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Abstract
We demonstrate for the first time, to the best of our knowledge, reconfigurable and real-time orthogonal time-domain detection of a high-bandwidth Nyquist signal with a low-bandwidth silicon photonics Mach-Zehnder modulator based receiver. As the Nyquist signal has a rectangular bandwidth, it can be multiplexed in the wavelength domain without any guardband as a part of a Nyquist-WDM superchannel. These superchannels can be additionally multiplexed in space and polarization. Thus, the presented demonstration can open a new possibility for the detection of multidimensional parallel data signals with silicon photonics. No external pulse source is needed for the receiver, and frequency-time coherence is used to sample the incoming Nyquist signal with orthogonal sinc-shaped Nyquist pulse sequences. All parameters are completely tunable in the electrical domain. The feasibility of the scheme is demonstrated through a proof-of-concept experiment over the entire C-band (1530 nm–1560 nm), employing a 24 Gbaud Nyquist QPSK signal due to experimental constraints on the transmitter side electronics. However, the silicon Mach-Zehnder modulator with a 3-dB bandwidth of only 16 GHz can process Nyquist signals of 90 GHz optical bandwidth, suggesting a possibility to detect symbol rates up to 90 GBd in an integrated Nyquist receiver.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. 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 signals offer the most efficient way of multiplexing in the wavelength domain since they enable a rectangular bandwidth [4]. Thus, several of such channels can be multiplexed to build a Nyquist-WDM superchannel without any guardband between the single channels [5]. A Nyquist-WDM superchannel can exploit the available channel bandwidth for data transmission in the maximum possible way. Such Nyquist-WDM superchannels can be further used along with other parallel transmission techniques such as polarization and space multiplexing [1,5,6]. Nyquist signals have some more unique advantages like 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 [4,7–12], which make them very attractive for communication purposes.
There has been an abundant exploration of Nyquist signal generation through sinc-shaped Nyquist pulse shaping and multiplexing techniques. However, the reception techniques are limited to a few. Detecting sinc-shaped orthogonal time-domain multiplexed channels requires 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) [13], or by a polarization-sensitive nonlinear optical sampling with synchronous control pulse trains of much higher bandwidth in a nonlinear optical loop mirror (NOLM) [7,10,11,14,15]. For the sinc-shaped orthogonal time-domain gate, linear optical sampling in a coherent receiver using Nyquist pulse sequences as the local oscillator (LO) [16–19], optical Fourier transform (OFT) [20], and optical parametric amplification [21] 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 [22–26]. 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 reconfigurable Nyquist pulse sources operating at different spectral bands nor tunable delay lines. Channel selection is achieved merely by phase shifts in the electrical driving signals to the modulator. Additionally, it is possible to demultiplex higher-order quadrature amplitude modulated (QAM) channels in a real-time and dynamic manner with a single MZM [5,6,27]. Nyquist-WDM superchannels can be demultiplexed without the need for optical filters by the adjustment of the local oscillator wavelength [5].
Based on the convenient setup and the basic integrability of the optical and electronic components, this detection 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 [28,29]. 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 [30,31]. Recently, sinc-shaped Nyquist pulse sequence generation with various silicon-based MZM structures has been demonstrated [23,32–34], and their quality has been analyzed in detail [35]. However, the demonstration of the reception of high-bandwidth Nyquist signals in any integrated platform with low-bandwidth equipment is yet to be reported.
Here we present for the first time, to the best of our knowledge, the experimental demonstration of the detection of high-bandwidth Nyquist signals in low-bandwidth silicon photonics. A high-capacity and high-bandwidth Nyquist QAM signal has been divided to three lower bandwidth signals 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). QPSK modulated Nyquist channels 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 receivers with single carrier symbol rates of 90 GBd.
2. MZM-based Nyquist receiver
The basic principle behind the integrated receiver is the multiplication between the received modulated Nyquist signal of optical bandwidth $B$ and an unmodulated sinc-shaped optical Nyquist pulse sequence with the same bandwidth and a repetition rate of $B/N$ in $N$ parallel receiver branches. This multiplication reduces the symbol rate of the incoming signal by the factor $N$ but preserves the symbol points for detection.
For an $N$-branch system, the receiver setup is illustrated in the upper part of Fig. 1 and the lower part illustrates the down-conversion for $N=3$. For the incoming high-bandwidth signal depicted in Fig. 1(a) and Fig. 1(b) the symbols are designated in red, blue and green dots. By the multiplication with a sinc-pulse sequence having an appropriate time shift (the red curve in Fig. 1(c)) will extract only the symbols designated in red. Similarly, the blue and green points can be extracted simultaneously in the second and third branches. As a result, the detector and signal processing electronics in each branch require only a bandwidth of $B/(2N)$.
