Compact Optical Sampler for Broadband Wireless Signals

Sampling is the first step in analog-to-digital conversion (ADC) and especially the photonic assistance of electronic ADCs may be a viable solution to address the bottleneck in processing the envisioned peak data rates of 1 Tbit/s for 6G and beyond wireless communication. Here integrated cascaded ring modulators (RMs) are proposed for the ultra-compact and energy-efficient optical down sampling of broadband wireless signals. The N time-interleaved, low-bandwidth sub-signals, can then be detected and processed with low-bandwidth electronics. This method is superior to electronic sample-and-hold circuits as it introduces no aperture jitter since it relies on multiplication rather than switching. In a proof-of-concept experimental demonstration with integrated cascaded ring modulators with an 18 GHz electro-optic bandwidth, a Nyquist sampling rate of 36 GSa/s is shown with a 12 GHz oscillator and $N = 3$ . Furthermore, the demonstrated system is capable of offering a sampling rate of 60 GSa/s for the 18 GHz wireless signals. Since RM designs with bandwidth exceeding 50 GHz have been shown in the literature, the proposed system could enable compact and energy-efficient Tbit/s wireless communication devices.

SECTION I. Introduction

With emerging technologies and applications, such as 6G and beyond, the Internet of Things, and autonomous driving, data rates are expected to continue to increase exponentially [1], [2], [3], [4]. As such, peak data rates of 1 Tbit/s are predicted for 6G and beyond [1], [2], [3], [4]. Assuming a 28 % overhead for forward error corrections [2], dual-polarization, and 16-quadrature amplitude modulation (16-QAM, as implemented in today’s optical 400 Gbit/s links) a bandwidth of 80 GHz is required for the reception of a 1Tbit/s signal limited to its Nyquist bandwidth. The required bandwidth may be reduced by higher spectral efficiency modulation formats and by a higher degree of space-domain parallelization. However, the former increases the requirements on the signal-to-noise ratio and the latter increases the complexity of the system. The available bandwidth of the standard CMOS technology is insufficient to reach 80 GHz [2] and consequently, electronics-based analog-to-digital converters (EADC) may be a key obstacle to achieving Terabit transceivers [3], [4], [5], [6], [7].

To circumvent the boundaries of pure EADC, photonics-assisted analog-to-digital converters (PADCs) have been proposed [4], [5], [8], [9], [10], [11], [12]. Integrated photonics-assisted signal processing, offers several advantages, including wide bandwidth, energy efficiency, resistance to electromagnetic interference, compact size, and compatibility with CMOS technology [13], [14], [15], [16], [17], [18], [19]. As sampling is the first step in any analog-to-digital conversion process, many optical sampling methods have been shown with linear sampling and also by harnessing nonlinear optical effects in highly nonlinear fibers or crystals [4], [5], [8], [9], [10], [11], [12].

One common approach is to use a mode-locked laser (MLL) as an ultra-short, low-jitter pulse source in a time-interleaved or frequency-interleaved parallel structure [20], [21], [22]. However, low-jitter fiber-based MLLs have long resonance lengths, leading to low pulse repetition rates in the MHz range. This would result in hundreds of branches for the real-time measurement of GHz signals. Recently, integrated MLLs with repetition rates in the GHz range have been developed [23]. However, these devices still have low output power, and integrating low-jitter MLLs on a CMOS-compatible platform remains difficult. Furthermore, a time-interleaving setup requires precise optical delay lines in the branches, complicating the design even more [22].

We have proposed a PADC that uses time-interleaving for the down-conversion of a high-bandwidth wireless signal into parallel low-bandwidth sub-signals through optical orthogonal sampling [4], [5], [12], [24], [25]. These sub-signals can then be detected and processed with low-bandwidth electronics and photonics. First, the input wireless signal is converted to the optical domain by modulating it on an optical carrier using a Mach-Zehnder modulator (MZM). The signal is then subjected to optical orthogonal sampling, where the input signal spectrum is convolved with a flat, N-line optical frequency comb (OFC) using N additional MZMs in an N-branch configuration [4], [12], [24], [25], [26]. In the time domain, this corresponds to multiplying the signal with orthogonal sinc-pulse sequences (SPSs). As we have shown, our approach eliminates the aperture jitter [4]. This allows for higher-resolution sampling of high-bandwidth signals using the low clock jitter of available oscillators down to 20 fs on integrated RF oscillators, with the potential for zeptosecond-level precision [27], [28]. Theoretically, sampling with ideal SPSs is error-free, and even with non-ideal components, errors are minimal [26]. The delay between branches can be fine-tuned by adjusting the phase of the sinusoidal RF driving the modulator, removing the need for optical delay lines.

This orthogonal sampling-based time-interleaving approach offers high flexibility in bandwidth, sampling rate, and parallelization, as all parameters are controlled by the RF frequencies driving the modulator. However, the orthogonal sampling of real-time signals requires a network of MZMs [4], [5], [12], [24]. These MZMs, with typical lengths of millimeters, consume power in the range of picojoules per bit [29], [30], [31], [32], [33]. Here, a more compact and energy-efficient setup is experimentally demonstrated by using integrated ring modulators (RMs). These RMs have a diameter of a few micrometers and, thanks to their compact design and resonance enhancement, consume far less power, in the femtojoules per bit range [29], [30], [31], [32], [33], [34]. Even when considering the power needed for thermal control, RMs are generally more power-efficient than MZMs [32], [35], [36]. Additionally, there have been efforts focused on designing athermal optical ring modulators [35], [36].

