III–V/Silicon Hybrid Non-linear Nanophotonics in the Context of On-Chip Optical Signal Processing and Analog Computing

We discuss the application of Silicon hybrid photonic integration technology for all-optical signal processing. The core is a photonic crystal nanocavity made of a III-V semiconductor alloy. This ensures ultra-fast and energy-efficient all-optical operation, which is crucial for scaling from a single device to a nonlinear photonic processor where ideally a large number of nonlinear elements cooperate. We discuss all-optical sampling as an immediate application of this technology and give an example of a future nonlinear integrated circuit based on this technology.


INTRODUCTION
Over the last decade, the increasing demand in bandwidth for communication and data processing has stimulated the emergence of alternative computing paradigms [1]. In this context, it has been suggested that photonic technologies such as optical interconnects [2] will address the large scale challenge in high performance computing [3]. Even more recently, research is focusing on neuro-inspired photonic circuits, for instance to implement deep convolutional networks [4] or reservoir computing [5]. Electro-optic photonic circuits with an electronic feedback or control have been considered here because the technology is available and already well-mastered. Reservoir computing or convolutional neural networks are however inherently non-linear systems [6] and a truly all-optical implementation would require a non-linear optical element. Moreover, all-optical signal processing removes the need of two-way conversion between the optical and the electronic domain whenever the information carried by the optical signal needs to be analyzed. Consider for instance a network where optical signals are exchanged between a multitude of nodes, according to the address carried at the head of a message, which has long been investigated in optical communication [7]. Avoiding unnecessary conversion on one hand, and integration on the other are of paramount importance to improve energy efficiency in communications and computing; therefore, the integration of energy efficient all-optical signal processing in a photonic chip is highly desirable in this context.
Here we discuss a novel integrated technology implementing an all-optical gate (AOG), a general purpose device acting on an incoming optical signal under the control of another optical signal, which necessarily relies upon a non-linear optical effect. There is a broad range of effects resulting into a non-linear optical response, with a general rule trading a fast response with a large power density. Energy-efficient AOGs are therefore challenging. Exploiting the long interaction length possible in non-linear fibers has enabled ultra fast AOGs, known as non-linear fiber loops [8]. A more compact implementation is based on the non-linear response of semiconductor optical amplifiers (SOAs), using four wave mixing (FWM), cross gain or cross phase modulation (XGM and XPM) [9,10]. The non-linear response can also arise from the dependence of the refractive index on the population of free carriers. In contrast to the electronic Kerr effect, this is slower but much stronger and it is therefore preferred for switching. A potentially more compact solution is based on passive semiconductor photonic circuits, whereby resonant enhancement compensates for a weaker non-linear response [11]. With the emergence of silicon photonics it has been pointed out how desirable is the availability of all-optical switching on this platform [12].
The assumption that the properties of silicon and the geometries of the resonators commonly available in silicon photonics are the most suitable for an ultra-fast and energyefficient AOG is however questionable. First, the resonant enhancement of the electromagnetic field in resonators scales as QV −1 with Q the quality factor of the resonator and V the modal volume. So the more confined the optical mode in the gate and the larger the Q-factor, the lower the switching energy, which is a strong reason for considering photonic crystal (PhC) cavities [13], as they feature strongly confined optical modes, down to the diffraction limit (λ/n) 3 [14], as well as ultrahigh Q-factors up to 11·10 6 [15].
PhC are patterned dielectrics with sub-wavelength features resulting into a large surface to volume ratio. This greatly enhances the role of surfaces, in particular in accelerating the dynamics of free carriers, which results into a much faster non-linear response. All-optical modulation in an AOG, where optical inputs are in the Telecom wavelength range and travel in plane, has been demonstrated in a silicon PhC cavity with switching time in the range of 100 ps [16]. Free carriers in PhCs made of GaAs have been found to relax much faster [17]. Thus, the combination of a faster nonlinearity with an optimized cavity led to an all-telecom alloptical device with < 10 ps response and very low energy per bit (100 fJ) [18]. The variety of semiconductor alloys of the III-V group allows further optimization, hence allowing a record low energy-per-bit consumption with a quaternary InGaAsP alloy [19], which eloquently demonstrates the benefit of III-V materials for all-optical signal processing. This makes a very strong case for the integration of III-V based AOGs in a silicon Photonic circuit, a mandatory requirement for addressing the complexity of photonic integration. This squarely falls within the domain of the hybrid photonic technologies, which have been developed for the integration of optical sources, necessarily based on III-V alloys. A very successful and versatile technology is based on wafer bonding techniques [20] which have been also capable of integrating photonic nanostructures. This paved the way to ultra-low power and compact nanolaser diodes on a silicon photonic platform [21]. Based on the heterogeneous integration of III-V photonic nanostructures, fast and efficient AOGs have been demonstrated [22], which opens the perspective of highdensity and energy-efficient photonic circuits for all-optical signal processing.
