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Abstract
Source-free all optical sampling, based on the convolution of the signal spectrum with a frequency comb in an electronic-photonic, co-integrated silicon device will be presented for the first time, to the best of our knowledge. The method has the potential to achieve very high precision, requires only low power and can be fully tunable in the electrical domain. Sampling rates of three and four times the RF bandwidths of the photonics and electronics can be achieved. Thus, the presented method might lead to low-footprint, fully-integrated, precise, electrically tunable, photonic ADCs with very high-analog bandwidths for the digital infrastructure of tomorrow.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Continuous development of digital signal processing (DSP) has revolutionized the functional capabilities of computing, storage and communication systems. A digital signal is essentially discrete in amplitude and time. In contrast, naturally occurring electromagnetic signals are always time-continuous analog signals. Therefore, the ultimate system performance is limited to the ability to discretize these analog signals in time and amplitude by an analog to digital converter (ADC) [1]. The basic functionalities of an ADC are sampling and quantization. Photonic ADCs have been proven to be superior to electronic ADCs in terms of speed and accuracy [2]. Different approaches like time-stretching [3] and parallel temporal and/or spectral processing [4,5] have been adopted to achieve digitization of large bandwidth signals. The above mentioned methods either use time-to-wavelength mapping for stretching a signal before low bandwidth parallel digitization or an ultra-short optical pulse as a source of sampling clock. As the very first step towards digitization is sampling, the quality of the sampling clock ensures the performance of an ADC. Because of the excellent phase stability of the pulses, traditionally, photonic ADCs have been implemented using a mode-locked laser (MLL) as a source of the sampling pulses [4,6,7]. Although mode-locked pulses have outstanding phase and amplitude jitter characteristics, generating pulses with a widely re-configurable repetition rate is not possible with MLLs because of the stringent phase locking condition.
For present day applications, an ADC should be integrated on a silicon chip. Integrated photonics offers compact, cost effective and efficient devices for exciting microwave photonic applications [8]. In comparison with other integrated photonic platforms, low power and high yield devices and systems are feasible in silicon photonics due to the possibility of photonic-electronic co-integration. This feature enables the possibility to achieve ADCs with much higher analog bandwidths and maybe even lower power consumption than possible with today’s electronic ADCs. However, a straightforward on-chip integration of MLL is yet to be shown on a silicon photonics platform. Moreover, most of the time-stretching approaches, mentioned above, use higher order optical non-linearities or strong dispersion, which are complicated to implement in an integrated photonics platform using commercial fabrication facilities.
Here, a source-free all optical sampling of pseudo-random microwave signal patterns has been demonstrated using a silicon Mach-Zehnder modulator (MZM) in an electronic-photonic co-integrated chip (ePIC). The method is based on the convolution of the incoming signal spectrum with a rectangular frequency comb of flexible bandwidth and line numbers. The rectangular comb with $\def\SHcy{\unicode{x0428}}k = 2n+1$ optical lines is generated from $n$ sinusoidal electrical signals. All sampling parameters like sampling rate, bandwidth, sampling time and so on can directly be adjusted in the electrical domain and precisely be adapted to the signal to sample. The sampling rate of the integrated device can correspond to three (with a single modulator) or even four (with two cascaded modulators) times the RF bandwidth of the integrated MZM [9]. Additionally, compared to ideal sampling, the only difference in this method is that the number of copies is restricted [10]. Since convolution is exploited, nonlinear distortions due to higher order sidebands can be filtered out. Thus, the method has the potential to offer very precise, high bandwidth, and cost effective integrated sampling devices for the digital infrastructure.
2. Principles of the source-free ADC
The basic principle behind the source-free optical sampling can be viewed as the convolution of the spectrum of the signal under test with a flat frequency comb consisting of a finite number of equidistant lines [9,11]. Ideal conversion of a continuous-time signal to a discrete-time equivalent as described in textbooks, usually consists of two steps: sampling followed by digitalization [12]. In ideal impulse train sampling, a bandwidth limited signal spectrum is convolved with an infinite Dirac delta comb of sufficient comb line spacing to produce an ideal sampled signal. To avoid aliasing, the sampling rate has to correspond to at least the bandwidth of the optical, or twice the bandwidth of the baseband signal. Thus, the ideal sampled signal is an unlimited number of signal spectra without spectral overlap. In contrast to sampling with an infinite frequency comb, sampling with a practical, rectangular frequency comb with $k$ uniform and phase-locked spectral lines with $\Delta f$ spacing leads to a multiplication of the unlimited number of spectral copies with a rectangular function.
