1. Introduction

Currently, the fastest real-time oscilloscopes achieve about 100 GHz conversion bandwidth and fully-integrated integrated circuit (IC) based analog-to-digital converters (ADC) around 40 GHz [1]. However, for both devices the available equivalent number of bits (ENOB) is limited by the aperture jitter of the sampling clocks in the order of hundred femtoseconds for microwave clock sources based on quartz oscillators [2], degrading the signal-to-noise ratio (SNR) of the digitized signal. Leveraging the extremely low timing jitter achievable with some classes of mode-locked lasers (MLL) [3], multiple photonically assisted ADC concepts have been investigated, including time stretching [4], spectral slicing [5] and time interleaving (TI) [6]. A common trait of the time- and frequency-interleaved ADC concepts is the down-conversion of the broadband signal by means of optical signal processing into multiple lower-speed signals that can be straightforwardly digitized by lower-speed, conventional electrical ADCs. This allows not only the digitization of broadband signals out of reach of the utilized electronic circuitry, but also reduced aperture jitter approaching that of the utilized optical clock [7].

In this work, we focus on the implementation of a pulse interleaver optimized for a TI architecture using a 25 GHz single-section semiconductor MLL as a light source and aimed at reaching up to 200 GS/s overall sampling rate, with a 100 GHz analog bandwidth comparable to that of best-in-class oscilloscopes and surpassing that of all-electrical chip-scale ADCs. Although a number of TI ADC systems have been reported in the literature [6,8–12], only a few employ on-chip integrated components [6,11,12], a fundamental requirement to scale the system up in a compact and robust form factor. The best integrated solutions demonstrated to date achieve 10 GHz conversion bandwidth with an ENOB of 3.5 [11] and 6.0 [12]. In the following, we present a concept to push the conversion bandwidth much further while maintaining signal quality with help of an equalization scheme. The pulse interleaver is implemented in a silicon nitride (SiN) photonic integrated circuit (PIC) in order to allow for high power handling [13] and thus improved SNR.

The expected capabilities of the entire ADC system are analyzed taking time- and frequency-domain crosstalk between the pulse trains into account [14–16]. Equalization of these in presence of different physical noise sources is further analyzed and presents an essential technique to scale up the bandwidth and ENOB of photonically enabled TI-ADCs. The interplay between the equalizer and system noise then leads to a tradeoff between analog bandwidth and sampling rate on the one hand and SNR and ENOB on the other, adjustable by the number of time interleaved channels. To the best of our knowledge, a cyclic equalization technique based on the system impulse response is applied for the first time in the context of optically enabled TI ADCs, showing a significant performance improvement.

After describing the TI ADC architecture in Section 2, we describe the implemented SiN pulse interleaver and pulse deinterleaver chips in Section 3. Section 4 describes the general problem of time- and frequency-domain crosstalk in TI ADCs and gives upper bounds for the system performance in the absence of equalization. The latter is introduced together with the modeled noise sources in Section 5. While the number of interleaved channels is assumed to be four up to that point, based on what was implemented in the chips, in Section 6 we expand the analysis to different channel numbers and exemplify the tradeoff between system bandwidth and ENOB. Section 7 takes a closer look at the ENOB limitations arising from the individual noise sources and discusses which technological constraints are the most important to further work on to extend the performance. The numerical models are entirely based on a Matlab code developed for this purpose and no dedicated commercial software was used.

2. Time interleaved ADC architecture

In this Section, we first present the system architecture of a four-channel TI ADC based on integrated pulse interleaver and deinterleaver chips consisting of a bank of four coupled (ring-)resonator optical waveguide (CROW) filters implemented in a silicon nitride platform, whose design and optimization is presented in Section 3.

In the TI ADC schematically represented in Fig. 1, a pulse train generated by an MLL with a pulse repetition time T is first demultiplexed into four channels by wavelength. To do so, the original pulse train is spectrally sliced into four pulse sub-trains, each with the same repetition period T, but with different center wavelengths. Designing the spectral passband filters to have a bandwidth significantly above that of the MLL free spectral range (FSR), the pulsed behavior is conserved at the expense of generating wider sub-pulses, since each sub-train is reduced in bandwidth. The sub-trains are subsequently routed through optical delay lines, incrementally delaying them relative to each other by increments of T/N, where N is the number of generated sub-trains, prior to being recombined. This results in interleaved pulse trains, allowing an N times faster sampling of an electrical signal by means of an electro-optic modulator (EOM), with each pulse taking an independent sample of the signal. In the analyzed system, we employ a dual output Mach-Zehnder modulator (MZM) to allow for differential detection, that is necessary to reduce the detrimental impact of laser relative intensity noise (RIN) and optical amplifier noise on the digitized signal quality, as analyzed in detail in Section 7. Each of the two outputs can be split again into N channels employing identical filters implemented at the front-end of a bank of parallel receivers. The differential photocurrents are subsequently converted by electrical ADCs clocked at a sampling rate of 1/T, coinciding with the initial repetition rate of the MLL and N times lower than that of the overall system. The resulting digital signals are interleaved back together by digital signal processing (DSP), so that reduced speed electrical converters can be employed to convert a signal with frequencies up to N times faster than their Nyquist frequency. As for frequency-sliced ADCs [7], with increasing number of slices (here pulse sub-trains), electronic aperture jitter plays a decreasing role due to the low speed of the electronic ADCs, so that MLL-jitter limited operation can in principle be obtained.

 

Fig. 1. Time-interleaved ADC architecture. Frequency (de)multiplexing and optical delay lines implementing differential group delays are employed to generate interleaved pulse trains with a higher overall repetition rate. After sampling of the electrical signal by means of a dual output EOM, the pulse trains are separated again and differentially received. The insets show the layout of the integrated pulse interleaver and deinterleaver components as implemented on the SiN PIC. The single inputs of both components, as well as the output of the interleaver, are implemented as edge couplers to minimize insertion losses. The outputs of the deinterleaver are implemented as grating couplers, that have higher losses but are also easier to package in large port counts.

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The pulse interleaver and deinterleaver have been realized in the LIGENTEC SiN platform with layouts shown in the insets of Fig. 1. Waveguide cores are fully etched in an 800 nm thick high-quality stoichiometric Si₃N₄ film fabricated by low pressure chemical vapor deposition (LPCVD) and fully clad by SiO₂. Due to the absence of two-photon absorption in the C-band and the reduced index contrast weakening scattering losses, this platform offers high-peak-power handling capability together with low propagation losses in the order of ∼0.1 dB/cm. These components have been conceived to rely on CROW filters, chosen for their high flexibility in synthetizing the desired flat-top and low group delay dispersion transfer functions, as described in Section 3. By opting for SiN, we aim to solve the problems reported in [6] by leveraging the lower waveguide dispersion and high power-handling capability offered by this platform compared to silicon-on-insulator (SOI) based PICs. The presented SiN structures have been experimentally verified to support up to 30 dBm input power without introducing any noticeable distortion in the filter transfer functions. Beyond 30 dBm, catastrophic failure has been observed at the input couplers.