This article describes the operation of AOGs based on a III-V on silicon (III-V/Si) hybrid nanophotonics as well as the underlying physical phenomena, and considers the perspective of integrated all-optical signal processing circuits. It is organized as follows: first we present in section 1 the working principle of an AOG based on an optical resonator. In section 2 we describe our hybrid III-V/Si PhC-based AOG and show its non-linear properties, and finally examples of application of these AOGs are given in section 3 and in the conclusion, respectively all-optical sampling and integrated nonlinear all-optical processing.

ALL-OPTICAL GATE BASED ON A SEMICONDUCTOR RESONATOR
An AOG based on an optical resonator or cavity works as illustrated in Figure 1. The system is composed of a resonator and a waveguide. The waveguide carries the optical signal (λ s ) to be processed as well as the optical control signal (λ c ), and the light is coupled to the resonator by evanescent waves, meaning a coupling distance, or distance between the waveguide and the resonator shorter than the wavelength of the signals. The resonator can be in-line or side-coupled to the waveguide, and without loss of generality, we consider here the sidecoupled configuration. The system is designed so that the wavelength of the signal λ s is tuned to a resonant mode of the cavity. Consequently, in the side-coupled configuration, the transmission of the signal through the gate is weak, corresponding to an OFF-state. The role of the control signal is to open the gate: each pulse sent to the gate induces a nonlinear effect in the cavity which results in a spectral shift of all the resonances. The signal is then off-resonance, and its transmission through the gate increases, leading to an ON-state.
The usual non-linear effects used in photonic structures are either Kerr effects or free-carrier effects. Although Kerr effects are much faster, free-carrier effects can be much stronger as we show below, and consequently much energy-efficient. Among free-carrier effects, the non-linear index change following the concentration of free carriers, or free carrier dispersion (FCD) is a well-known effect in the context of photonic devices (electrooptic modulators and switches) and it has been very accurately modeled for some materials, in particular InP, GaAs and InGaAsP at telecom wavelengths [23]. The strength of the effect, or the magnitude of ∂n ∂N | FCD , with n the refractive index and N the number of free carriers, depends on the proximity to the edge of the electronic bandgap. For instance in InP, for photon energies close to the bandgap, another free-carrier effect, namely bandfilling, dominates, whereas for much smaller energies the more general FCD described by the Drude model contributes [23]. In both cases, the refractive index decreases with increasing free carrier population, which induces a blue shift of the optical resonances. When considering the limit of long pulses compared to the carrier lifetime τ c , one can obtain a "Kerr-equivalent"  non-linearity of a few orders of magnitude stronger than actual Kerr effects. One can write: with n 2,FC the "Kerr-equivalent" non-linearity, n FC the freecarrier non-linearity, α the absorption term (here linear), and hω the photon energy. As an example, in InGaAsP, assuming n FC = ∂n ∂N | FCD = −8.10 −26 m 3 , α ≈ 300 m −1 , τ c ≈ 100 ps and incident light at 1550 nm, one obtains n 2,FC ≈ 2.10 −14 m 2 W −1 , compared to Kerr non-linearity n 2 = 3.10 −16 m 2 W −1 [24]. From now on, the non-linear effect employed in all-optical gates mentioned in this article will be FCD, unless precised otherwise.
