MZM is applied via a probe in ground-signal-signal-ground (GSSG)
configuration. (c) Optical transfer characterization of the two arms in terms
of DC input to the heaters, integrated with the two arms of the Si-MZM. (d)
Measured electro-optic response of the MZM. The 3 dB bandwidth of 16 GHz is
indicated with a dashed line.

The Si-MZM chip was fabricated in a BiCMOS technology from IHP (SG25H5_ePIC).
This technology allows monolithic integration of high-frequency driver
circuits along with the electro-optical phase shifters for the MZMs to enhance
the modulation efficiency and bandwidth of the modulator. The modulator used
for the experiment is a segmented MZM with distributed linear drivers, as
shown in Fig. 3(a) and 3(b). The overall length of the device is 6.25 mm. As a
metric for modulation efficiency, the measured $V_{\pi}$ of 420 mV is
considerably lower than the best-reported state-of-the-art monolithic
approaches [35]. As shown in Fig. 3(a), the MZM chip contains segmented MZM
and fully differential drive electronics. The on-chip driver incorporates a
pre-amplifier with a 100 Ohm differential input resistance. The subsequent
main driver is designed in a distributed manner for driving the phase shifter
segments (PS) of the MZM using a push-pull scheme. To achieve full phase shift
for high-speed operation, and considering the maximum achievable voltage swing
from the SiGe transistors limited by collector-emitter breakdown limitations,
the total effective phase shifter length for each arm was chosen to be 6.24
mm. For the DC bias point setting of the MZM, additional on-chip heater
structures, controlled via external voltage sources, have been placed in each
arm. Electrical signals are applied either by bondwires for DC connections
(Fig. 3(b)) or via probes for the RF signals. For a full $2\pi$ phase shift of
the MZM bias point, maximum electrical power of 90 mW must be applied to the
thermal phase shifters. The DC extinction ratio was measured to be 40 dB and
37 dB for the two arms by sweeping the input voltage to the heaters (Fig.
3(c)). The electro-optic response of the modulator is shown in Fig. 3(d).

###  III-B Results and discussion

In the first experiments, we were demultiplexing standard data signals. The
symbols were shaped digitally by raised-cosine filters with $1.0$ roll-off
factor and baseband width of 4 GHz, for each low symbol rate channel. Thus, in
the 24 GHz channel bandwidth, an aggregate data rate of 12 GBd was multiplexed
with three optical sinc-sequences, each modulated with a 4 GBd data stream,
corresponding to a 0.5 symbols/sec/Hz spectral efficiency. The result for the
data content in one of the three sinc sequences can be seen in Fig. 4 for QPSK
and 16-QAM data formats transmitted via 10 and 30 km of fiber. The other
signals can be demultiplexed by $120^{\circ}$ phase shifts of the RF signal
driving the modulator. The eye diagrams correspond to the in-phase component.
The corresponding signal metrics such as $Q$-factors and average-EVM values
have been presented in Table. I. All the measurements of signal metrics were
done following the decision threshold method [36] for $3\times 10^{5}$
recorded bits. For these experiments, a direct measurement of the bit-error-
rate (BER) was not possible, since no errors occurred during the measurement.
To avoid a long data acquisition time, the BER values can be estimated from
the $Q$-factors (in linear scale) for two-level signals following the
relationship $\mathrm{BER}_{est}\approx(1/2)\mathrm{erfc}(Q/\sqrt{2})$, [37].
The measured $Q$-factors for the demultiplexed QPSK signals after 30 km
transmission correspond to estimated BER values in the order of $10^{-17}$.
These values are well below the $4.5\times 10^{-3}$ limit for the hard-
decision forward error correction (HD-FEC) codings with 7% overhead [38].

Figure 4:  Measured Symbol constellation and eye diagram for one demultiplexed 4 GBd QPSK (a,b), and a 4 GBd 16-QAM signal (c,d) from an orthogonal sinc-sequence multiplexed channel with a symbol rate of 12 GBd (24 GHz bandwidth) originating from a single carrier at 193.4 THz. Experiments were carried out for 10 km (a,c) and 30 km (b,d) SMF transmission. TABLE I: Measured performance metrics of one demultiplexed 4 GBd data channel from a 12 GBd multiplexed channel with a carrier frequency of 193.4 THz. Format | Distance |  $Q$-factor | Average EVM
---|---|---|---
| (km) | (dB) | (%)
QPSK | 10 | I $=20.42887\pm 1.04338$ | $9.9889\pm 0.4216$
Q $=19.96499\pm 0.51241$
QPSK | 30 | I $=18.46182\pm 0.64159$ | $13.1057\pm 0.5449$
Q $=18.268\pm 0.25387$
16-QAM | 10 | I $=14.75606\pm 0.40704$ | $6.6485\pm 0.1887$
Q $=13.58524\pm 0.26846$
16-QAM | 30 | I $=12.03721\pm 0.22764$ | $9.27\pm 0.1891$
Q $=11.102\pm 0.16626$

In another set of experiments, each low-capacity channel was modulated with
Nyquist signals of $B/4=8$ GBd symbol rate having 4 GHz baseband width. Here
the symbols were shaped by sinc-shaped pulses. We used digital filtering by
raised-cosine filters with $0.0$ roll-off factor and baseband width of 4 GHz
for this purpose. Again, three of such signals were multiplexed via optical
sinc-sequences of 24 GHz bandwidth. Thereby, a 24 GBd Nyquist-QPSK channel was
created with a theoretically maximum spectral efficiency of 1 symbol/sec/Hz.
In the experiments we were restricted by the bandwidth of our arbitrary
waveform generator to a maximum data rate of 48 Gbit/s. Thus, modulation
formats higher than QPSK could not be generated in this bandwidth.