While the current PIC only implements the passive components, it paves the way to the realization of a fully integrated system in which the EOM and PDs could also be integrated, for example working on a hybrid silicon/silicon nitride platform [17]. The integration of the system can be pushed even further by integrating a rare-earth [18] or semiconductor based MLL [19,20] on-chip, even though in the latter case locking to a lower jitter reference will probably remain a requirement to achieve low jitter operation. Microcavity generated combs [21,22] present a further alternative with a high potential for integration. The system reported here is actually intended to be operated with a single-section semiconductor MLL actively locked to a lower jitter solid-state laser, as a means to upconvert the latter’s repetition frequency, and the experimentally recorded spectrum of a concrete device serves for the system evaluation.

As described in detail in the next sections, the requirements of the optical filters, in terms of bandwidth and channel count, have to be carefully chosen based on the spectrum generated by the utilized light source. Employing semiconductor MLLs, for example, while straightforwardly providing relatively high power and large FSRs that are essential to reach high sampling rates, also limits the total usable spectrum bandwidth and thus the number of channels that can be implemented. In addition, the integrated components used here are also constrained in FSR by the technological choices and the utilized device topology. This makes the use of the equalization techniques developed in this work that allow extending the number of channels beyond these basic limitations all the more compelling. A study of the tradeoffs constraining scalability and system performance must be performed in order to properly target the pulse interleaver specifications.

3. CROW filter design and implementation

The design of the CROW filter, the basic building block of our architecture, is primarily constrained by the MLL properties and by the chosen PIC technology. Assuming an MLL with an FSR of 25 GHz and a useable spectrum of > 12 nm, as intended to be used here, a four-time increase of the effective pulse repetition time can be achieved by employing a four-channel interleaver consisting in filters with a passband of 360 GHz, such that an overall sampling rate of 100 GS/s can be reached. To achieve this, the CROW filters are required to have an FSR of at least 1.44 THz (4 × 360 GHz), which is already challenging to achieve due to the increased bending losses in the SiN platform constraining the minimum radius of the utilized rings. At the radius required for a 1.44 THz FSR, 16 µm, bending losses already start to play a significant role in the utilized SiN technology. Furthermore, implementation of the high coupling coefficients necessary to obtain the desired filter bandwidth requires a racetrack configuration to increase the length of the rectilinear coupling sections, so that further reduction of the bend radius becomes necessary to maintain the targeted FSR.

To allow for small bending radii and at the same time keep bending losses at an acceptable level, waveguides are tapered inside the rings. They are kept narrow in the rectilinear coupling sections in order to increase the coupling strengths and are gradually widened in the bends to allow for higher mode confinement and therefore lower bending losses, as shown in Fig. 2. This approach is similar to the one we used in [23] to enable highly overcoupled rings with high FSRs in a resonantly assisted (RA-)MZM. Shortly before this paper was sent out to review, a similar approach was also independently reported to have been applied to SOI based CROW filters [24].

 

Fig. 2. 6^th-order CROW filter realized with racetrack rings with adiabatically tapered waveguides adopted to ensure high coupling strengths in the straight sections and increased mode confinement in the bends, reducing bending losses. The actual waveguides are surrounded by dummy structures to increase the homogeneity of the fabrication process.

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As already mentioned, the high flexibility of CROW filters in terms of filter shape and the relative ease of synthetization have been the main factors in selecting them for filter implementation. By carefully choosing the filter order, i.e., the number of rings, and the coupling coefficients between resonators, many different filter shapes can be obtained [25]. In our application, we aim at keeping the group delay ripple (dispersion) across the (drop) passband as low as possible, since it would otherwise increase the width of the filtered pulses beyond their power spectrum limited pulse width. At the same time, we aim to generate pulse shapes with a low time-bandwidth product to reduce inter-channel crosstalk (see Section 4). Therefore, we target to approximate a Gaussian filter that provides a maximally flat group delay. Unfortunately, a Gaussian filter is not realizable with a finite order, hence a suitable approximation must be adopted. Bessel and van Vliet functions [26] are among the most accurate approximations of a Gaussian filter. After careful analysis of the transfer functions obtainable with these, both in terms of amplitude and phase (see Fig. 3), and also comparing the required filter orders, we opted for a 6^th order van Vliet filter.

 

Fig. 3. Comparison between Gaussian, Bessel and van Vliet functions in terms of (a) power and (b) group delay. A Gaussian amplitude profile is targeted to ensure a smooth comb filtering resulting in pulses with a low time-bandwidth product, while a flat group delay in the passband is required to not broaden the generated pulses beyond their power spectrum limited pulse width.

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Fig. 3 compares a Gaussian filter to its van Vliet (6^th order) and Bessel (6^th and 7^th orders) approximations. The utilized van Vliet approximation results in a reduced bandwidth at the –3 dB point (220 GHz), but in similar –1 dB and –5 dB bandwidths. In the following, filter bandwidths are given as their full width at the –5 dB point for both Gaussian filters and their van Vliet approximation. Following this nomenclature, Fig. 3 corresponds to filters with a 360 GHz bandwidth as used in the experimental realization. To the best of our knowledge, this work also presents the first implementation of integrated filters with a van Vliet approximation of a Gaussian function.

To obtain such filters, the design shown in Fig. 2 has been adopted. The poles synthetization results in a set of power coupling coefficients κ² = [0.901 0.617 0.305 0.369 0.296 0.105 0.379], with junctions ordered from the input (bottom) to the drop bus waveguide (top). To allow for such high coupling coefficients, a racetrack configuration is necessary, enabling phase matching between the waveguides forming the couplers. Based on 3D FDTD simulations, a rectilinear junction length L_RT = 11.25 µm has been selected and the gaps between waveguides set to g = [0.4 0.545 0.685 0.65 0.69 0.87 0.645] µm. Due to the contribution of the rectilinear couplers to the racetrack circumference, the bending radius had to be further reduced from 16 µm to 12.2 µm in order to achieve the targeted FSR of 1.44 THz. Adopting single mode waveguides with such tight bends would result in unacceptable bending losses of 7 dB/cm and an additional 2 dB losses in the overall CROW filter transfer function. Therefore, a ring design with tapered waveguides has been adopted, as shown in Fig. 2. Single mode waveguides, with a width w₁= 0.6 µm in the coupling region, are being tapered to multi-mode waveguides with a width w₂ = 1.5 µm in the bends, allowing for higher mode confinement and reduced bending losses without compromising the coupling strength in the straight couplers.

Since the pulse interleaver is composed of four channels, the resonant wavelengths of the respective CROW filters have been spectrally shifted relatively to each other by adding small waveguide segments to every ring belonging to filters for a given channel, whose length is being incrementally increased as one moves from one channel to the next. This allows for a drastic reduction of the power consumption, since active channel tuning is no longer needed if fabrication tolerances are sufficiently tight. Nevertheless, all CROW filters have been provided with metal heaters to allow for fine tuning of the resonant wavelength, as shown in Fig. 4. All the thermal tuners of a given CROW filter are connected in parallel and share a single set of electrodes, as individual tuning of the rings was not expected to be necessary. The meandered shape of the metal heaters increases their efficiency, allowing for tunability of the central CROW filter wavelength up to 560 GHz, almost half of its FSR, by biasing the heaters with a cumulative DC current of 400 mA and a total power consumption of 3.48 W for an entire CROW filter.