The rectangular comb in time domain is a superposition of time-shifted ideal (zero-roll-off factor) sinc-shaped Nyquist pulses separated by $k-1$ zero crossings such that [13,14],
Mathematically, this is equivalent to the Fourier transform of an infinite Dirac comb multiplied with a rectangular filter. Therefore, if we define an infinite Dirac comb ($\SHcy_{\Delta f} (f)$) and a flat top rectangular filter as :Thus according to Eq. (3), in frequency domain the sampling leads to a limited number of equidistant copies of the signal spectrum. The only difference to ideal sampling is that the number of spectral copies is limited by the width of the rectangular function. According to Eq. (4), in the equivalent time domain the sampling is a multiplication between the bandwidth limited signal $s(t)$ and an infinitely stretched sinc-shaped Nyquist pulse sequence, where each pulse is shifted by $k-1$ zero crossings. This process has been graphically demonstrated in Fig. 1. A signal spectrum convolved with a five line comb generates five equal copies of the spectrum. In the time domain, this corresponds to the multiplication of the signal with a sinc pulse sequence with four zero crossings. The sampling points are the integral over the repetition time of the pulse sequence. Practically the sampling points can be obtained by a low-bandwidth photodiode (PD), i.e. the PD bandwidth should correspond to the inverse repetition time of the pulses. In the figure, the intensity as measured by a photodiode is shown. However, a coherent detection with a balanced receiver and a local oscillator will ensure the full field sampling [10].
Fig. 1. Schematic illustration of the all optical sampling method. A bandwidth limited signal spectrum is convolved with a frequency comb with $k$ spectral lines. In time-domain, it corresponds to a sampled version of the signal with a sinc-shaped Nyquist pulse sequence having $k-1$ zero crossings between individual pulses, as expressed by Eq. (3). As a photodiode is only sensitive to power, the intensity has been depicted. The corresponding sampling points are the integral over the repetition time of the pulses in the sequence.
A flat, coherent frequency comb with a given number of lines can be generated from a single line using one or more electro-optic Mach-Zehnder modulators with suitable bias conditions [13,14]. Recently, this comb generation method has been demonstrated on a silicon photonics platform [15]. This idea was further extended to generate spectral replicas of the input spectrum having equal spectral powers [9,11]. As described earlier, this operation can be seen as the convolution with a finite frequency comb in the frequency domain, which translates to a multiplication of the signal with a sinc pulse sequence in the time domain. A comparison of conventional sampling techniques using MZM [4,6] and the method presented here can be seen in Fig. 2(a) and 2(b), respectively. For conventional sampling (Fig. 2(a)), the optical input signal is a sequence of short optical pulses, generated by an MLL for instance. In the frequency domain, this is a number of frequency lines separated by the repetition rate of the laser and multiplied with the Fourier transform of the time shape of these pulses (Fig. 2(c)). The signal to sample is an RF signal applied to the RF input of the MZM (Fig. 2(d)). The result of this operation is several spectral copies of the signal to sample (Fig. 2(e)). Due to the nonlinearities of the MZM, unwanted copies of the spectrum fall inside the sampled signal spectrum and cannot be filtered out.
Fig. 2. Conventional optical sampling with an MZM (a) and the proposed method (b). For the conventional method, an optical pulse sequence (a frequency comb (c)) is multiplied with the RF signal to sample (d). The result is wanted spectral copies of the input spectrum and due to nonlinear modulator impairments unwanted spectral copies inside the wanted ones (e). For the proposed method the signal to sample is in the optical domain (f), whereas the sampling signal is just one single sinusoidal frequency line (g). The nonlinear impairments of the modulator lead to unwanted spectral copies outside the spectrum of the wanted ones (h). Thus, an additional filter might remarkably reduce them.