For one demultiplexed Nyquist-QPSK signal branch with a symbol rate of 8 GBd,
the symbol constellations and eye diagrams are presented in Fig. 5, with the
measured signal metrics presented in Table. II after 10 km and 30 km of SMF
transmission. The optical signal-to-noise ratio values before demultiplexing
were around 37 dB and 33 dB respectively after 10 km and 30 km of fiber
transmission for the measurements involving 8 GBd QPSK signals. As shown in
Fig. 6, all the three demultiplexed 8 GBd Nyquist-QPSK signals from the 24 GBd
Nyquist channel have similar performance for a certain distance of fiber
transmissions. All of the measured BER values are far away from the limit for
HD-FEC coding with 7 % overhead.

Figure 5:  Measured Symbol constellations and eye diagrams for one demultiplexed 8 GBd Nyquist-QPSK signal from a Nyquist channel of 24 GHz bandwidth around 193.4 THz after (a) 10 km and (b) 30 km SMF transmission. TABLE II: Measured performance metrics of one demultiplexed 8 GBd Nyquist-QPSK signal from the 24 GBd Nyquist channel around 193.4 THz. Format | Distance |  $Q$-factor | Average EVM
---|---|---|---
| (km) | (dB) | (%)
Nyquist- | 10 | I $=18.61079\pm 0.17767$ | $12.3597\pm 0.1567$
Q $=18.29439\pm 0.12573$
QPSK | 30 | I $=16.22659\pm 0.36605$ | $15.9707\pm 0.9316$
| Q $=16.1480\pm 0.3467$
Figure 6: Measured $Q$-factors (in black) and estimated BER values (in red)
for different transmission ranges of all three 8 GBd Nyquist-QPSK signals
demultiplexed from the 24 GBd Nyquist channel.

The optical spectra of the multiplexed (dashed lines) and demultiplexed (solid
lines) signals around a single carrier at 193.4 THz for demultiplexing with a
flat, three-line rectangular comb can be seen in Fig. 7. Please note, that the
demultiplexing is based on a convolution with the three-line comb. Thus, the
spectrum after multiplexing has a rectangular shape (dashed lines) and the
spectral content broadens due to the demultiplexing . However, the whole
information of the signal is just in the $B/3$ fraction of the bandwidth
around the carrier (red rectangle), resulting in a required electrical
detector bandwidth of $B/6$. For Fig. 7(a), three 4 GBd QPSK signals were
multiplexed within the 24 GHz bandwidth and for Fig. 7(b), three Nyquist-QPSK
signals of 8 GBd symbol rate were multiplexed in the same bandwidth (dashed
curve).

Figure 7: Measured Optical spectra before (dashed curves) and after (solid
curves) demultiplexing without any transmission fiber of significant length.
For (a) three 4 GBd QPSK signals were orthogonally time multiplexed in a 24
GHz bandwidth (blue rectangle). For (b) three 8 GBd Nyquist-QPSK signals were
multiplexed in the same bandwidth. The red rectangle shows the spectral region
of the data information after demultiplexing.

Furthermore, to evaluate the optical operation bandwidth, Nyquist-QPSK signal
transmission experiments were carried out at different carrier frequencies. We
chose three nominal central frequencies of 195.90 THz (1530.3341 nm), 193.40
THz (1550.116 nm), and 192.65 THz (1556.151 nm) in accordance with the
recommendation of the international telecommunication union (ITU-T
G.694.1(10/20)). The experimental setup adopted here is the same as the
previous one except for the operating laser frequency. The spectrum at 193.4
THz (1550.116 nm) has already been presented above. The measured optical
spectra for the other two frequencies after demultiplexing have been presented
in Fig. 8, and the data transmission metrics are summarized in Table. III for
30 km SMF transmission.

It can be seen that the performance of the demultiplexer is very similar at
this wide frequency range spanning almost the full C-band (1530 nm - 1560 nm)
with estimated BER values of the order of $10^{-10}$ after 30 km of SMF
transmission. A limitation in the operational wavelength range would mainly be
determined by wavelength-dependent grating couplers for optical coupling to
the chip and on-chip multimode interferometers used for splitting and
combining the MZM arms. However, the basic principle can be implemented for
any carrier frequency of interest belonging to any communication band.

