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Experimental Demonstration of a Silicon-Photonics WDM
NFT Soliton Transmitter
J. Koch1*, A. Moscoso-Mártir2, J. Müller2, A. Tabatabaei Mashayekh2, A. D. Das2, F. Merget2,
S. Pachnicke1, J. Witzens2
(1) Chair of Communications, Faculty of Engineering, Kiel University, Kaiserstraße 2, 24103 Kiel, Germany
(2) Institute of Integrated Photonics, RWTH Aachen University, Campus Blvd. 73, 52074 Aachen, Germany
jonas.koch@tf.uni-kiel.de
Abstract: We experimentally demonstrate a silicon-photonics transmitter capable of modulating
and optically merging solitons with different frequency and time spacing based on the nonlinear
Fourier-transform, offloading electronics. Two soliton channels successfully transmit up to
5000 km.
OCIS codes: (060.4370) Nonlinear optics, fibers; (250.3140) Integrated optoelectronic circuits.
1. Introduction
Today’s communications systems require a steady increase in data rate and hence spectral efficiency. This requires
high signal powers, at which fiber nonlinearities ultimately limit the transmittable amount of data. Many approaches
are being followed to cope with the inherent nonlinearity of the fiber-optic channel. One approach is the nonlinear
Fourier transform (NFT), which is a tool to linearize the nonlinear propagation through the fiber [1]. Using the NFT,
the information is encoded in parallel sub-carriers (eigenvalues (
!
" #$
of the Lax operator determined by the ideal
nonlinear Schrödinger equation (NLSE)). Here,
!
stands for discrete complex-valued eigenvalues, which modulate
solitons, while
#
spans the whole real axis and describes the dispersive part of the signal, which can be compared to
the common Fourier transform. All eigenvalues and their modulated spectral amplitudes (
%
&
!
$
" %&#$
) pass through an
idealized noiseless and lossless fiber in a purely linear manner without interference [1].
In this paper, the discrete (solitonic) part of the spectrum is utilized solely. Here, multiple eigenvalues can be combined
by sophisticated numerical algorithms to create higher-order solitons, which maintain solitonic behavior. However,
the digital-to-analog conversion of such pulses can be demanding in terms of sampling-rate and vertical DAC
resolution [2]. To decrease the DAC requirements, we propose to merge first-order solitons in the optical domain
instead [3], thus combining optical and electrical processing to offload the electronics where they run into their
performance limitations. This requires a high degree of accuracy in terms of the separation of the merged solitons in
the time and frequency domains, which can be ensured by the degree of stability afforded by a monolithically
integrated silicon photonics (SiP) transmitter [4]. In this paper, we present the realization of an SiP transmitter (Tx)
that can modulate up to four first-order solitons and multiplex them with a variable time-delay by means of a delay
network implemented with coupled (ring-) resonator optical waveguide (CROW) optical add-drop multiplexers
(OADMs) [5]. The fabricated transmitter supports up to 4 channels for a combined data rate between 8 Gb/s and 16
Gb/s depending on the selected channel time spacing [4]. Initial tests modulating and multiplexing two first-order
solitons are presented here to demonstrate the feasibility of optical soliton multiplexing with an architecture optimized
for merging partially spectrally overlapping pulses [4]. The proposed solution shows that a pulse containing multiple
eigenvalues can be created in a scalable manner with reduced requirements for the electro-optical conversion.