 

Fig. 4. Micrograph of the 4-channel pulse interleaver including CROW filters and optical delay lines. Metal heaters are meandered to increase their efficiency, in order to maintain reasonable tuning ranges given the low thermo-optic coefficient of SiN.

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The experimental characterization of the pulse interleaver revealed a good agreement with design targets, as shown in Fig. 5. The power transfer function of the first channel CROW filter is compared with the ideal van Vliet filter used as a design target [Fig. 5(a)]. Apart from a slightly smaller bandwidth, there is an almost perfect agreement between the two without any tuning. The insertion losses of the CROW filter, 3.5 dB, are also in close agreement with theory assuming effective waveguide losses of 0.3 dB/cm (including excess junction losses).

 

Fig. 5. (a) Comparison between the power transfer function of the modeled (grey) and measured (blue) CROW filter. (b) Spectra of the four channels composing the pulse deinterleaver overlaid over the spectrum of a 25 GHz FSR MLL. The measured filter shapes degrade for the higher channel numbers, since the structures are placed consecutively down a single bus and have partially overlapping spectra. (c) Measured spectra of the 4 sub-combs resulting from filtering the targeted MLL spectrum with the CROW filters (done here with the deinterleaver chip providing four distinct outputs).

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The spectra of the four CROW filters are plotted in Fig. 5(b), as measured on the pulse deinterleaver chip (right inset in Fig. 1). Without any active tuning, the resonant wavelengths are already offset from each other by the desired values. The center wavelengths of the filters have been assessed by calculating the first moment of each transfer function, weighting frequencies by the transmitted power on a linear scale. This leads to values of λ₁= 1553.5 nm, λ₂= 1556.9 nm, λ₃= 1559.9 nm and λ₄= 1562.8 nm for the four channels, corresponding to channel separations of 425.6 GHz, 371.5 GHz and 348.3 GHz, respectively, with acceptable deviations from the 360 GHz target. It is important to note that the separation between the first and second channel is larger than the target because the spectrum dropped by the first CROW from the common bus is not affected by following channels, while following channels already see a depleted spectrum on their low wavelength tail, skewing the first moment extracted from the dropped spectra. In other words, this is not due to manufacturing tolerances, but rather to the design. Comparing the first moments to expected values, the deviation of frequency differences from design is below ±20 GHz for all four channels, showing the excellent repeatability of the platform. It should also be noted that while in Fig. 5(a) chip interface losses have been normalized out, Fig. 5(b) shows the transfer functions fiber-to-fiber, burdened by 3.5 dB input edge coupling losses and 10 dB output grating coupler losses. An improved grating coupler design, realized on the same platform but on a later run, showed reduced 5.25 dB losses.

While the absolute position of the resonances is harder to guarantee, it is not essential to the function of the device, so long as all the relative spectral alignments are accurate, as all CROW filters are guaranteed to overlay with the spectrum of the targeted MLL irrespectively of their absolute position. The spectrum of a 25 GHz single section quantum-dash semiconductor MLL [27] is overlaid in grey to show the spectral alignment. It is apparent that the outermost channel, channel 4 plotted in purple, overlays the MLL spectrum with two passbands corresponding to adjacent resonance orders. Consequently, as one resonance moves out of the MLL spectrum, the next one over moves into it. This is also apparent in Fig. 5(c), in which the spectra of the sub-combs recorded after filtering of the MLL by the CROW filters have been plotted. While pulse sub-train 4 has two spectral distributions separated by one CROW FSR, this is not an issue in the absence of strong dispersion, i.e., so long as the corresponding pulses stay together, as the resulting 1.44 THz beat-note in the time-domain pulse shape is too fast to be recorded by the downstream opto-electronics.

The low thermo-optic coefficient of SiN furthermore results in a high temperature stability. The CROW filters have been thermally characterized by sweeping the overall chip temperature from 20° C to 40° C using a thermo-electric cooler (TEC) and by assessing the first moment of the recorded transfer functions. Resonant wavelengths have been measured to red-shift with a coefficient of 18 pm/°C. Moreover, as explained above, the system is immune to global shifts in resonance wavelengths and thus to shifts in chip temperature so long as both the interleaver and the deinterleaver subsystems are initially matched and subject to temperature variations of the same magnitude, which can be ensured by implementing them on the same chip. Incidentally, a similar technique has been applied to thermal control of resonant ring modulator (RRM) arrays in wavelength division multiplexed (WDM) transceivers [28].

4. Time and frequency crosstalk

At the system level, crosstalk between different channels can significantly hinder the performance of the TI ADC. This crosstalk can originate in the time or frequency domain.

For one, creating pulse sub-trains by slicing the MLL spectrum results in the generated sub-pulses to have a larger pulse duration, since their spectra are reduced in bandwidth by a factor N, set to 4 in the above. If the resulting pulse width exceeds the time delay between two consecutive pulse trains, T/N, pulses start to overlap in time. The electrical input signal levels at adjacent sampling times then start to impact the value of the modulated pulse power. We refer to this as time-domain crosstalk. It is important to underline that by reducing the filter bandwidth, for example in order to slice the comb spectrum into more sub-trains, the spectrum of the sliced pulses will also decrease, leading to further broadening of the pulses in time, increasing therefore the time-domain crosstalk. On the other hand, increasing the filter bandwidth at a fixed channel count also increases the spectral overlap between adjacent channels, introducing frequency-domain crosstalk at the deinterleaver implemented after the modulator. Instead of entirely routing each pulse sub-train to its dedicated receiver, parts of the sub-trains are routed to receivers of the neighboring channels, in particular since their spectrum is also broadened by modulation. Consequently, the choice of filter bandwidth sets an important tradeoff determining the overall performance of the converter.