In an AOG, free carriers are injected upon absorption of the control signal. In order to obtain a high transmission contrast of the gate, the spectral shift of the cavity resonance should be comparable to its linewidth (or FWHM, full width at half maximum), as illustrated in Figure 1. To do so, a sufficiently large energy has to be injected and absorbed in the cavity to reach the required density of free carriers. If a total energy U is sent to the cavity, then the density of electromagnetic energy W in the cavity writes W = U V mod , with V mod the modal volume of the cavity modes. Knowing that the modal volume decreases from about 10 −8 cm 3 , typical of Fabry-Perot laser diodes, to 4 · 10 −14 cm 3 for a PhC cavity [14], the required energy will be more than five orders of magnitude smaller in the latter. Specifically, the target carrier density is about 10 17 cm −3 , which would require the absorption of about 4 · 10 3 telecom photons, which corresponds to about 1 fJ.
A more accurate estimate considers the spectral shift required to change the transmission from a minimum to a maximum, which equals ≈ FWMH = ν Q , and leading to the corresponding carrier density N. Combining with the mode volume this gives: where ν is the frequency of photons, h the Plank's constant, Q the quality factor of the cavity and τ the photon lifetime according to 2πτ ν = Q. Note that the photon lifetime sets the lower limit to the time response of the AOG. This equation evidences that the product U · τ is basically constant once the geometry (V mod ) and the material ( ∂ν ∂N ) are fixed. Thus, the best way to reduce the switching energy with no loss of speed is to reduce the modal volume of the resonator. This is illustrated in Figure 2 which plots the performance of different types of AOGs, following the figure of merit switching energy vs. speed. By passing from ring resonators to more compact PhC cavities, like 1D PhC "nanobeams" [42] or even more confined H 0 cavity [18], the switching energy has been reduced from about 10 4 fJ to a several tens of fJ, and even sub-fJ energies using an optimized quaternary alloy [19]. Moreover, there was no degradation of the speed, featuring about 50 ps switching time in average and even shorter than 10 ps for GaAs-based PhC cavities [18,41]. It is apparent from the figure that PhC-based AOGs use much less energy than ring resonators in general, which is clearly related to a much smaller mode volume. They are also faster, because carrier dynamics is accelerated by the strong surface recombination. The connection to the surface/volume ratio is apparent: in typical PhC slabs, the typical distance L to the closest surface is 100 nm, when the diffusion length in bulk semiconductor is about 1 µm. Bulk recombination becomes thus negligible compared to surface recombination, which is well-captured by the Schockley model [43]: with τ carriers the carrier lifetime in the PhC, τ bulk the carrier lifetime in bulk semiconductor, and S the surface recombination velocity. The carrier relaxation time, hence the switching speed, depend critically on S, which has been confirmed through more accurate calculations in Tanabe et al. [44]. Surface recombination velocity can be modified, hence optimized through surface passivation (slowing down dynamics) or by adding a layer with stronger recombination velocity. The latter has been used to reduce the relaxation time in InP based PhC down to about 15 ps [22]. Conversely, surface passivation by atomic-layer deposition (ALD) was employed to increase the very fast carrier lifetime of GaAs from 1 to 10 ps, allowing larger non-linear effect in the cavity [41]. Indeed, if a long carrier lifetime limits the operation frequency of the gate, a too short lifetime in contrast prevents from inducing a large non-linear effect due to a too weak carrier photogeneration, limiting the dynamical contrast of the AOG. Besides surface recombination, p-doping a III-V semiconductor to allow only the much faster electrons to move also results in a substantial acceleration of the dynamics. This has been also demonstrated with PhC cavities [45] decreasing the switching time to 30 ps. Note that the time decay of the nonlinear process can be shorter than the carrier lifetime, owing to the fact that two different processes lie behind carriers dynamics: diffusion and recombination. In very compact PhC cavities which display highly confined optical modes, the initial small volume where carriers are generated results in a high carrier density gradient, leading to a very fast diffusion in the material. In this case the decay of the non-linear effect is dominated by this fast diffusion, and thus characterized by decay time that can be several times shorter than the real carrier lifetime in the structure, like switching times of 20-50 ps in an InGaAsP 2D PhC cavity compared to initial carrier lifetime of hundreds of picoseconds [19]. A different yet effective strategy to increase the speed of AOGs is to introduce a Fano-like resonance, resulting in a strongly asymmetric lineshape. This also results into a larger transmission contrast when keeping energy and material fixed and has been demonstrated to be very effective for all-optical switching [40,46]. To sum up, in order to optimize the performance of compact AOGs based on optical resonators, the volume must be reduced to decrease the needed switching energy, which can be done by playing with the geometry of the resonator, or with the switching transfer function using for instance Fano resonances. The choice of the material enables also to tune the non-linearity efficiency, as well as the dynamics of the gate. When looking at Figure 2, it can clearly be seen that PhC-based AOGs are very close to reach the same performance of much bigger and energy consuming devices such as SOAs [27] and thus address the challenges of fast all-optical signal processing and computing in an integrated platform.