For all of the optical Nyquist reception techniques reported so far, external pulse sources are required for sampling [7,10,11,14,15,17–19]. However, for the method presented here, 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 [22,23]. The multiplication occurs for the full-field, thereby achieving coherent sampling [24,25].
Fig. 1. Basic configuration of a Nyquist signal receiver using MZMs and sinc-shaped Nyquist pulse sequences. In the upper part, a complete generalized system is shown where an optical Nyquist signal of bandwidth $B$ is divided into $N$ Nyquist channels of baseband bandwidth $B/(2N)$. The lower part presents the signal processing steps for one of the branches and $N=3$ (the MZM is driven with one sinusoidal radio frequency). The input Nyquist signal $s(t)$ can be expressed as a sum of time-shifted ideal sinc-pulses modulated with the data symbols (in (a)). The same Nyquist signal can also be seen as the summation of time-shifted sinc-sequences modulated with the data symbols (in (b)). The sinc-sequence shown here represents a rectangular 3-line comb. After undergoing, sinc-sequence sampling at one of the MZMs, the sampled signal $\tilde {s_l}(t)$ is shown in (c). Finally, after low bandwidth detection the low bandwidth Nyquist signal $s_l(t)$ is shown in (d). Note that if the MZM is driven with a single RF tone, the corresponding sinc-sequence will have two zero crossings between two peaks. Thus for the extraction of the full information, $N=3$ parallel branches are required. The black lines correspond to optical and the blue to electrical connections. RF4: $n$-tone RF signal source, MZM: Mach-Zehnder modulator, RFG: single tone radiofrequency generator, LPF: electrical lowpass filter, CD: coherent detector.
The operation principle for a receiver with $N$ branches is presented in the upper part of Fig. 1. A Nyquist signal of optical bandwidth $B$ is detected 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 RF tone and the RF bandwidth of the modulator has to be just $B/3$ for a three-branch system. An even number of lines can be achieved by changing the operating point of the modulator, and it can be used for the method as well. But it needs the effective suppression of the carrier, which can be experimentally challenging, and therefore the signal-to-noise ratio increases [4]. Alternatively, a dual-drive MZM can be used for effective carrier suppression along with the suppression of the second-order sidebands. However, in our experiment, we were driving the integrated MZM with one RF frequency. Thus, we chose the simplest setup for the proof-of-concept experiment.
After the orthogonal time-domain sampling with the correct input phase shifts, the signal with the optical bandwidth $B$ is detected in each branch with a baseband 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 [36]. However, it can also be generated all-optically via modulation and time-domain multiplexing of spectrally shaped mode-locked laser pulses [7] or Nyquist pulse-sequences synthesized by one or more cascaded modulators [4,5,37]. Therefore, we shall show how regardless of the origin, the high-bandwidth Nyquist signal can be divided into 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 $B$ [4,23,24]. This three-line sinc-sequence can be used to transmit three multiplexed Nyquist channels with a symbol rate of $B/3$ for three single channels or an aggregated symbol rate of $B$ if the three channels are multiplexed to one single Nyquist channel in the optical bandwidth $B$. So, regardless of ideal sinc pulses or sinc-sequences are considered, if the signal consists of different orthogonal sub-channels, or it is one single high-bandwidth Nyquist channel, 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,
with $l=1,2,\ldots,N$, 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,
Therefore, if the incoming high-bandwidth signal is split into $N$ branches, the division 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. Besides, the above mathematical discussion implies that the treatment is valid for any $N$. 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).
As can be seen from Fig. 1, for the demultiplexing, $N$ orthogonal sinc-sequences are required at the receiver. Thus, the time delay between the $N$ sequences is important, which can be ensured by the adjusting the electrical phases at the input to the modulators [4]. There can be a transmission delay because of the length mismatches in the three demultiplexer arms (between the splitter and the MZM). For our experiment, it was not the case. However, in a situation where the delay exists due to some design space constraint and different waveguide routing, it can be fully compensated by tuning the electrical phase at the input of the respective modulator. Suppose there is a change in the fiber length and a delay due to transmission. In that case, the alignment of one of the branches ensures that all the other branches will be automatically aligned due to the fixed phase difference between them. An alignment of the sinc-sequence to the signal can be achieved by scanning one of the sinc-sequences through the incoming signal by changing the electrical phase from 0 to $2\pi /N$ and monitoring the resultant eye diagram.
3. Experiment and results
In this section, the proof of concept experimental details, characterization of the silicon photonic MZM, and data transmission results are presented. First, the performance of the Si-MZM as a Nyquist time-domain receiver 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 receiver based on the presented MZM.