Figure 8: Measured Optical spectra at central frequencies of (a) 192.65 THz, and (b) 195.90 THz after demultiplexing a 24 GBd Nyquist-QPSK channel to three 8 GBd Nyquist QPSK channels for 30 km SMF transmission. TABLE III: Signal metrics for the demultiplexed 8 GBd Nyquist QPSK signal at different central frequencies after 30 km SMF transmission Central frequency |  $Q$-factor | Average EVM
---|---|---
(THz) | (dB) | (%)
192.65 | I $=15.92985\pm 0.29706$ | $16.1480\pm 0.3467$
Q $=15.91293\pm 0.16985$
193.4 | I $=16.22659\pm 0.36605$ | $15.9707\pm 0.9316$
Q $=16.1480\pm 0.3467$
195.95 | I $=16.174\pm 0.43588$ | $16.0940\pm 0.2871$
Q $=16.13527\pm 0.50083$

The demultiplexing of the Nyquist data channel is based on the convolution
between the incoming optical signal with the bandwidth $B$ and the three-line
frequency comb, generated in the modulator by driving it with one single RF
frequency $\Delta f$. For a CW optical line as input, a flat three-line
frequency comb with a frequency spacing of $\Delta f$ would be the result of
the convolution. Thus, as long as the modulator can generate this three-line
comb for a CW input, it would be able to demultiplex a corresponding Nyquist
data signal with a bandwidth of $3\Delta f$. Therefore, to demonstrate the
tunability of the pulse repetition rate and bandwidth, we have generated flat
rectangular three-line optical frequency combs (OFCs) of different frequency
spacings $\Delta f$. The bandwidth of the comb ($3\Delta f$) defines the
maximum possible aggregate symbol rate per carrier for demultiplexing. The
input radio frequency to the modulator was varied for an unmodulated CW
optical input, and waveform measurements were carried out with an oscilloscope
after photodetection. The output OFCs of bandwidth ($B=3\Delta f$) are
presented in Fig. 9(a)-9(c) for input radio frequencies of $\Delta f=$10 GHz,
20 GHz, and 30 GHz respectively. The flatness of the measured combs was around
0.1 dB. Although the modulator’s 3 dB electro-optic bandwidth is 16 GHz (see
Fig. 3(d)), OFCs with a much higher spacing could be generated. The RF power
to the modulator was kept constant at 4 dBm while the input voltage to the
thermal phase shifters was varied to suppress the carrier relative to the
sideband in order to get the desired flat comb. However, this over-driving
comes at the expense of decreased optical output power of the comb as evident
from Fig. 9. However, even for the 90 GHz comb the signal to noise ratio is
still around 20 dB, which should be sufficient for demultiplexing

Figure 9: Measured Optical spectra of non-filtered three-line rectangular
phase locked OFCs of (a) 10 GHz, (b) 20 GHz, and (c) 30 GHz spacing under
identical RF input power. (d) Measured Nyquist pulse sequence of 60 GHz
bandwidth, generated with the 16 GHz modulator. The values for the power
difference between the comb and next unwanted sideband are noted.

Due to nonlinearities associated with the carrier dispersion effect and
nonlinear transfer function, silicon PN junction modulators have a higher
nonlinear response compared to LiNbO3 modulators based on the linear electro-
optic effect (Pockels effect). These nonlinearities result in higher order
sidebands in the modulated spectra. The difference between the comb power and
the next unwanted sideband is noted for Fig. 9(a) and 9(b). It is worth noting
that no optical filters were used to suppress the unwanted sidebands and the
suppression was very high. The results show considerable improvements upon the
reported ones for silicon modulators [29, 31]. In Fig. 9(d) a measured pulse
waveform is presented for an OFC of 20 GHz spacing, resulting in a 60 GHz comb
as shown in Fig. 9(b). It resembles the ideal pulse waveform (in black-dashed)
very closely with a root mean square error (RMSE) of 0.699%. Pulses beyond
this bandwidth were not measurable with available experimental resources.

##  IV Conclusions

In conclusion, we have experimentally demonstrated real-time reconfigurable
demultiplexing of quadrature amplitude modulated Nyquist channels in silicon
photonics over the entire C-band, where all the parameters like channel
selection and channel bandwidth can be electrically controlled. Due to
limitations in the transmitter electronics we were restricted to single
carrier line rates of 48 Gbit/s. However, with a modulator having 16 GHz 3 dB
bandwidth, it was possible to generate three-line rectangular phase locked
frequency combs with 30 GHz comb spacing leading to 90 GHz sinc-pulse
sequences. It is the highest bandwidth flat optical three-line frequency comb
reported so far in silicon photonics. The technology platform facilitates
monolithic integration of photonic and electronic components on the same
silicon substrate. Among other devices, this technology offers silicon
germanium hetero-bipolar transistors with up to 220 GHz transit frequency and
germanium photodiodes with more than 60 GHz electro-optical 3 dB bandwidth
[26]. Hence, the presented Si-MZM based demultiplexing technique enables the
demultiplexing of Nyquist signals with single carrier symbol rates up to 90
GBd (corresponding to five times the electro-optic bandwidth of the modulator)
in a coherent Nyquist transceiver with three parallel silicon photonic
receivers of only 15 GHz detection bandwidths.

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