In more general terms, the overall system bandwidth, as limited by the MLL spectrum as well as by the FSR of the filters, also defines the maximum achievable sampling rate in this TI ADC architecture. Referring to the MLL FSR as δν, to the available spectrum width as Δν, and further assuming the available spectrum to be sliced into N sub-combs without guardbands, the sub-pulse duration Δt can be estimated as

Equation (3) shows an important limitation of TI-ADCs with the single modulator architecture used here, in line with what was similarly derived in [14]. In contrast to spectrally-sliced ADCs, whose overall signal processing bandwidth scales directly with the available spectral width of the MLL [7], the sampling rate of the TI-ADC scales as the geometric average of comb spectral width and comb FSR. With the current devices as described in Section 3, the available spectrum is limited by both the MLL spectrum and the CROW FSR. To increase the latter, more sophisticated designs have to be investigated, for example employing resonators in a Vernier configuration [30] or with Bezier bending sections [31]. The comb FSR, on the other hand, is limited both by the utilized light source technology as well as the sampling rate of the utilized electrical ADCs. It thus becomes all the more important to extend this envelope with advanced signal processing techniques, as shown in the next section. Equation (2) also shows that starting directly with an MLL with a very low pulse repetition rate, such as e.g. commercial low jitter fiber or solid-state lasers, results in a very inefficient use of the available optical spectrum. The large number of channels that would be required to sufficiently upconvert the sampling rate would result in very narrow sub-comb spectra and much broadened pulses in the time domain. Even with best-in-class high repetition rate solid state lasers with a pulse repetition rate of 2.5 GHz and a 250 fs pulse width [32], we estimate a maximum sampling rate reduced to 60 GHz due to the much smaller FSR. Thus, for the TI-ADC architecture to yield a high sampling rate, high repetition rate fiber lasers [33,34], long-term stabilized semiconductor MLLs [35] as intended to be used here, or combs generated by four wave mixing in small on-chip microcavities [21,22] are suitable light sources. It should be noted though that the combination of the TI ADC concept used here with time stretching, as described in [36] (Fig. 37), overcomes the limitation described by Eq. (3) and could in principle result in a system bandwidth directly proportional to Δν, albeit at the price of an even higher system complexity.

Detailed analytical and experimental investigations of time-domain crosstalk in photonically assisted TI ADCs have already been reported in [15,16] and a more qualitative description of frequency-domain crosstalk presented in [14]. We extend the analysis by numerically modeling a full TI-ADC system with a complete physical description including exact CROW filter shapes and experimentally recorded MLL spectra and noise properties, to determine the practical limitations of both types of crosstalk. Moreover, we use the information on crosstalk extracted from the system’s impulse response to apply a powerful cyclic equalization scheme (Section 5) and investigate its performance in presence of physical noise. The 25 GHz FSR MLL is modeled with comb line power levels given by the measurement shown in Fig. 5(b). The MLL is first modeled as noiseless, i.e., each tone is represented by an ideal Dirac function (Subsection 5.1). Optical and electronic noise sources are then included and analyzed in detail in Subsection 5.2. The electric ADCs are modeled as ideal integrating ADCs, with an integration window filling the full 40 ps corresponding to the pulse sub-train repetition time and centered on the pulses of their associated sub-train. They are assumed to have an ENOB of 6, in reach of electronic state-of-the-art ADCs going up to the required 12.5 GHz analog frequencies and 25 GS/s sampling rates [37,38]. The resulting quantization noise is not included in the basic model in Subsection 5.1 that is used to assess the capabilities of the optical front-end of the system. It is however introduced in Subsection 5.2 together with the physical noise sources. Section 6 is dedicated to exploring the performance limits of the system, assuming the PIC to be correspondingly redesigned with a different number of channels and adjusted filter passbands (that are being resynthesized with a physical CROW filter model). There, architectures with 6 and 8 channels are being investigated in detail.

In order to keep the MZM operating close to the linear regime, the applied electrical signal is assumed to have a peak-to-peak strength of 0.2V_π/π and to be applied in dual-drive, push-pull configuration, i.e., a given MZM output E-field varies between sin(π/4 ± 0.1). While MZMs with increased linearity have been shown [39] and nonlinear equalization methods have been applied to compensate the nonlinearities arising from large signal operation of regular MZMs [40], the main focus here are the limitations arising from the interplay of MLL spectrum and the (de)interleaver, so that the MZM is assumed to be operated in a small signal regime, for simplicity, and MZM-related aspects are not analyzed in more depth.

5. Digital signal processing and noise

In order to partially compensate for the inter-channel time- and frequency-domain crosstalk described in the previous section, we introduce a cyclic feedforward equalizer (FFE) in the digital signal processing domain. Considering the time-interleaved nature of the ADC, corrections have to be cyclical [41]. Due to the inter-channel crosstalk (leakage), this correction cannot be applied to single channels only in order to obtain best performance and is implemented as a form of multiple-input, multiple-output (MIMO) equalization. This is solved by applying the FFE filter to samples generated by all four channels, but by switching the coefficients depending on the channel of the sample that is being recovered. I.e., four (N) sets of FFE coefficients are derived that are being cyclically applied.

In order to obtain the FFE coefficients, the impulse response of the TI-ADC is first generated for each of the four cycle times (i = 1 … 4) by inputting a sinc-shaped signal to the EOM with a central lobe duration of two TI-ADC sampling times (20 ps measured between 1^st zero crossings for the four channel configuration) and a center time coinciding with that of the corresponding optical pulse, so that the signal features a zero crossing at all other sampling times. Using a sinc shaped input pulse also ensures that finite signal frequencies below the Nyquist frequency of the overall system are injected into the TI ADC, so that problems due to unnecessary frequency crosstalk, as resulting e.g. from inputting a Dirac peak, are not incurred. The uncorrected response is recorded after interleaving the outputs of the four electrical ADCs, in order to obtain the cycle-time dependent channel response a_ij, with j indexing the output sample after interleaving and a_i0 the main sample “synchronized” with the input pulse, i.e., timed such that it reflects its value in the absence of inter-channel crosstalk and intra-channel distortion. These cycle-time dependent responses are used to build a matrix A describing the time-dependent channel response given by

This matrix is then inverted and 2M+1 FFE coefficients (j = –M … M) kept and later applied for each of the 4 cycle times. This cyclic FFE is first applied to the TI-ADC model in the absence of noise, to verify its basic applicability, and later applied in presence of quantization noise and various physical noise sources such as laser RIN, amplified spontaneous emission (ASE) from the optical amplifiers, shot noise and thermal receiver noise.

A basic requirement for linear equalization to work well is that the inter-channel crosstalk behaves as linear interference. For time-domain crosstalk this is a reasonable assumption, since system-level signal leakage is then additive and simply proportional to the strength of the pulse at adjacent sampling times. For frequency domain crosstalk the situation could be more complex due to signal-signal interference arising from the squaring function of the photodiodes. However, since the modulator is assumed to be operated in a small drive voltage range, interferences are primarily between the average field resulting from the 3-dB EOM bias and the coupled-over frequency components (signal-carrier interference), so that here too close to linear interference is observed. Hence linear equalization can be expected to substantially improve the signal quality. As modulation amplitudes are being increased, more complex nonlinear equalization may have to be implemented to obtain optimum performance.

5.1 Cyclic equalization in the absence of noise

First, the cyclic FFE is applied to the model in presence of time- and frequency-domain crosstalk only, i.e., no noise sources are taken into account in addition to deterministic sources of distortion. Figure 6 shows in deep blue the response of the system when converting a radio-frequency (RF) signal without applying any equalization, with the CROW filter bandwidths set uniformly to 360 GHz. This serves as a baseline to evaluate the beneficial effect of the cyclic FFE. The decay of the SNR at higher frequencies prior to equalization is mostly a consequence of the system effectively integrating the input signal across the pulse duration, resulting in low pass filtering as further analyzed in Section 6. When the equalization is applied, adopting 11 taps (M = 5), a considerable improvement of the digitized signal quality can be observed, plotted in Fig. 6 with the pink curve. In this four-channel configuration the SNR does not improve much beyond 60 dB as the number of taps is further increased, so that the residual noise floor is likely to be due to small nonlinearities in the system, as already introduced above (MZM transfer function, signal-signal interference). It is, however, so much above the achievable SNR in presence of physical noise that we chose to focus the remainder of the paper on the latter. In the following, by introducing multiple noise sources affecting the TI-ADC, both in the optical and in the electrical domain, we verify the robustness of the equalization scheme against noise.