The convolution method is shown in Fig. 2(b). The signal to sample is in the optical domain and applied to the optical input of the MZM (Fig. 2(f)). The MZM is driven with a sinusoidal frequency at its RF-input (Fig. 2(g)). The result is three equal copies of the input spectrum (Fig. 2(h)). The nonlinearities of the modulator again lead to unwanted copies of the spectrum. However, as can be seen from the figure, these unwanted spectral copies are outside the spectrum of the sampled signal and might be drastically reduced by a filter. Additionally, for the convolution method the modulator is driven with a single sinusoidal frequency in the linear regime of the modulator. Consequently, the residual nonlinearities are quite low. An in-depth comparative discussion about the effects of nonlinearities on the generated frequency comb and the quality of resulting sinc pulses has been presented in Ref. [15] for integrated silicon and commercial $\mathrm {LiNbO}_3$ MZMs. Usually, LiNbO3 modulators show a higher sideband suppression than integrated modulators. In Ref. [13] with two coupled commercial modulators, a sideband suppression of 27 dB has been achieved. The integrated silicon modulator used in Ref. [15] achieved a sideband suppression of 13 dB and here we will show a suppression of 16 dB. Please note from (Fig. 2(h)), the bandwidth of the sampling pulses corresponds to three times the bandwidth of the sinusoidal input frequency $\Delta f$. Thus, modulators with an RF frequency of $\Delta f$ can generate sampling pulses with three times this bandwidth. For two cascaded modulators, this bandwidth can be increased to four [13]. If the signal to sample is in the electrical domain, it has to be transferred to the optical domain before it can be sampled by the proposed method. Due to the nonlinearities of conventional MZM, this transfer process might lead to distortions of the transferred signal. Nevertheless, these distortions can be drastically reduced by special modulators with high linearity [16] or by rectangular optical filters [17,18]. The integration of these rectangular optical filters is possible on a silicon photonics platform as well [19,20].
In order to increase the number of spectral copies, the modulator has to be driven with more than one input frequency or one or more additional modulators have to be added. If more than one input line is used, the modulator nonlinearities would lead to undesired spectral copies inside the desired spectra. If the unwanted sidebands of the first modulator are filtered out, this would not be the case for adding an additional modulator. For implementation on an electronic photonic co-integrated silicon chip with low footprint, the simplest way is to use one MZM and drive it with a single or $n$ frequencies from an on-chip oscillator to generate three or $2n+1$ equal copies of the input spectrum.
The proposed integrated Nyquist ADC architecture can be seen in Fig. 3. The incoming optical signal to sample is split into $k$ branches, where each branch contains one MZM along with a photodiode and associated post detection electronics. If each MZM is driven with $n$ equispaced sinusoidal frequencies of $\Delta f$ spacing and the device consists of $k=2n+1$ branches, the real-time sampling rate of the device would correspond to the bandwidth of the generated pulses (i.e. $k\times \Delta f$). For a single sinusoidal input frequency, this would result in a sampling rate of three times the RF bandwidth of the incorporated modulators. The time shift of the sampling points can be achieved by a simple phase change of the electrical input signal. Thus, the method is completely tunable and can be fully adapted to the signal to sample. Additionally, no optical delay lines are required for parallelization. These delay lines would limit the tunability of the device and they would lead to an additional unequal attenuation, which has to be compensated for. For the sampling of optical signals no extra optical source is required. Moreover, the electrical signal is just one or $n$ sinusoidal frequencies. Thus, an integrated RF source is sufficient and no expensive arbitrary waveform generator is required [21]. Various kinds of high speed integrated MZMs with RF bandwidths of up to 100 GHz have already been demonstrated in a silicon photonics platform [22,23]. Thus, the presented method would enable integrated fully tunable real-time sampling devices with sampling rates of up to 300 GSa/s and with two cascaded modulators even up to 400 GSa/s.
Fig. 3. A conceptual integrated Nyquist time-interleaved ADC architecture. The chip will include electronics and photonics on the same platform. Key components of the chip are an optical splitter, MZMs, RF generator, RF phase shifter, receiver electronics and digital electronics for signal processing. $\Delta \phi$ refers to the RF phase delay between the branches and $k$ is the number of branches. A prototype ePIC chip layout with three branches can be seen in the inset. Since an integrated device with all components is not available yet, for the presented proof of concept all optical sampling experiment one integrated modulator along with an integrated driver has been used. This serves as one branch of the proposed integrated Nyquist ADC.