Tana2005
Silicon [16] Tana2007 Implanted silicon [38] Husk2009 GaAs [18] Noza2010 InGaAsP [19] Comb2013 InP [39] Bazi2014 InP + QW on silicon [22] Yu2015 InP Fano PhC [40] Moil2016 GaAs PhC + ALD [41] the latter reference. The III-V nanoresonator is heterogeneously integrated on a silicon-on-insulator (SOI) circuitry using adhesive bonding through a thin layer of polymer (benzo-cyclobuthene or BCB), following the same process as in Bazin et al. [22]. The structure is shown in Figure 3A: it is made of a few (typically 10) micrometer long rib with sub-wavelength (650 × 260 nm) cross section and an apodized periodic pattern of holes, which are patterned above the SOI waveguides by electronic writing and inductively-coupled plasma (ICP) etching. The structure is then entirely encapsulated with SiO 2 . Thin surface layers of InGaAs drastically enhance surface recombination, by more than one order of magnitude than in bare InP [50], resulting into a short carrier lifetime which varies between 10 and 30 ps [22]. A crucial aspect of the design is the apodization of the periodic pattern, which is optimized to minimize radiative leakage [42], a critical aspect in periodic structures embedded in a solid cladding. The design consists in a row of holes with constant radius (120 nm) and increasing period from a minimum which is here around 350 nm, but which can be adjusted to precisely target a resonance frequency. The apodization creates an effective "potential well" for photons which is adjusted to define the spatial width of the cavity mode. This also determines the free spectral ranges between resonances, which is here tuned to obtain two resonances around 1,550 nm, separated by about 10 to 20 nm.
The cavity is evanescently coupled to the underlying silicon rib waveguide shown in Figure 3A, with a coupling distance of 350 nm. The coupling strength is controlled by the accurate vertical alignment (better than a few tens of nm) of the cavity and the waveguide; the coupling strength can be increased relatively to the intrinsic loss (Q int ≈ 10 5 typically [51]) in order to set the resonator in the strongly overcoupled configuration, thereby ensuring very low coupling losses.
For the purpose of optical characterization, the sample is accessed from optical fibers to the gate via grating couplers at the SOI waveguide edges, and the angle of the fibers is optimized to set the maximum of the couplers transmission at a wavelength near the first order modes of the cavity. Each grating coupler brings 7 to 8 dB losses at their transmission maximum, which accounts almost totally for the transmission losses of the gates, because the propagation losses of the SOI waveguides reach 2.4 dB/cm and the waveguides are <1-cm long. An example of raw transmission spectrum shown in Figure 3B, which here has not been corrected with the parabolic response of the grating couplers, reveals three resonances, corresponding to transmission minima at 1,528, 1,549, and 1,569 nm, with loaded quality factors equal to 860, 620, and 100, respectively. So the losses of the loaded cavity are much higher than the intrinsic losses to ensure strong overcoupling as mentioned above, hence a large transmission contrast (resonances' minima are at least 10 dB below transmission). This also enables to set the photon lifetime τ in the cavity to be about 1 ps, a fraction of the effective carrier lifetime, in order to avoid further increase of the switching time. As discussed in the previous section with Equation (2), with this choice we trade speed (τ ) for energy efficiency (U), as here the cavity lifetime is about one order of magnitude shorter than in the all-optical switching experiment [22]. From the transmission contrast (minimum transmission T 0 at resonance, normalized such that T = 1 out of resonance), intrinsic Q factors are extracted through Q int = Q √ T 0 , namely 3,200, 2,500, and 500. Unlike suspended PhC cavities which can feature very high Qfactors of several millions [15], not suspended membranes show lower Q-factors, up to more than a couple million in silicon [52]. Looking at the same type of cavity as the ones we use, an intrinsic Q-factor of 10 5 was obtained in a not suspended PhC cavity made of InP [51]. In comparison, intrinsic losses in our cavities are much larger, and we believe that the losses are dominated by linear absorption induced by the InGaAs layers. Consequently the scattering losses alone should be as low as in similar structures with InGaAs layers like in Bazin et al. [22], where they obtained an intrinsic Q-factor of 17,000. But it should be pointed out that very high Q-factors are not needed for switching functions, because this would limit the speed operation of the gate due to long photon lifetime in the cavity. Here intrinsic Q-factors of the order of 10 4 are sufficient to ensure both low losses and a short time response.