 

Fig. 6. Modeled SNR and ENOB of the digitized signal at the output of the time interleaved ADC as a function of the frequency of injected sinusoidal sine waves. The performance without noise, without (deep blue line) and with (pink line) equalization, is compared to the performance with noise, again without (light blue line) and with (purple line) equalization. Error bars indicate 3σ confidence intervals of the performance averaged over 100 stochastic simulations.

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5.2 Cyclic equalization in presence of aggregate noise

In this section, the detrimental effect of multiple noise sources affecting the converter is assessed and the robustness of the equalizer verified. Table 1 summarizes the assumptions made in regard to noise and system modeling.

Table 1. Noise and system model assumptions, numerical settings.

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Starting from the MLL, RIN is modeled. Comb lines are directly subjected to RIN at the laser output. Even though mode-locking largely suppresses mode partition noise in semiconductor MLLs, individual comb lines still feature much higher RIN than the overall laser output power [42,43]. Here, each line is assumed to feature independent RIN with a power spectral density of –120 dBc/Hz in the noise offset frequency range up to 4 GHz, after which it is assumed to drop down to shot noise levels. This level of RIN is typical as measured on single section semiconductor MLLs [42,43]. The RF linewidth of the MLL, corresponding to phase noise that is uncorrelated across comb lines and to the long term jitter of the pulse train [44], is not modeled here as the short simulation times of 4 ns are not sufficient to properly take it into account with physically relevant linewidths. However, its impact on the performance of the TI ADC is discussed in the outlook in Section 7.

In addition to laser noise, ASE, ubiquitous shot noise and receiver thermal noise impact the system performance. To compensate for the estimated 27.45 dB insertion losses of the full system, including the two SiN PICs (9 dB for the first and 15 dB for the second chip), an EOM (3 dB due to two edge coupling interfaces) and the receiver arrays (0.45 dB corresponding to 90% quantum efficiency), an erbium-doped fiber amplifier (EDFA) is assumed to be interposed between the MLL and the first SiN chip. The EDFA is modeled as having a 22.5 dB gain, limiting the chip input power to 28 dB, 2 dB below its damage threshold, and a noise figure of 4.5 dB. A second amplification stage, consisting in a quantum well semiconductor optical amplifier (booster optical amplifier, BOA) operated in the linear regime, is boosting each EOM output with a 9.5 dB gain limited by the BOA output saturation power of 18 dBm. While EDFAs would have provided better performance here too (see outlook), BOAs have been assumed at the modulator outputs to improve the integrability of the solution. Also replacing the first EDFA, that is interposed between the MLL and the first SiN chip, by a BOA is not possible without an architecture change, due to the large power at the output of the EDFA that far exceeds the typical saturation power of semiconductor devices. To further increase the integrability of the solution, it would, however, be possible to replace the EDFA by a pair of BOAs, with the first placed before and the second placed after the SiN chip. However, this would also lead to a reduction of the performance reported in the following, both due to the increased noise figure of the BOA acting as the first amplifier stage and due to the moderately low power levels then entering the second BOA.

The transimpedance amplifiers (TIAs) of the photoreceiver are assumed to have an input referred current noise of 20 ${{pA} / {\sqrt {Hz} }}$ integrated up to the 12.5 GHz Nyquist frequency of the electrical ADCs. Additionally, the conversion system also suffers from the quantization noise of the electrical ADCs, assumed to have an ENOB of 6 as already described above [37,38]. Other than these two aspects, the receiver electronics are assumed to be ideal, i.e., free of nonlinearities and of bandwidth limitations below the Nyquist frequency of the electrical ADCs. The gain of the TIA is also chosen such that the full range of the electrical ADCs is used when inputting the sine tones in the following simulations, to minimize the impact of quantization noise.

Since the EOM is operated in the small signal regime, RIN would be very detrimental in a single-ended optical signaling scheme, i.e., using an EOM with a single output, in which case RIN would be primarily applied to the average power and thus be a form of additive noise. Consequently, the EOM is assumed to have complementary outputs with a differential signaling scheme (Fig. 1), as is typically done in analog optical links and has also been implemented in TI-ADCs [11]. It should be noted, however, that this does not completely cancel the effect of RIN. The large additive noise is canceled once the differential optical signal is recovered. There remains, however, a noise term proportional to the product of the laser RIN with the differential optical signal, that is much weaker (as the signal is much weaker than the average optical power) but ends up a main limiting factor on the noise performance in the following. Fig. 7 reports a detailed link power budget. The power drops also comprise the losses associated to the rejected comb lines (Chip 1), the modulation and power splitting penalty of the modulator, and the 6 dB losses associated to selecting one out of four pulse trains prior to a given photodiode (Chip 2), in addition to the actual insertion losses reported above.

 

Fig. 7. Detailed link power budget. The EDFA gain is limited to 22.5 dB to prevent damaging the first SiN chip. The BOA gain is limited to 9.5 dB to avoid running into saturation.

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We simulate the response of the photonically-assisted TI ADC aggregating all the non-idealities described above to analyze the overall system performance. As shown in Fig. 6 with the light blue curve, noise results in a substantial degradation of the digitized signal, limited at low frequencies by the physical noise and at high frequencies by the deterministic signal distortions of the TI ADC. When applying the equalization (purple line), the TI-ADC response is seen to increase close to the expected noise floor over the entire range of signal frequencies. Thus, the FFE is seen to still adequately remove signal distortion, but to be limited, as expected, by the non-deterministic physical noise floor.

6. System optimization

6.1 Evaluation of the optimal number of channels

While so far the analysis has been done based on the four channels actually implemented in the PIC, this channel count was conservatively chosen and does not necessarily present the optimum. In the following, we discuss the TI ADC performance as a function of channel count based on the considerations described in the previous sections and identify two sweet spots at 6 and 8 channels for the utilized CROW filter and MLL devices.