The inset of Fig. 3 shows a possible electronics-photonics co-integrated silicon ADC chip consisting of three sampling branches. A standard multimode interference splitter divides the input into three branches with three parallel MZM driven by phase-shifted RFs. The sampled signals will then be detected by the photodiodes and processed in parallel by DSP electronics either externally or even on the same chip. The photonic BiCMOS technology platform used for the present demonstration supports all these key elements like frequency synthesizer circuit [24–26], highly tunable RF phase shifters [27–29], as well as integrated photodetectors [30].
To practically implement this idea, a proof-of-concept characterization of the most important step i.e. on-chip source free sampling is necessary. Therefore, in a move towards a fully-integrated silicon photonic ADC, a chip with the core optical component, an MZM, was fabricated along with integrated driver electronics. The technological aspects of such an ePIC MZM with low power requirement and flexible control of the amplitudes of spectral lines are described in the next section.
3. Device technology
Among several silicon photonic technologies, silicon electronic-photonic platforms are of particular interest for their high scalability, cost-efficiency in fabrication, as well as energy-efficiency due to less parasitics compared to non-monolithic solutions. The majority of electronic-photonic technologies deploy a silicon-on-insulator (SOI) approach in a complementary metal-oxide-semiconductor (CMOS) process, where transistor performances are less affected by additional process steps needed for the photonic integration [31]. While in non-monolithic platforms electro-optical (EO) responses were reported up to 41 GHz with an extinction ratio (ER) of 4.1 dB using external drivers [32] or 40 GHz in a flip-chipped transmitter configuration [33], best monolithically integrated MZMs including on-chip CMOS drivers were reported up to 20 GHz with an ER of 4.7 dB [34] and 24 GHz with an ER of 4.5 dB [35]. The prototype in this work was as well fabricated with a local-SOI approach, but in IHP’s photonic BiCMOS platform, providing bipolar silicon germanium (SiGe) transistors with unity-gain frequencies up to 190 GHz [36] as well as germanium photodiodes with a bandwidth up to 67 GHz [30]. Providing high transit frequencies in addition to high breakdown voltages, makes bipolar transistors a preferable choice over MOS transistors [36]. The silicon photonic MZM with on-chip bipolar transistor driver with the best performance was reported to have an EO response of 24 GHz while delivering an ER of 13 dB [37].
The two main modulation mechanisms, which can be exploited in silicon waveguides, are the temperature and plasma dispersion effect. The change of the refractive index due to temperature is quite effective, but too slow for most applications. The plasma dispersion effect describes the change of the refractive index due to a change of the density of free or static carriers [38]. In order to utilize that effect in silicon, a rib waveguide is doped to form a pn diode (see Fig. 4(a)). By equalization mechanisms, a charge depletion region is formed. When applying a reverse voltage to the diode, the depletion width, and hereby the overlap of the depletion zone with the mode profile, can be modulated. Since the junction capacitance, which determines the intrinsic bandwidth of the pn diode, is extremely small at reverse voltage, the depletion mode of operation is recommended for high-speed performance. In depletion mode the pn diode can be modelled as a series resistor $R_S$ and junction capacitance $C_J$ (see Fig. 4(a)) [39]. Low-ohmic contacts were realized by highly doped regions. The modulation efficiency and insertion loss (IL) of these depletion-type phase-shifters were reported to be $V_\pi L =$ 2.9 Vcm and 10 dB/cm at a reverse bias of 1.5 V [39] and were verified in our measurements.
Fig. 4. (a) Cross-section of lateral pn-doped phase shifters. Electrical interconnects from phase shifters to metal stack/backend-of-line (BEOL) by Aluminium vias. (b) MZM detail: As in a regular push-pull driving method the driver applies a differential signal to the phase shifter arms. Electrodes are terminated on the chip by 50 $\Omega$ resistors. Si phase-shifters are reversed-biased through $V_{\mathrm {pn,bias}}$. The light is coupled into the chip via grating couplers and a fiber array. Temperature phase tuners are implemented to control the MZM bias point. (c) Fabricated MZM chip including driver electronics (yellow) and (d) MZM chip without driver for characterization. Grating couplers (GC) were used for optical coupling and GSSG probes were used for RF signal input. All dc inputs were bonded to a printed circuit board (PCB). (e) Simulated and measured electro-optical $S_{21}$ response. The 6 dB bandwidth has been marked with a dashed line.