Based on the linear characterization, some properties of the non-linear dynamics of the AOG can be anticipated. First, the depth of each resonance indicates the maximum achievable switching contrast of the gate, thus between 8 and 15 dB in the sample studied above, and secondly the spectral linewidth λ or FWHM (related to the loaded Q factor) directly affects the energy required for switching. Following these results, the time response of non-linear behavior of the gate was characterized through time-resolved pump-probe measurements. As shown in Figure 4A, the transmission spectrum of a resonator with at least two resonances is considered. While one mode is on resonance with the pump, the other resonance is probed with a broadband and short (< 1 ps) pulse, allowing the measurement of the time resolved transmission spectrum, from which the spectral shift is extracted. The procedure is detailed in Moille et al. [41]. An essential point here is that the spectral shift of the modes is identical. This condition is indeed well-satisfied as the two modes share approximately the same volume and overlap to the same population of excited free carriers. The pump pulses fed into the samples featured typically between 0.05 and 0.25 mW average power with a pulse duration of 6 ps and repetition rate 36 MHz, resulting in a peak power of 37 to 183 mW coupled into the waveguide, assuming coupling losses of 8dB. This corresponds to a switching energy from 0.22 to 1.1 pJ. The pulse duration was chosen to be close to the effective carrier lifetime to reach a trade-off between high non-linear effect and short recovery time [41]. The power in the probe was at least 2 orders of magnitude lower than the pump. Note that these pump powers values do not correspond to the dissipated power in the cavity, because only a fraction of the injected pump is absorbed in the cavity, thereby limiting heating in the nanostructure. Moreover, we would not be limited by thermal effects here, for the following reason: thermal effects are triggered by the pump absorbed inside the cavity, and the pump signal is periodic, with a time period much shorter than the typical thermal relaxation time (1 µs). This implies that the thermal effect remains constant in time, resulting only in an offset of temperature in the system leading to a fixed thermal spectral shift of the resonances, easily compensated. Figure 4B represents the typical response of the nanobeam AOGs during the pump-probe measurement, namely the instantaneous spectral shift of the probed resonance as a function of the pump-probe delay. A few picoseconds after the excitation, the resonance exhibits a fast (determined here by the pump pulse duration) blue-shift reaching 120 GHz (−0.96 nm), followed by a slower relaxation which is very well-fitted by a single exponential with a time constant of 8.5 ps. Note that the precision of the frequency shift is given by the resolution of the optical spectrum analyzer used to measure the spectra for each time delay, which is 5 GHz. This time-resolved spectral measurement gives insight on the switching capabilities of the gate: Figure 4C shows that the transmission lineshape is essentially blue-shifted with minor distortion. More importantly, the 10 dB depth of the resonance is retrieved here as a transmission contrast of 10 dB, over a spectral width of at least 40 GHz. This large operation bandwidth is important when processing a signal, to avoid signal distortion when passing through the AOG. It is worth comparing with earlier measurements on III-V/Si hybrid gates [22], and we note that the recovery time may change by a factor two. This indicates that surface recombination critically depends on the properties of the InGaAs layer, which might vary from one fabrication batch to another. This stabilization issue should be resolved in a future industrialization phase with manufacturing clean room facilities. The non-linear process is essentially dominated by the switching energy and the detuning of the pump. Indeed, a slight blue detuning of the pump improves the power transfer to the cavity as the resonance starts to be blueshifted [53]. Accordingly, pump-probe measurements were performed with a range of pump wavelengths around the pumped resonance to find the optimum pump detuning. The results are reported in Figure 5A, note that they pertain to a different sample than the results shown in Figure 4. As expected we observed an influence of the pump detuning on the frequency shift, and the optimum pump detuning seems to be around +60 GHz (−0.5 nm), which is consistent with previous experiments [41,53]. However there does not seem to be an influence on the recovery