Figure 8 shows modeled pulse shapes in the frequency and time domains when implementing three to eight channels. These were obtained numerically by applying the CROW filter transfer functions to the experimentally recorded MLL spectrum, also assuming MLL pulse widths to be Fourier transform limited at the input of the first chip. In each scenario, the CROW filter transfer functions have been re-synthetized according to the channel count in order for the cumulative bandwidth to fill all the available spectrum provided by the MLL and the filter FSR. Thus, when N channels are considered, each CROW filter has a –5 dB bandwidth of 1.44/N THz. Therefore, in the case of three channels, each spectral slice comprises a larger number of lines, leading to the generation of narrower sub-pulses. Significant and unnecessary down-time can be seen between the pulses when these are evenly distributed across a full repetition period. This comes at the price of a diminished maximum sampling rate of 75 GS/s. Increasing the number of channels, the width of the generated sub-pulses increases due to the reduced number of spectral lines in each. Combined with the closer packing resulting from the increased channel count, this leads to a reduction of the down-time and finally to a significant temporal overlap between the pulses in the eight channel configuration. Conservatively, a four channel configuration was chosen for the PIC design, while for the further system modeling a more detailed performance analysis, including noise and equalization, has been carried out to identify the optimal number of channels.

 

Fig. 8. Evolution of the modeled pulse shapes in the frequency and time domains with channel number. The top row shows the sliced MLL spectra assuming the bandwidth of the CROW filters to be retargeted according to the number of channels. The bottom row shows the corresponding sub-pulses in the time domain, after being incrementally delayed, as obtained in the individual channels after the deinterleaver.

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Figure 8 intuitively shows the existing tradeoff between high sampling rate, enabled by a high channel count, and time-domain crosstalk, induced by the progressive overlap of interleaved pulses. This simple representation, however, does not quantitatively show a clear optimum in the performance of the converter. Even though at the higher channel counts significant time-domain overlap between the pulses is observed, it is unclear to what extent this can be mitigated by the cyclic equalization. Therefore, a detailed study of the system performance, including aggregate physical noise and cyclical equalization, has been performed to identify the optimal number of channels. All the noise sources described in Section 5 are simultaneously enabled in the model and the SNR levels which can be obtained with different channel counts are recorded with and without applying the FFE. Since noise is physically modeled and added where it is generated in the signal flow, the analysis also comprises any interaction between noise terms that may occur. Figure 9(a) reports the obtained SNR levels, analyzing systems with three to ten channels. A large number of taps has been assumed (201) in order to reveal the performance limits of the system; the actual number of taps that is required before performance plateaus out can be extracted from Fig. 9(b). Two main scenarios are of particular interest: a six-channel system results in a conversion rate of 150 GS/s with a signal quality of 4.6 ENOB, while a system with eight channels allows for a conversion bandwidth up to 200 GS/s with an average ENOB larger than 4. Further increasing the number of channels, the obtainable ENOB drops to values far too low to be competitive with state-of-the-art converters, although allowing for higher conversion rates. In the following, we therefore analyze in more detail the scenarios comprising six and eight channels.

 

Fig. 9. The system performance in terms of SNR and ENOB when sweeping the number of channels from three to ten. In (a), a large tap number of 201 is assumed throughout. Increasing sampling rate comes at the expenses of lower digitized signal quality due to time- and frequency-domain crosstalk as well as the effect of physical system noise. Solid lines report the signal quality without equalization, dashed lines with equalization. (b) Evolution of the SNR averaged over the full conversion bandwidth for each scenario shown in (a) as a function of the number of taps utilized in the FFE. Star symbols show the number of taps selected for the scenarios that are further analyzed in the following.

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As mentioned above, the analysis of different number of channels brings into play another variable, namely the number of taps adopted in the FFE necessary for the equalization to be effective. As the channel count increases, crosstalk becomes more pronounced and therefore more equalization taps are required to counterbalance it. This results in an additional parameter which needs to be tailored in each specific scenario to achieve the best tradeoff between signal quality and system complexity. While a high number of taps provides a better equalization of the digitized signal, it also adds latency. An excessive number of taps also results in increased sensitivity to physical noise as observed in the data. While in Fig. 6 (11 taps) the performance after equalization corresponds to the noise floor already seen in the non-equalized data at low signal frequencies, the equalized performance seen in Fig. 9(a) at higher channel counts is significantly below, particularly for the 9 and 10 channel configurations. This comes from the fact that for noise that is uncorrelated across the samples prior to equalization, as is for example the case here for ASE and shot noise, the noise variance after equalization grows as the sum of squares of the FFE coefficients, that grows to numbers significantly larger than 1 as the number of taps is increased in the presence of significant distortions at high channel counts.

For each scenario reported in Fig. 9(a), the SNR averaged over the full conversion bandwidth has been recorded sweeping the number of taps used in the equalizer with results plotted in Fig. 9(b). The performance can be seen to first grow with the number of taps, but to later plateau out due to improved signal reconstruction being voided by an increased sensitivity to noise. While in the absence of noise the equalization works very well up to high channel counts, albeit at the cost of increased tap numbers and latency, the achievable SNR is much more limited in the presence of noise as seen by the performance drops at 9 and 10 channels. Without noise, an SNR above 60 dB can be reached up to 6 channels and an SNR above 52 dB, 44 dB and 41 dB with 8, 9 and 10 channels, respectively. This performance may be limited by the response of the TI ADC not being fully linear, as already discussed above. However, the SNRs in the presence of noise are much lower, limited to the values shown in Fig. 9(b). For a system comprising six channels, an 11-tap FEE seems to be the optimal choice, resulting in an ENOB above 4.6, while for eight channels 21 taps lead to an ENOB of 4. The selected working points are highlighted in Fig. 9(b) with stars and will be assumed in the following when equalization is applied. Section 7 continues with an in depth analysis of the system’s performance limitations, including a breakdown across different noise sources, but before that we will have a closer look at the optimum filter bandwidths, in the next subsection.

6.2 Evaluation of the optimal filter bandwidths

In the above, the filter bandwidths have been simply assumed to be 1.44 THz/N for both the pulse interleaver and the deinterleaver at the receiving subsystem. While this is a reasonable initial assumption, this section is dedicated to verify whether additional performance enhancement can be achieved by tweaking the bandwidth. As anticipated above, large bandwidths lead to spectral overlap between adjacent channels, increasing frequency-domain crosstalk. On the other hand, reduced bandwidths cause a widening of the sub-pulses, increasing time-domain crosstalk. Moreover, effective filter bandwidths above 1.44 THz/N cannot really be achieved in the current architecture consisting in cascaded CROW filters, as the spectrum sliced by each of the filters would already be depleted by the upstream filters, so that increasing filter bandwidth significantly above 1.44 THz/N is not expected to help.

Figure 10 shows the SNR of the digitized signal and the corresponding ENOB modeled for different filter bandwidths, assumed here to be identical in the interleaver and deinterleaver subsystems. As expected, for systems with six and eight channels, filter bandwidths of 240 GHz and 180 GHz, corresponding to 1/6^th and 1/8^th of the overall available spectrum, respectively, give very close to the optimum performance. A very slight improvement in the six-channel system seen in the noiseless case when the filter bandwidth is reduced to 192 GHz proves to be insignificant once noise and equalization are being applied.

 

Fig. 10. SNR and ENOB of the digitized signal at the output of the time interleaved ADC, when processing sinusoidal signals at the frequencies reported on the abscissa, for (a) the six-channel and (b) the eight-channel configuration. Filter bandwidths are assumed to be identical at the interleaver and deinterleaver and are varied around their nominal value 1.44 THz/N (black curve). Dashed lines show the signal quality in absence of noise and without equalization, solid lines show the overall performance in presence of noise and equalization.