Although for high-speed operation the depletion mode is favourable, the phase changes due to applied voltages are quite low. Thus, phase shifter arms with a length of a few mm would be necessary for a silicon Mach Zehnder modulator. A traveling wave MZM, based on a transmission line (TL) theory, must be considered for precise results. The main design targets in a traveling wave MZM are to match the velocities of the electrical and optical modes, as well as to match the RF termination resistor to the wave impedance of the TL. While distributing the effective phase shifter into multiple segments, those segments can be treated as lumped elements [22]. This approximation is acceptable when the size of the phase shifter segment is smaller than $1/10$th of the free-space RF wavelength, which relates to 1 mm at 30 GHz. The wave impedance $Z_L$ and group delay $\tau _L$ of a transmission line, which is loaded with a pn phase shifter of certain length, can be calculated as
where $Z_0$, $\tau _0$, and $C_0$ are the wave impedance, group delay and length dependent capacitance of the unloaded TL and $C_J$ the phase shifter-length dependant junction capacitance [40]. A 50 $\Omega$ wave impedance and termination resistance was targeted for the electrical waveguides so that an identically designed passive MZM could be characterized with a vector network analyzer. As well, the TL was designed to match the simulated optical group delay of 12.4 ps. The total effective phase shifter length was 3.2 mm, which accounts to a theoretical $V_\pi$ of approximately 9.1 V.The on-chip driver is designed as a linear push-pull driver (see Fig. 4(b)), having a simulated 3rd order intercept input power (IIP3) of 11 dBm according to the complete electro-optical system co-simulation. The driver was designed to deliver 3 Vpp from a 500 mVpp source into each of the two phase shifter-loaded TLs. The measured electro-optical $S_{21}$ response shows a 6 dB-bandwidth of approximately 12 GHz (see Fig. 4(e)) at 5 V reverse voltage, which is significantly lower than expected. This can be mainly attributed to high microwave losses and imprecise electro-optical simulation models. However, the next prototype features drivers at each phase shifter segment. By this approach, improved transmission lines can be designed and the bandwidth can be extended by means of peaking techniques in the electronics. The MZM bias point is set by a temperature phase tuner in one of the Mach-Zehnder arms, because changing the bias voltage over the phase shifters would alter their junction capacitance and therefore lead to a change in the wave impedance of the loaded TL, and consequently to a severe termination mismatch. The temperature elements were realized by metal routing in close proximity to the waveguide. When sweeping the voltage of the temperature elements, or more precisely sweeping the current, a DC extinction ratio of approximately 27 dB (Fig. 6(a)) was measured. Figure 4(c) shows the layout of the MZM with the driver. The effective phase shifter section has a length of 3.2 mm. Grating couplers (GC) for optical coupling as well as the driver add up to a total length of 4.5 mm. The width of the MZM in the phase shifter section only amounts to 500 µm, but bond pads for electrical connections as well as the fixed pitch of the fiber array lead to a total width of 1 mm, hence the footprint is 4.5 mm$^2$, but in a configuration with multiple MZMs, as in our proposed Nyquist time-interleaved architecture (see Fig. 3), the total width can be reduced to an integer-multiple of the individual phase shifter section width. The passive MZM (see Fig. 4(d)) suffers geometrically from the same constraints on width of a fiber array but doesn‘t need as many electrical interconnects. However, each arm was equipped with a GSSG input configuration, for differential S-parameter characterization.