time, as shown in Figure 5C. Assuming that the fluctuations of the response time come from measurement uncertainties, we derived the latter by calculating the standard deviation of values reported in Figure 5C and found it to be close to 1 ps. Increasing the switching energy induces also  interesting behaviors on the non-linear process: in Figure 5B, one can see a linear behavior as a function of the pump energy, up to a saturation level when reaching about 1.1 pJ and a nonlinear shift of 200 GHz (−1.6 nm). This saturation is due to the fact that the more pump power is injected, the further the pumped resonance is shifted by FCD, thereby reducing the amount of light coupled into the cavity. This goes on until higher powers do not compensate the decreasing coupling, resulting in a saturating non-linear shift. This is consistent with the fact that the saturation occurs when the resonances are shifted by more than half the FWHM of the pumped resonance, as it can be seen in Figure 5B. We note that chirped pulses may considerably extend the blue shift, as demonstrated in Serna et al. [54]. Finally, as shown in Figure 5D we observed a slight increase of the recovery time when increasing the switching energy. This is likely due to a saturation of the surface recombination process when many carriers are generated due to a high pump power, which slows down the relaxation of the free-carrier effect. Based on these results it is concluded that the hybrid III-V/Si AOGs technology is comparable in performance to other AOGs, which is apparent in Figure 2. Energy efficiency could however be improved by playing with the material non-linearity like in Nozaki et al. [19], or with the design of the cavity by using Fano cavities like in Yu et al. [40]. Nonetheless alloptical processing with signals up to several tens of GHz are possible, consistently with earlier experiments [19,39,53]. Importantly, this comes with an integrated photonic platform, thereby considerably extending the capabilities for a broad range of applications.

Photonic Analog-to-Digital Conversion
Sampling, through which a modulated analog signal is converted into a discontinuous analog signal, is a substantial part of the analog-to-digital (A/D) conversion process. The latter is constantly present in daily life or in research and industry labs when using devices or instruments relying on the acquisition of analog signals like sounds, images or any physical signal. As an example, in the context of radars or wideband radio communications, signals have a narrow spectrum around a high frequency carrier (10-100 GHz), and the A/D conversion is performed after demodulation to the baseband. It would be simpler to digitize directly on the high frequency signal, implying available A/D converters (ADCs) operating at high frequencies.
But, as illustrated in Figure 6A, the inherent difficulty when sampling a high-speed signal lies on the fact that a small time error of the clock (periodic signal which gives the sampling instants) results in a high amplitude uncertainty on the sampled signal, limiting the resolution. This time error is called the time jitter, and electronic clocks exhibit time jitters of at least 60 fs [57]. As a consequence, electronic ADCs can hardly process signals of several tens of GHz with a sufficiently high resolution, as shown in Figure 6B. The use of low-time-jitter optical sources, like mode-locked lasers featuring down to subfemtosecond jitter [58], would remove the electronic ADCs bottleneck and the sampling rate could be increased without inherent resolution loss [37]. This defines the concept of photonic-assisted ADCs, where for example a low-time-jitter optical pulse train (the clock) is modulated by an RF input (the signal to be sampled) before being digitized [55,59]. Now, following the advances in the development of all-optical signal processing devices and optical data links, it seems logical that all-optical A/D conversion, or at least all-optical sampling, with both the clock and the signal in the optical domain, should also be implemented, in order to directly convert optical signals without preliminary optical-to-electrical conversion, as illustrated in Figure 7. Thus, AOGs are essential elements to create all-optical sampling devices, with the clock being the control signal which activates the gate to sample the incoming optical signal, as shown in Figure 7. The performance criteria for all-optical sampling devices are the maximum input frequency, and the resolution: both criteria are complementary and form a figure of merit whose limiting factor is the time jitter of the clock, which is illustrated in "Walden's graph" in Figure 6B.