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Time-crosstalk originates primarily from the first filter stage, the interleaver in which sub-pulses are generated and interleaved (left inset in Fig. 1). The second filter bank, at the deinterleaver, simply implements WDM demultiplexing, at which frequency-domain crosstalk takes primarily place. Consequently, it could in principle be advantageous to reduce the bandwidth in the deinterleaver further. We performed additional simulations fixing the bandwidth of the first filter bank to 240 GHz and 180 GHz for the two scenarios under investigation, while reducing the bandwidth of the second filter bank. While we previously observed such independent tweaking of the filter bandwidths to be beneficial at lower channel counts (four), in the six and eight channel configurations analyzed here no further improvement could be obtained, possibly due to filtering of the already reduced spectral range of the individual channels leading to excessive signal clipping.

7. System limitations and outlook on further improvement

In the previous sections, we have shown how to properly choose the many interdependent parameters defining an integrated optically-enabled time-interleaved ADC. Fixing the number of channels, filter bandwidths and number of equalization taps to the selected working points as defined above, we can proceed with a more detailed analysis of the final system performance. In particular, the contribution of each noise source is analyzed separately in order to understand where the limitations of our architecture lie. The outlook at the end of this section provides a perspective on how to further improve the system performance by changing the technological constraints.

In Fig. 11, the response of the converter is reported when individual noise sources are applied to the model as well as in presence of aggregate noise (black curve), in the two scenarios under investigation. The SNR profiles in presence of thermal noise only are undistinguishable from curves modeled without noise and can thus be taken as a baseline for the system performance. It is thus also apparent that the system is not limited by thermal noise. However, the BOAs after the MZM remain necessary, as shot noise at the photodetector would otherwise limit the SNR due to the low signal levels at that point. This can be easily verified with a back-of-the-envelope calculation using the power levels labeled in Fig. 7 and taking into account the small signal modulation at the EOM.

 

Fig. 11. SNR and ENOB of the digitized signal at the output of the time interleaved ADC, when processing sinusoidal signals at the frequencies reported on the abscissa, for (a) the six-channel and (b) the eight-channel configuration. Simulations are run turning on one noise source at a time, as well as with all noise sources turned on together (black curve). Error bars indicate the 3σ confidence intervals of the performance averaged over 100 stochastic simulations. Filter bandwidths are set to their nominal values. 11 taps are used in (a), 21 taps are used in (b).

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ASE and shot noise as well as MLL RIN are the dominant noise sources and similarly contribute to the noise floor at low frequencies. However, at high conversion rates, the effect of the MLL RIN drops. This trend is not fully understood, but appears to also be present in the absence of equalization when exaggerated RIN levels are numerically assumed (as otherwise the effect of RIN would be hidden by the decaying performance of the ADC due to deterministic signal distortion at high frequencies).

The order of magnitude of the RIN limited SNR floor at low tap numbers, at which the equalizer does not significantly worsen the noise floor, can be simply estimated as $- 10 \cdot {\log _{10}}({{{10}^{ - RIN[{d{B_c}/Hz} ]/10}} \cdot BW/n} )$, where n is the number of comb lines in the interleaved pulse spectra and BW the empirically observed 4 GHz cutoff frequency of the RIN [43]. This simple formula is a consequence of the differential detection removing the additive RIN noise (i.e., that is independent of the input signal strength), so that the residual RIN remains proportional to the signal strength and can be straightforwardly converted into an SNR. Summation of the optical power of multiple comb lines with uncorrelated RIN in a single pulse results in a reduction of the overall normalized noise variance, hence the dependence on n in the formula. Estimating the number of comb lines per pulse as n = ∼7, ∼6 and ∼4 for the four, six and eight channel configurations, we obtained an estimated RIN limited SNR of 32.4 dB, 31.8 dB and 30 dB, respectively, close to what is seen in the more complete numerical simulations.

Another interesting feature, clearly visible in Fig. 11(b), is the oscillatory behavior of the SNR across signal frequencies. By modifying the number of taps (2M+1), we numerically verified that the number of oscillations in the entire frequency range up to the Nyquist frequency of the TI ADC is exactly equal to M. The signal frequencies at the local maxima of the SNR correspond to multiples of the Nyquist frequency of the TI ADC divided by M+1/2 and thus to exactly an integer number of signal periods fitting in the time window spanned by the equalizer coefficients. For cosine type signals that are symmetric relative to the central tap and have a strong magnitude at the edge of the equalizer window, this leads to a minimization of the truncation error, given the anti-symmetric nature of the FFE coefficients at large indices, i.e., away from j = 0 [see Fig. 12(c)].

 

Fig. 12. (a) Exemplary impulse response of an 8-channel system used to train the cyclic FFE. Its Fourier transform (b) features significantly lower values at high frequencies. The red curve indicates the fit with a sinc square power spectral density. This results from the signal being integrated over the optical pulse acting as an integration window. (c) Exemplary set of coefficients used in the cyclic FFE, as resulting after matrix inversion (see Section 5). Notably, the FFE coefficients decay relatively slowly, trending as the inverse of the tap index j as a consequence of the sinc pulse shaped excitation and with alternating signs.

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Inspecting Fig. 11, one might also notice a consistent drop in SNR close to the Nyquist frequency. This is particularly pronounced in panel (b) for the eight-channel configuration and generally becomes more pronounced at high channel counts [compare to six channels, Fig. 11(a), and four channels, Fig. 6]. This effect also disappears if a very large number of taps is considered, notice for example that it completely disappears in Fig. 9(a) in which 201 taps have been considered. This too can be tracked down as arising from the oscillatory behavior of the FFE coefficients, which in turn is a consequence of the signal attenuation at high frequencies in the uncorrected response that needs to be compensated for by the equalizer. Figures 12(a) and 12(b) respectively show an exemplary (uncorrected) impulse response of the eight-channel system and its discrete Fourier transform (DFT), from which it is readily apparent that high-speed signals are being attenuated. As already mentioned above, this attenuation is primarily a consequence of the input signal being effectively integrated across the pulse durations, resulting in low pass filtering. To verify this, we overlaid the power spectral density (PSD) of the DFT with a sinc square shaped fit. Approximating the optical pulses as square shaped with a duration of one sample interval, one would have expected the sinc square fit to be about 50% wider. This is however not surprising as the actual optical pulses fill substantially more than one sample duration in the eight-channel configuration, see Fig. 8. As a consequence of this attenuation, the equalizer needs to reamplify high signal components, leading to the rapidly oscillating behavior of the FFE coefficients shown in Fig. 12(c). Since for a DC signal, the error resulting from truncating the FFE coefficients for |j|>M results from a direct summation of the truncated coefficients, the alternating signs lead to a reduction of the error. On the other hand, for a signal approaching the Nyquist frequency, convolution of the signal with the FFE coefficients leads to a rectification of the latter, so that the summation of the truncated coefficients leads to a much larger error. Thus, not surprisingly, the reamplification of the high-frequency signals comes with an SNR penalty for the latter when the FFE coefficients are taken in too small an equalizer window. In view of these artifacts seen in the system performance, it appears that a smooth windowing of the FFE coefficients might have been preferable, which could be the subject of a future study. While a larger number of taps could also have served to remove this performance drop, in order to maintain reasonable system complexity and latency we have opted to keep the number of taps at 21 for the eight-channel system. A slight reduction of the nominal bandwidth from 100 GHz to 94 GHz would however result in a reasonable ENOB being maintained that is not excessively penalized by this drop.