2. Experimental setup and transmitter link budget
The experimental setup is depicted in Fig. 1. After data generation and modulation (QPSK), 60 blocks of 2000 first-
order solitons (
'!"#$ ()*+
,
-." )
,
/01
) are being transmitted. Since only two channels with a time spacing of 500
ps are used, the resulting data rate is 4 Gb/s in this experiment. The electrical signal is generated by an arbitrary
waveform generator (Keysight M8196A) using 88 GSa/s with an electrical bandwidth (BW) of around 30 GHz that is
amplified to achieve 4 Vpp. On the transmitter side, two lasers with 100 kHz linewidth, wavelengths of
!%(
)+23435
,
67,
and
!&()+2348
,
67"
and powers of 11 dBm and 15 dBm, respectively, are used and coupled together
using a 3-dB coupler prior to being injected into the chip. The utilization of different power levels for the two channels
is needed to balance the extra insertion loss (IL) added by the delay network to the second channel. The total injected
power of 13.4 dBm is close to the maximum possible input power of 16 dBm limited by the damage threshold of the
input grating coupler (GC), with IL = 3.75 dB. Inside the chip, 2nd-order CROW OADMs (IL = 2 dB, BW = 7.5 GHz)
route the two carriers to complementary input ports of one of the IQ Mach-Zehnder modulators (MZMs), after which
they are also picked up at the complementary output ports, allowing the emulation of two channels with a reduced
amount of hardware [4]. The designed IQ-MZMs [6,7] have 4.4 mm long phase shifters, a BW of 14 GHz optimized
for the present application, a VpL of 2.86
9
:;7
and below 4 dB IL. Operated with close to optimum 4 Vpp signals,
given the RF losses of interposed cables and of the PCB, and biased to achieve full extinction during soliton shaping,
the IQ MZM introduces an IL and modulation penalty of 7.7 dB, defined here as the attenuation of the peak power
after modulation since the average power is very dependent on soliton pulse packing and thus on the modulation
format. Afterwards, channel 2, that due to experimental restrictions carries the same information as channel 1, is
delayed by 500 ps (IL = 4 dB) as a means to emulate two independent channels. Both channels are multiplexed onto
one bus waveguide using two 4th-order CROW OADMs (IL = 3 dB, BW = 17.5 GHz). Finally, a multimode
interferometer coupler (MMI), with IL > 3dB due to reciprocity, combines the bus waveguide with a second bus
waveguide that can carry another two channels spectrally overlapping with those of the first one, enabling dense
spectral packing of soliton pulses. The signal is then routed off chip via a second GC. Since we have used only two
channels for the experiments, the second bus connected to another IQ-MZM was not used. Including interconnection
and monitor tap losses (3 dB), we obtain a soliton peak power of -18.2 dBm per channel. More details on the chip
architecture can be found in [8].
The optical output signal of the chip is pre-amplified before being fed into a fiber-optical loop consisting of four spans
of 50 km True-Wave non-zero-dispersion-shifted fiber (NZDSF) and EDFA amplifiers, to reach an average launch
power of -4 dBm for the two combined channels that fulfills the soliton condition. At the Rx side, an additional EDFA
boosts the signal to a sufficient power level to be detected by the coherent receiver (Neophotonics μICR-Class 40,
BW = 40 GHz). Excess ASE noise is then filtered out with a bandpass filter (BW = 20 GHz) centered on the channel
under test and the polarization set. The local oscillator (1 kHz linewidth) wavelength is set to the channel under test.
Analog-to-digital conversion is done using a Keysight DSOZ334A oscilloscope (80 GSa/s). After analog-to-digital
conversion, a digital filter set to the bandwidth of the transmitted first-order solitons is implemented. Afterwards, the
signal is synchronized and normalized into NFT units. Thereafter, an NFT is employed and the fiber-induced linear
phase rotation is de-rotated. This is followed by the carrier-frequency-offset compensation and phase recovery. An
optional linear MMSE equalization [9], which uses the known deviations of λ (correlated to deviations of
%&!$
), is
also implemented. Finally, the received
%
&
!
$ is demodulated, and bit-errors are counted for the detection of the BER.
3. Results and discussion
Figure 2(a) shows the resulting raw BER for different transmission distances with and without MMSE equalization
applied to channel 1. Without any equalization, a transmission reach of 4200 km is achieved with BERs below the
assumed 14.5% overhead SD-FEC limit of 1.25e-2. The MMSE equalizer (2000 training symbols) is leading to BER
improvements, especially for lower transmission distances. This leads to a transmission distance of 5000 km below
the SD-FEC limit. The qualitative gain of using the MMSE-equalizer is depicted by the constellations in Figs. 2(b)
and 2(c). Here, one can see the impact of noise reduction on the constellation, leading to nearly error free transmission
up to 3400 km. Similar results were obtained for channel 2.
One point of interest in the BER curves is at the transmission distance of 4600 km, where the BER is worse than at a
longer transmission distance of 5000 km. This can be explained by the nature of soliton collisions as is exemplarily
depicted in Fig. 3. Here, the eye-diagrams of the received soliton pulses are shown after different transmission
distances. In order to create these diagrams, the receiver filter is set to 50 GHz with a center wavelength of 1546.79 nm,
between the carrier wavelengths of the two transmitted channels. Besides, the receiver local oscillator is also set to
Fig. 1. Block diagram of investigated link. First-order solitons are created digitally and converted into analog signals by an arbitrary waveform
generator. Two solitons are then transduced and optically merged to higher-order solitons by a PIC, combining electrical and optical processing.