Frontiers in Physics | www.frontiersin.org 8 September 2019 | Volume 7 | Article 133 FIGURE 7 | Comparison between photonic-assisted and all-optical sampling. Photonic-assisted switches require an RF analog input, implying optical-to-electrical conversion of the incoming optical analog signal. In contrast, all-optical sampling devices can directly process optical signals, avoiding electrical conversion. In both configurations, at the output of the sampling device one retrieves the clock pulses modulated by the amplitude of the input analog signal.
In the following subsection we describe our all-optical sampling experiment using our hybrid III-V/SOI PhC-based AOGs, as briefly described in Constans et al. [60].

All-Optical Sampling Experiment via III-V/SOI PhC-Based AOG
The performance criteria of an AOG as an all-optical sampling device are: 1. the switching contrast or transmission contrast, which impacts the resolution of the sampled signal, 2. the response time, which limits the maximum input frequency, and 3. the switching energy, here the energy sent to the AOG at each clock pulse, also the energy needed to generate one sample, expressed in Joule per sample or J/bit.
As the maximum frequency which can be resolved is related to the switching window ( t ≈ 8-20 ps at a few 100s fJ switching energies, as measured during the pump-probe experiments described in the previous section), with our fast PhC-based AOGs the expected limit here close to 50 GHz, but could possibly extend to 100 GHz. We note that a short burst of pulses separated by 10 ps has been resolved during our sampling experiment using a PhC non-linear gate [41]. In order to demonstrate the sampling performances of our AOGs we performed all-optical sampling measurements at a sampling rate of 2 GS/s (samples/second) with the experimental set-up shown in Figure 8. The 2 GHz clock signal (f c ) is generated by a tunable actively mode-locked laser driven by a RF synthesizer. The optical signal to be sampled is a CW signal from a tunable laser modulated by a Mach-Zehnder modulator which is driven by a second RF synthesizer, synchronized to the first one.
The corresponding input frequencies f in range from 2 to 40 GHz. In contrast to the pump-probe experiments, here both signal (λ s ) and clock (λ c ) spectrally match a resonance of the cavity. Signal and clock are sent to the AOG in a counter-propagative configuration: the clock is fed into the AOG by a circulator which at the same time extracts the sampled signal transmitted by the AOG. This avoids interaction between the clock and the signal in the fibers before the AOG. Then an optical bandpass filter is used to extract the sampled signal from the residual clock. The sampled signal is finally amplified with a low-noise EDFA, and again filtered to reject the amplifier noise. We used of fast photodiode (40 GHz) to detect the samples and send them to an oscilloscope.
The parameters of the AOG are 10 dB-deep resonances featuring 15 ps recovery times. The clock source and the amplifier were set to obtain 8 ps pump pulses and an average power of 9 mW at the input of the fiber which couples the light to the grating couplers. This means about 90 mW peak power and 0.7 pJ/bit coupled into the AOG waveguide. Before the sampling experiment, we characterized the gate function of the AOG with a fast sampling oscilloscope (70 GHz), for a CW signal and for a signal modulated at 20 GHz. The results are shown in Figure 9. We measured a switching window of <20 ps taking into account the response of the photodiode (about 10 ps), and a switching contrast of 10 dB, consistently with pump-probe measurements.
We next assessed the sampling capability of the AOG, by sampling and reconstructing known sinusoidal optical signals at frequencies from 8 to 38 GHz. To do so, the optical samples were acquired in the baseband after photodetection and lowpass filtering. The acquisition was performed by a digital real-time oscilloscope. In order to extract the signal-to-noise ratio (SNR), Frontiers in Physics | www.frontiersin.org 9 September 2019 | Volume 7 | Article 133  the acquired samples were folded over four periods of the baseband signal as shown in Figure 10, and the samples were fitted by an harmonic function. By comparing this fitting function to an ideal sinusoid, we obtained the SNR as well as the harmonic distortion. By inspecting the plots of the measured samples for different input frequencies in Figure 10, it is noted that the noise increases for increasing frequencies, leading to a SNR decreasing from 28 to 15 dB. In contrast, harmonic distortion decreases with increasing frequencies. A comparison with recent literature considers all-optical sampling based on FWM in a 12-meter long highly non-linear fiber, achieving digitization of as high as 100 GHz optical signal at a 10 GS/s sampling rate, with an effective resolution of 6 ENOB (Effective Number Of Bits, see Figure 6B), corresponding to SNR = 36 dB [61]. The larger bandwidth and sampling rate and better resolution are achieved at the cost of a substantially larger energy of 52 pJ/bit (2 orders of magnitude) and a large footprint, but illustrate the performance potential of all-optical techniques, where the key is the miniaturization.