The detailed considerations of the noise related performance limitations bring us to a more general discussion of the achievable performance. In the scenarios investigated above, the ENOB drops to 4.6 and 4 for the six and eight channel configurations, with analog bandwidths up to 75 GHz and 100 GHz when a sufficient number of taps is used. Since this is slightly lower than that of best-in-class high-speed real-time oscilloscopes that feature an ENOB up to 5 at 100 GHz, further improvement would be desirable to make this optical solution more attractive. Notably, the assumed MLL RIN by itself already results in a significant ENOB penalty, which already drops to 5.2 and 4.5 for the two scenarios when all other noise sources are excluded. Consequently, the RIN performance of the employed MLL is critical and reduced RIN light sources should be utilized. A great deal of attention has been given to improving the noise performance of semiconductor MLLs by adding low loss intra-cavity delay-lines, as enabled by heterogeneous integration in silicon photonics [19,20]. While substantial improvements have been achieved in regards to optical and RF linewidths, unfortunately much less attention has been given to the improvement and characterization of the laser RIN. Techniques previously used to improve the RIN in an optical communications setting consisting in sending individual lines through a saturated semiconductor optical amplifier (SOA) [45,46] would lead to prohibitively complex systems due to the large number of required comb lines. However, studies on mode-locked fiber lasers have shown that the laser RIN also strongly correlates with intra-cavity losses and greatly improves with the latter [47], so that one may also realistically expect the integration of low loss silicon or SiN delay lines into semiconductor MLLs, which has already been done to improve their RF linewidths, to also improve their RIN performance, a critical aspect that should be worked on in the future. Alternatively, generation of optical frequency combs from a single carrier with electro-optic modulators [48], as also used in [5], does not suffer from the relatively high RIN of optically filtered semiconductor MLLs, but does inherit the long-term jitter of the employed RF signal unless the latter has also been stabilized, e.g. by locking to a low jitter solid-state MLL [49]. Finally, microcavity generated combs [21,22] might provide a suitable low RIN alternative.

The other limiting factor is the ASE and shot noise, arising from the high interface losses and therefore the need for reamplification. The link power budget shown in Fig. 7 is limited by the saturation power of the BOAs, limiting the power reaching the photodetectors. BOAs also have a higher noise figure than EDFAs, primarily due to the increased insertion losses. To overcome these limitations, replacing the second amplification stages with two EDFAs would result in an overall ENOB close to 5 for the six-channel and of 4.3 for the eight-channel configuration, albeit at the cost of a bulkier and more power hungry solution. A better alternative would of course be the reduction of the link losses. As introduced in Section 3, a new grating coupler design has shown improved coupling losses of 5.25 dB in the utilized platform. In addition to this, system losses could be minimized by further integration, e.g. by implementing the full system on a single chip, for example with help of thin-film lithium-niobate modulators [50] as well as on-chip integration of the light source, removing the need for such large amplification. Increasing the modulation index at the MZM would also be helpful to improve the link budget, even though its transfer function nonlinearities would then increasingly become a problem.

Lastly, but not less importantly, in conversion systems the acquisition time in continuous operation is limited by the timing jitter of the employed oscillator [7], in our case dictated by the jitter of the MLL. Integrated semiconductor MLLs with comparable repetition rate to the one used here and stabilized with optical self-injection have been shown to reach RF linewidths as low as Δf = 2 kHz [51]. Over the 4 ns simulation times modeled here (t_max), this corresponds to an average timing jitter of $\Delta t = T\sqrt {\pi \Delta f{t_{\max }}} /2\pi $ = 32 fs and a jitter limited SNR of –20log₁₀(2πf_sigΔt) = 33.9 dB compatible with an ENOB of 5.3, where f_sig = 100 GHz is the maximum signal frequency and the factor inside the square root in the jitter calculation has been divided by two to take the average dephasing over the simulation time into account (as opposed to the dephasing at the end of the simulation time only). However, best-in-class real time 100 GHz oscilloscopes can continuously record samples over a time window of 10 ms [52], maintaining the specified ENOB over that duration. In order to maintain a 40 fs jitter and an ENOB of 5 at 100 GHz over this time period, an RF linewidth of 1.3 mHz is required. While much lower jitter in the attosecond range has been achieved by benchtop Ti:Sapphire lasers [3], this is far out of reach of semiconductor MLLs unless active locking to a lower jitter reference is implemented. As already suggested, high repetition rate fiber lasers [33,34] or microcavity generated combs [21,22] might provide lower jitter alternatives to semiconductor MLLs, with microcavity generated combs in particular presenting a high potential for integration.

As a final outlook on this work, it should also be mentioned that the components required to build this system are all relatively cost effective compared to the price at which 100 GHz real-time oscilloscopes are currently being sold at. In particular, the required 12.5 GHz electro-optic receiver and electric ADC bandwidths, while high-speed, are substantially below the capabilities of the latest commercial components. The attractiveness of optical solutions might thus also lie in enabling broadband real time sampling at a more attractive price point, although this optical technology is still at too early a stage to make a more precise assessment, as significant challenges remain on the integration side.

8. Conclusion

The design, implementation and experimental characterization of a pulse interleaver, integrated on a silicon nitride platform, has been presented. This device is meant to be employed in a time-interleaved photonically-assisted ADC to generate frequency- and time-interleaved pulse trains with increased effective repetition rate from an MLL source and perform WDM demultiplexing before electrical conversion. System level modeling predicts that with this technology and an off-the-shelf 25 GHz single section semiconductor MLL, an RF signal could be digitized with a 150 GS/s sampling rate and an ENOB of 5 implementing six channels or, alternatively, with a 200 GS/s sampling rate and an ENOB of 4.3 implementing eight channels. Since the noise performance is limited by laser RIN, ASE and shot noise, the achievable ENOB can be increased with improved semiconductor MLLs and by reducing the system losses. This device concept is a step forward towards an optically enabled ADC solution integrated at the package level.

The main limitation of the current system in regard to sampling rate lies in the limited FSR of the CROW filters, resulting from the relatively high bending losses of silicon nitride waveguides, as well as the finite optical bandwidth of semiconductor MLLs. A detailed analysis of frequency- and time-domain crosstalk arising from this has been presented. In order to compensate the corresponding signal distortion, cyclic feed-forward equalization has been introduced for the first time in the context of optically-enabled time-interleaved ADCs showing the ability to recover performance at the fundamental noise floor limit.