For the sake of experimental simplicity and due to a lack of high-bandwidth equipment, 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 [5]. Afterward, we received each of them separately by the silicon photonic MZM. Following the theory section, this is equivalent to dividing one single, high data rate Nyquist signal into $N$ lower data rate sub-channels.
3.1 Experimental setup and device
For the experimental demonstration, a setup as illustrated in Fig. 2 was adopted. A wavelength-tunable CW laser with 100 kHz linewidth was modulated with a Nyquist signal containing three different data streams that are orthogonally multiplexed with sinc-shaped Nyquist pulse sequences in the time-domain (see Eq. (1)). The electrical signals were generated from arbitrary waveform generators (AWGs) operating with a sampling rate of 48 GS/s. Please note that according to Eq. (1) and Eq. (4), the result is the same as if one single channel had been modulated with a Nyquist signal with three times the bandwidth. After transmission through standard single-mode fiber (SMF), the Nyquist signal was subjected to the silicon electronic-photonic co-integrated MZM. The insertion loss of the MZM without any applied voltage was measured to be around 9 dB excluding the grating coupler losses. The relatively high number can be attributed to the long MZM phase shifter arms designed to achieve a full $\pi$ phase shift at high-speed operation. After 20 m SMF transmission, a coherent detector detected the low symbol rate 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 lowpass 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 generated Nyquist signal at the transmitter. As the transmitter was limiting the symbol rate to $B=24$ GBd, the receiver bandwidth was restricted to 4 GHz ($B/6$) via low pass digital filtering. EDFAs along with BPFs to reduce the amplified spontaneous emission noise were used to compensate for the coupling losses of the chip. Polarization diversity was not employed in the proof of concept experiment.
Fig. 2. Schematic illustration of the experimental setup. A single carrier from an integrated tunable laser assembly (ITLA) is modulated with high-capacity Nyquist signals. After transmission through single-mode fiber (SMF), the channels are processed by the Si-MZM before detection by a coherent detector. The structures of a typical single-polarization coherent detector (CD) and the offline digital signal processing (DSP) stages are shown in the insets on the right side. AWG: arbitrary waveform generator, EDFA: Er-doped fiber amplifier, BPF: bandpass filter, MZM: Mach Zehnder modulator.
Fig. 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 an RF 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 using BiCMOS technology from IHP (SG25H5_ePIC). This technology allows monolithic integration of high-frequency driver circuits and 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 [38], 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 [39]. 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 bond wires 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).
3.2 Results and discussion
For the proof-of-concept experiments, a 24 GBd Nyquist-QPSK channel was created in an optical bandwidth of 24 GHz (maximum spectral efficiency of 1 symbol/sec/Hz) by three low-bandwidth sub-channels modulated with Nyquist signals of $B/3=8$ GBd symbol rate. Here the symbols were shaped by digital filtering using raised-cosine filters with $0.0$ roll-off factor and baseband width of 4 GHz. In the experiments, we were restricted by the sampling rates (48 GS/s) of the used arbitrary waveform generators to a maximum data rate of 48 Gbit/s. For the Nyquist pulse sampling at the modulator, we adopted the driving condition to the modulator at which sinc-shaped Nyquist pulse sequences could be generated [4,23,32]. The RF power to the modulator was kept constant at 4 dBm while the input voltage to one of the thermal phase shifters could be varied to adjust the carrier power relative to the sidebands to get the desired flat rectangular three-line comb. During the experiment, the Arm-1 bias (see Fig. 3) was adjusted to around 2.35 V to get the desired comb. It is to be noted that the input voltage to the Si-MZM is not directly applied to the silicon PN phase shifters but to the co-integrated segment drivers. A large input RF power will saturate the on-chip drivers. Beyond saturation, the power in the fundamental frequency does not increase while the higher-order harmonics rise significantly. We found 4 dBm as a suitable input power that compensates for the electrical losses from the probe setup while keeping the power in the harmonics low. Low higher harmonic power leads to a better quality of the generated Nyquist pulses necessary for the experiments [35].
For one of the 8 GBd Nyquist-QPSK signal branches, the symbol constellations and eye diagrams are presented in Fig. 4, with the measured signal metrics presented in Table 1 after 10 km and 30 km of SMF transmission. The optical signal-to-noise ratio values before division 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. 5(a), all the three 8 GBd Nyquist-QPSK signals from the 24 GBd Nyquist channel have similar performance for a certain distance of fiber transmissions. All the measured BER values are far away from the limit for HD-FEC coding with 7 % overhead.
Table 1. Measured performance metrics for 1/3 of the 24 GBd Nyquist-QPSK channel around 193.4 THz.