4. Source free optical sampling experiment
To demonstrate the convolution-based source-free all-optical sampling, an experimental proof of concept setup as depicted in Fig. 5 was adopted using the electronic-photonic co-integrated silicon intensity modulator described in the previous section. The signal to be sampled was generated in the electrical domain by a pseudo random pattern generator (PG, Anritsu MP1800A). This signal was encoded on an optical carrier generated from a distributed feedback laser diode (LD) by a commercial $\mathrm {LiNbO}_3$ MZM and then launched into the integrated silicon modulator through a fiber array coupled to the on-chip grating couplers. Please note that this optical source would not be necessary if the signal to be sampled is already in the optical domain. The signal was amplified prior to the silicon chip by an erbium doped fiber amplifier (EDFA). A polarization controller (PC) ensured proper input polarization to the chip. The coupling loss was 12 dB per grating coupler, mainly due to the inefficiency of the coupling arrangement. The optical insertion loss of the device was around 6 dB as measured with respect to a short reference waveguide coupled by the same fiber array. To compensate for the very high coupling losses, subsequent amplification stages were used consisting of a pre-amplifier and an EDFA. Two $1$ nm bandpass filters (BPF) were used after each amplifier to mitigate the amplified spontaneous emission noise. Before visualization of the signals in the time domain by an electrical sampling oscilloscope (Agilent 86100C), they were transformed to the electrical domain by an 80 GHz Finisar photodiode (PD). An optical spectrum analyzer was used to monitor the flatness of the spectrum. The silicon modulator, which acts as the convolution-based sampling device, was driven by a radio frequency generator. The input radio frequency was split using a balun which gives a differential ($\pi$ shifted) output. This differential signal was fed to the on-chip electronic driver using a ground-signal-signal-ground (GSSG) probe. The RF power used for the generation of flat, equal copies of the input spectrum was around 6 dBm at each of the signal inputs of the GSSG probe. A synchronization between the signal to sample and the sampling pulses was established as depicted by the dashed line in Fig. 5. The operating point of the MZM plays a pivotal role for the generation of equal copies of the input spectrum [13]. Thus, the on-chip heaters were used as phase shifters to steer the operating point towards achieving spectral copies with the same amplitude. The feasibility of such control mechanism is confirmed by the experimentally measured optical power transfer function of the modulator with respect to the dc voltage applied across the heater element as shown in Fig. 6(a). Evidently, the maximum extinction ratio of the used MZM is around $27$ dB. In order to obtain a flat spectrum as depicted in Fig. 6(b), a dc input voltage of around 2.1 V was applied to the heater. To avoid any nonlinearities within the electrical drivers and higher order sidebands within the modulation, the modulator has to be driven with a low power electrical signal. The voltage for maximum possible carrier suppression was 2.15 V and the chosen operating point of the modulator was 2.1 V. Nevertheless, it was sufficient to generate an equalized carrier and the sidebands with enough power, as can be seen in Fig. 6(b). The flatness of the generated comb was 0.04 dB. Hence, the flatness is better than that achieved with other integrated modulators (0.42 dB, Ref. [15]) and even better than that of commercial $\mathrm {LiNbO}_3$ modulators (0.18 dB, Ref. [13]).
Fig. 5. Experimental setup for all optical source free sampling with sinc shaped Nyquist pulse sequence. LD: laser diode, PC: polarization controller, MZM: Mach-Zehnder Modulator, EDFA: Er-doped fiber amplifier, PG: pattern generator, RFG: radio frequency generator, BPF: band pass filter, PD: photodiode.
Fig. 6. (a) Power transfer characteristic of the used Si-MZM with respect to the dc input voltage to the heating element. The operating point for comb generation and sampling experiment is marked with a red circle. (b) Experimentally measured three line optical comb with 12 GHz spacing generated from an unmodulated CW laser.
If instead of an optical spectrum, a continuous wave (CW) is used as the input and the modulator is driven with just one RF frequency, the output of the modulator corresponds to three equal copies of this CW wave, or a rectangular three-line comb. Such a three-line comb results in a sinc-pulse sequence with two zero crossings between individual pulses as expressed by Eq. (1) in Sec. 2. with $k=3$. A sinc pulse sequence generated from a 12 GHz input RF, is depicted as an orange curve in Fig. 7(a). The equivalent spectrum is shown in Fig. 6(b). Since the photodiode is only sensitive to the power of the optical signal, the resulting pulse sequence is equivalent to the square of Eq. (1). The red curve in Fig. 7(a) refers to the theoretical pulse sequence for a three-line comb with $\Delta f = 12$ GHz spacing. As can be seen, besides the quite high noise amplitude due to the bad coupling efficiency of the setup, the measured curve follows the theory very well. The repetition time of the pulses is $(12 \ \textrm {GHz})^{-1} = 83.33 \ \textrm {ps}$, while the pulse duration (from the maximum to the first zero crossing) is $(3 \times 12 \ \textrm {GHz})^{-1} = 27.778 \ \textrm {ps}$. Figure 7(b) shows the generated pulse sequence if the modulator is driven with $n=2$ sinusoidal RF input frequencies of 5 and 10 GHz. Thus, the result is a $k=2n+1=5$ line comb with a pulse duration of 40 ps and a repetition time of 200 ps.