The future integration of the whole sampling circuit, including the optical sources, the combiners to combine both inputs, and the filters to isolate the signal, will highly reduce insertion losses and the need for further amplification, thus improving the SNR and the resolution of the sampling process. Besides this leads to the implementation of more complex integrated sampling architectures, like multichannel sampling in order to increase the final sampling rate, as it is described in the following section.

CONCLUSION AND OUTLOOK: INTEGRATED NON-LINEAR ALL-OPTICAL PROCESSING
The manufacturing capabilities of the CMOS foundries used for silicon photonics enable complex integrated photonic architectures, which have been used for optical signal processing [55,56,62,63], optical computing [4,5], and quantum optics where integration enables high precision and controllability [64]. In contrast, the demonstration of photonic integrated architectures for all-optical signal processing are more challenging and only a few approaches seem to have reached the scale of a non-linear integrated circuit [65][66][67][68][69].
Relying on the higher non-linearity of III-V semiconductor alloys, the hybrid III-V/Si technology turns out highly relevant to provide non-linear elements that can fit in already existing silicon photonic architectures. Combined to the low footprint and the energy efficiency displayed by fast hybrid PhC-based AOGs, this opens the perspective of building scalable and low-power-consuming integrated silicon photonic circuits including fast non-linear functions, leading to high-performance all-optical signal processing, such as optical pulse shaping,  optical time-division multiplexing. In this perspective, an integrated silicon photonic circuit with two hybrid AOGs has been developed. This architecture is meant to perform all-optical sampling through time interleaving. Interleaving techniques enable to scale the sampling rate up, while keeping the same clock frequency [70]. In wavelength-interleaved systems, consecutive sampling pulses have different central wavelengths, and the corresponding samples can be switched to different outputs using a wavelength demultiplexer [62]. In time-interleaved devices, as illustrated in Figure 11A, each sampling gate sees the signal to be sampled with a different time delay, obtaining as many samples in a single period of the clock (with one different output for each gate). In other words a fast serial input pulse train is converted into multiple parallel lower-rate pulse trains. The integrated approach for time-interleaving enables to avoid the issue of the synchronization of the clock pulses toward each gate, which is easily controlled by adjusting the length of each path.
The hybrid silicon photonic circuit fabricated to perform time interleaving is shown in Figure 11B. The mastery and flexibility of silicon photonics allow to build this circuit using splitters and combiners, time delay lines and crossings (mandatory for this architecture implemented in 2D), resulting in an architecture rather simple compared to time interleaved electronic ADCs [71]. Both the signal to be sampled and the control signal (control pulses) are splitted and distributed with the same amount of power to the different gates, here two gates, via multimode interferometers (MMIs), as shown in Figure 11B. So the injected total switching energy scales with the number of gates of the circuits. Here the signal is fed into the two gates with a 50 ps delay between the gates, meaning that the clock has a time period of 100 ps, or 10 GHz repetition rate. The two pump paths are optimized to have the same length and the same propagation time within 100 fs to ensure the simultaneous activation of both AOGs.
This work contributes to the transition from non-linear photonic devices to non-linear photonic circuits. By combining the advantages of silicon photonics with high performance AOGs, this technology is relevant to a very broad range of applications, well-beyond all-optical sampling. In particular, they could implement an ultra-fast and energy efficient non-linear activation function which is an essential ingredient of photonic neural networks [4].

DATA AVAILABILITY
The datasets generated for this study are available on request to the corresponding author.

AUTHOR CONTRIBUTIONS
For the original results of this article, the III-V epitaxies were fabricated by GB and IS. The design of the nanocavities were designed by FR and LC, and the silicon photonic sampling circuits by AR and SC. The fabrication process for the III-V/Si samples and the silicon circuits owe to the contribution of FR, XC, and LC. All measurements were performed by AR, SC, and LC.

ACKNOWLEDGMENTS
We acknowledge Renatech for the use of clean room facilities.