Laser λ1/2
2x2
Coupler
CO Rx ADC
50 km
50 km 50 km
Recirculating
loop
( x km)N200
50 km
Digital Filter
Synchronisation & Normalization
NFT & linear backshift
CFO compensation
Carrier-phase correction
Optional MMSE EQ
Demodulation
BER
AWG
AOM
AOM
INFT & Denormalization
Data Generation & Modulation
b( )λ λ = 0.5j
50 GHz
20 GHz
100 GHz
40 GHz
30 GHz30 GHz
PCB
SiP
Lasers
λ2
λ1
1546.79 nm, so that both channels are received at the same time. Figure 3 shows that a “collision-cycle” of ~1000 km
is the result of the frequency spacing and the dispersion-parameter of the employed NZDSF (1035 km for
<
( 24+,-. =
&
67 =>7
$
'%" ?! ( *4@A
,
67$
. This leads to maximally separated solitons at distances of
)***,>7 = B" B C D
, and
total collisions at distances of
+**,>7 E)***,>7 = B
. Since the distance of 4600 km is close to such a full collision
(exemplarily depicted in Fig. 3, center, at 600 km), cross-phase modulation of the channels leads to shifts of the
eigenvalues and their modulated NFT coefficients, worsening the BER performance. This is most pronounced at the
point of full collision and is a consequence of the NFT being applied to the 2 channels individually. This is especially
visible after using an MMSE equalizer, in which case this phenomenon can also be seen at a distance of 3400 km
(close to a collision), where the BER is comparable to the BER at 3800 km (close to full separation) even though the
latter is at a considerably longer distance. This can be considered as a soliton WDM penalty [4].
3. Conclusions
In this paper, we have presented an experimental 2-channel WDM soliton transmission employing an SiP transmitter
for the soliton modulation and merging. In these experiments, 2 Gb/s per channel were transmitted up to 4200 km
below the SD-FEC limit without equalization and up to 5000 km by using an MMSE equalizer. Additional
equalization techniques could be used to improve the maximum reach, for example by taking WDM interactions of
closely multiplexed solitons into account [4,10]. The presented transmitter can multiplex up to 4 channels with closer
frequency and time spacing, leading to DWDM soliton transmission with higher data rates. These could be further
scaled up by adding more channels without increasing DAC requirements, exploiting polarization diversity and by
concomitantly exploiting the dispersive (continuous) portion of the spectrum. In this way, the soliton transmission
would act as an add-on to the already available system bandwidth.
4. References
[1] S. K. Turitsyn et al., “Nonlinear Fourier transform for optical data processing and transmission: advances and perspective,” Optica 4(3), 307-
322 (2017).
[2] J. Koch et al., “Transmission of Higher Order Solitons created by Optical Multiplexing,” J. Lightw. Technol. 37(3), 933-941 (2019).
[3] S. Li et al., “Optical signal processing in the discrete nonlinear frequency domain,” Proc. Opt. Fiber Commun. Conf. & Expo., W2A.40 (2018).
[4] J. Koch et al., “Silicon Photonics DWDM NLFT Soliton Transmitter,” Proc. 21st ITG-Symposium on Photonic Networks, 93-100 (2020).
[5] F. Xia et al., “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt.
Expr. 15(19), 11934-11941 (2007).
[6] F. Merget et al., “Silicon photonics plasma-modulators with advanced transmission line design,” Opt. Expr. 21(17), 19593-19607 (2013).
[7] S. S. Azadeh et al., “Advances in silicon photonics segmented electrode Mach-Zehnder modulators and peaking enhanced resonant devices,”
Proc. SPIE 9288, 928817 (2014).
[8] A. Moscoso-Martir, et al., “Silicon Photonics DWDM NLFT Soliton Transmitter Implementation and Link Budget Assessment,” Proc. Europ.
Conf. Integr. Opt. (ECIO), Paris, France, June 2020.
[9] T. Gui et al., “Alternative Decoding Methods for Optical Communications Based on Nonlinear Fourier Transform,” J. Lightw. Technol. 35(9),
1542-1550 (2017).
[10] J. Koch, et al., “Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication,” J. Sel. Top. in Quant. Electron.
(Early Access). DOI: 10.1109/JSTQE.2020.3045222.
Fig. 2. Transmission results for channel 1. (a) BER as a function of distance without equalization (blue, x) and after employing an MMSE equalizer
(red, triangle). For readability, the SD-FEC (1.25e-2, dashed line) limit is included. (b) Received constellation without equalization and (c) received
constellation after the MMSE equalizer after 3400 km transmission.
Fig. 3. Eye-diagrams of received solitons after different transmission distances. Here, the receiver-filters and local-oscillator were set so that both
channels could be received in one measurement. Both solitons collide at around 500 km (depicted 600 km, due to the 200 km loop length) and are
maximally separated again after 1000 km transmission.