All the measurements of the signal metrics were done following the decision threshold method [40] 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 interval. We were also limited by the capacity of the digital storage hardware used for offline DSP. Thus, recording a higher amount of data for the offline DSP was impossible. Therefore, BER values were estimated from the $Q$-factors (in linear scale), following the relationship $\mathrm {BER}_{est}\approx (1/2) \mathrm {erfc}(Q/\sqrt {2})$ [41]. An optical signal-to-noise ratio (OSNR) dependence of the BER for a Nyquist OTDM transmission system based on non-integrated LiNbO3 modulators was carried out using the same formula where the experimental and computed values agreed closely [6]. Later in this section, we will present that, although the modulation mechanism is different, the quality of the generated Nyquist pulses from the silicon modulator is comparable to that produced by the LiNbO3 modulators. Therefore, the demonstrated silicon modulator-based Nyquist receiver should follow a similar OSNR dependence except for a constant offset arising from the fiber-to-chip coupling loss and the insertion loss.
Fig. 4. Measured Symbol constellations and eye diagrams for 1/3 of the 24 GBd Nyquist channel with a carrier of around 193.4 THz after (a) 10 km and (b) 30 km SMF transmission. The residual 66% of the channel information can be detected by a phase shift of the sinusoidal frequency driving the modulator, or by two additional parallel branches.
Fig. 5. (a) Measured $Q$-factors (in black) and estimated BER values (in red) for different transmission ranges of all three 8 GBd parts received from the 24 GBd Nyquist channel. (b) Measured Optical spectrum before (dashed curves) and after (solid curves) division without any transmission fiber of significant length. The red rectangle shows the spectral region of the data information after division. The required detector bandwidth in each branch corresponds to half of this bandwidth (green region).
The optical spectrum of the transmitted Nyquist signal (dashed lines) and the divided signal (solid lines) around a single carrier at 193.4 THz can be seen in Fig. 5(b). Please note that the division is based on convolution with the three-line comb. Thus, the spectra of the input Nyquist signals have a rectangular shape (dashed lines), and the spectral content broadens due to the division. However, the whole information of the signal is confined in the $B/3$ fraction of the bandwidth around the carrier (red rectangle), resulting in a required electrical detector bandwidth of $B/6$ (in green).
Furthermore, Nyquist-QPSK signal transmission experiments were carried out to evaluate the optical operation bandwidth 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 division have been presented in Fig. 6, and the data transmission metrics are summarized in Table 2 for 30 km SMF transmission.
Fig. 6. Measured Optical spectra at central frequencies of (a) 192.65 THz, and (b) 195.90 THz after dividing a 24 GBd Nyquist-QPSK channel into three 8 GBd sub-channels for 30 km SMF transmission.
Table 2. Signal metrics for the 8 GBd Nyquist QPSK signals at different central frequencies after 30 km SMF transmission
It can be seen that the performance of the receiver 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.
The division of the high-bandwidth Nyquist data channel into the low-bandwidth sub-channels 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 detect a corresponding Nyquist data signal with a bandwidth of $3\Delta f$. Therefore, to demonstrate the pulse repetition rate and bandwidth tunability, 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 symbol rate per carrier. The input radio frequency to the modulator was varied for an unmodulated CW optical input, and the waveforms were captured in an oscilloscope after photodetection. The output OFCs of bandwidth ($B=3\Delta f$) are presented in Fig. 7(a)–7(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 one of 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. 7. The most critical source of the signal to noise ratio associated with the Nyquist pulses is the existence of the spurious harmonics. However, even for the 90 GHz comb, the SNR is still around 20 dB. Simulation and experimental results have shown that even at 20 dB, the generated Nyquist pulses follow the theoretical waveform very closely with negligible root mean squared error [35]. Thus sideband suppression of 20 dB should be sufficient for the presented method.
Due to nonlinearities associated with the carrier dispersion effect [42] and nonlinear transfer function (cosine shaped), 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. 7(a) and 7(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 [32,34]. In Fig. 7(d) a measured pulse waveform is presented for an OFC of 20 GHz spacing, resulting in a 60 GHz comb as shown in Fig. 7(b). It almost resembles the ideal pulse waveform (in black-dashed) with a root mean square error (RMSE) of 0.699%. Pulses beyond this bandwidth were not measurable with available experimental resources.
Fig. 7. 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 measurement was carried out at the oscilloscope with 64 times averaging. The values for the power difference between the comb and the next unwanted sideband are noted.
4. Conclusions
In conclusion, we have experimentally demonstrated real-time reconfigurable detection of high-bandwidth Nyquist channels in low-bandwidth 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 3 dB bandwidth of 16 GHz, 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 [29]. Hence, the presented Si-MZM based detection technique enables the reception 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.
Funding
Bundesministerium für Bildung und Forschung (13N14879); Deutsche Forschungsgemeinschaft (322402243, 403154102, 424607946, 424608109, 424608191, 424608271).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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