Fig. 7. Optical sinc pulse sequence of different repetition rate and all optical sampling of microwave signal with them. (a) Experimental (orange) and theoretical (red) pulse sequence generated from a three line comb of 12 GHz spacing. (b) Pulse sequence generated from a five line comb with 5 GHz spacing. (c),(d) All optical sampling of microwave pattern (blue) with pulse sequences (orange) corresponding to three line comb of 7 GHz spacing and five line comb of 5 GHz spacing respectively.
If the optical CW wave is replaced by the signal to sample, the MZM driven with one RF frequency produces three copies of the optical input spectrum, whereas the same MZM driven with two RF frequencies produces 5 copies of the input spectrum. As discussed in Sec. 2, in the time domain this convolution corresponds to a multiplication between the input signal and the sinc-pulse sequence. As a signal to sample an arbitrary microwave signal has been used. This signal is depicted by the blue line in the Figs. 7(c), 7(d) and 8. In Fig. 7(c) and Fig. 8, the input signal was sampled by driving the MZM with just one sinusoidal RF line with a frequency of 7 GHz and 12 GHz respectively, whereas Fig. 7(d) corresponds to the sampling with two sinusoidal input frequencies of 5 and 10 GHz. For the sake of experimental simplicity, the clock input of the pattern generator was the same as the pulse repetition rate.
Fig. 8. All optical sampling of microwave pattern (blue) with pulse sequence (orange) corresponding to a three line comb of 12 GHz spacing. The red points correspond to the integration over one period of the corresponding sampling pulse.
The noisy output behaviour in Fig. 7 and Fig. 8 can be attributed to the quite bad coupling efficiency of 12 dB per facet, which required successive amplification stages. Improving the coupling efficiency and especially using on-chip PDs, as offered by the same integration platform, will eventually lead to improved noise performance [30]. However, the nonzero dc floor associated with the sampling pulses does not affect the sampling process as the result is a multiplication by a constant factor throughout the signal to sample. We have calculated the sampling points by an integration over the repetition rate of the Nyquist pulses, as described in Sec. 2. As can be seen in Fig. 8, although the proof of concept results are quite noisy, the sampling points follow the signal to sample quite well. The standard deviation of the calculated sampling values from the measured signal values were found to be 0.0035 V for Fig. 8.
As described in Sec. 2 one MZM can be seen as one branch of an ADC. By parallel sampling with RF phase shifts and time interleaving, the real-time sampling rate for Fig. 7(c), 7(d) and Fig. 8 would correspond to 21, 25 and 36 GSa/s, respectively. Another important factor defining the sampling quality is the aperture jitter of the clock. The jitter values of the presented device depend mainly on the jitter of the microwave source used to generate the sinusoidal signal [13]. Microwave sources with jitter values in the zeptosecond range have already been demonstrated [41]. However, if the microwave source has to be integrated on the same ADC chip, higher jitter values must possibly be tolerated.
5. Conclusion
A source-free all-optical sampling, based on the convolution of the signal spectrum with a frequency comb, has been demonstrated for the first time by an electronic-photonic, co-integrated silicon device, to the best of our knowledge. The method is able to sample the whole field (amplitude and phase) and it has the potential to achieve very high precision and low aperture jitter.
The on-chip RF drivers ensured very low RF power requirements. The method offers a very flexible and precise control over the pulse repetition rate, pulse width and duty cycle directly in the electrical domain. Thus, the device can be easily adapted to the signal to sample and no thermo-optic or electro-optic tuning of delay lines is necessary.
With an RF input of 12 GHz sampling rate of 36 GSa/s has been achieved. By a parallelization, straightforward with silicon photonics, the method has the potential to achieve real-time sampling rates of three and up to four times the RF bandwidths of the integrated components. Thus, with 100 GHz modulators, already shown in silicon photonics, real-time sampling rates of 300 and even 400 GSa/s might be possible.
As silicon photonics enables the co-integration of all key components of the ADC, the presented method can lead to low footprint, low electrical power, fully integrated, precise, electrically tunable, photonic ADCs with very high-analog bandwidths. This might assist to keep pace with the gradually increasing data rates in the worldwide digital infrastructure.
Funding
Deutsche Forschungsgemeinschaft (SCHE 1821/8-1, SCHN 716/15-1,2, SCHN 716/18-1).
Acknowledgments
The authors would like to acknowledge Janosch Meier from TU BS for fruitful mathematical discussions.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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