Our design incorporates two cascaded integrated RMs with a 10-micron radius, 0.85 V$\cdot $ cm modulation efficiency, and 18 GHz 3-dB electro-optic (EO) bandwidth [29], [30]. For the generation of a flat comb, the RM requires 4.5 dBm RF power. For comparison, a previously integrated MZM with two 3.2 mm phase shifters required 14 dBm of RF power [34], [37]. Cascaded RMs have traditionally been used in wavelength-division multiplexing (WDM) systems for their filtering capabilities. However, this paper demonstrates that aligning the resonant frequencies of two cascaded RMs creates a compact optical sampler. In this setup, a broadband wireless signal is converted to the optical domain by the first RM and sampled by the second. With our proof-of-concept three-branch PADC, the system achieves up to 60 GSa/s at an 18 GHz input frequency, limited by the RM design. However, RMs with electrical bandwidths ranging from 50 GHz to over 110 GHz have been demonstrated [33], [38], [39]. Recently, a plasmonic micro-racetrack modulator with an electrical bandwidth of 176 GHz has been demonstrated [40]. Additionally, by overdriving the modulators beyond their 3-dB bandwidth, even higher frequencies are possible. A 50 Gbps on-off keying (OOK) signal was generated with an 18 GHz-EO bandwidth RM and a 200 Gbps pulse amplitude modulation-4 (PAM-4) signal with a 64.1 GHz RM [29], [30], [33], [40], for instance. Since for the sampling of 1 Tbit/s (dual-polarization 16-QAM) an 80 GHz RM followed by 50 GHz RMs are necessary, and 27 GHz photodetectors and electronics would suffice in a three-branch system, the presented method may enable compact and energy-efficient terabit receivers.

SECTION II. Integrated Cascaded RM-Based Compact Optical Sampler

The fundamental principle of orthogonal sampling is shown in Fig. 1. As illustrated in Fig. 1(a), any bandwidth-limited signal (with bandwidth B, shown in black) can theoretically be represented as a sum of discrete, time-shifted, orthogonal sinc pulses (colored curves), each weighted by the corresponding sampling point. By multiplying the signal with a sinc pulse at the right time shift, individual sampling points can be precisely retrieved. However, sinc pulses are unlimited in time, making them a mathematical idealization rather than practical [4], [5], [12], [24].

FIGURE 1.

Schematic illustration of an N -branch analog-to-digital conversion of a broadband wireless signal with ring modulators and sinc-pulse sequences. (a) The broadband wireless signal B can be expressed as a sum of time-shifted weighted sinc pulses. (b) The same signal can be represented with N SPSs, each of which with N -1 zero-crossings. In the block diagram, the wireless signal is converted to the optical domain by a RM and then split and processed in parallel in N branches. (c) The result of the down sampling in one of the branches. The dashed line shows the original signal and the solid line the signal after the ring modulator. (d) Down-converted signal in one of the branches after filtering (solid line). As can be seen, this low-bandwidth signal preserves the original sampling points which can be detected with low-bandwidth electronics. Please note that the low-bandwidth electronics may accomplish the filtering directly. LD: laser diode, RM: Ring modulator, RFO: Radio-frequency oscillator, EADC: Electronics analog-to-digital converter.

Sinc-pulse sequences (SPS) are also orthogonal but, in contrast to single sinc pulses, they are a flat, phase-locked comb with N frequency lines separated by $\Delta f$ . This can be easily generated by a radio-frequency oscillator (RFO) and by adding a DC bias [4], [5], [12], [24]. The SPS has a repetition rate of 1/$\Delta f$ and contains N-1 zero-crossings. When weighted with periodic sampling points, the SPS carries 1/N of the total sampling points. As shown in Fig. 1(b), the original signal (black curve) can be fully represented by N identical, time-shifted, and weighted SPSs (colored curves).

The sampling of wireless signals is depicted in the block diagram of Fig. 1. The received signal is first converted to the optical domain by modulating it onto a laser diode with a RM. As long as the carrier frequency together with half of the bandwidth of the received signal is lower than the bandwidth of the ring modulator (for our integrated RM <18GHz) this can be done directly with the received signal. For higher carrier frequencies and THz signals, the received signal has first to be down-converted to the baseband. The optical signal is then power-split into N branches for parallel optical sampling. The accompanied loss of power in the single branch can be compensated by a higher optical power of the laser diode. It should be noted that for our experiment, only two cascaded RMs were available. Therefore, only one branch was tested. However, since the whole information of the signal can be retrieved by changing the phase of that branch, this is no loss of generality. In the first sampling stage, the split signal is multiplied by the first SPS. In the equivalent frequency domain, this corresponds to a convolution of its signal spectrum with an N-line, flat comb of bandwidth B, and frequency spacing $\Delta f$ . This is done by another RM with its resonant frequency aligned to the first RM.

The sub-Nyquist sampling produces a down-converted sub-signal with $B/N$ bandwidth. This sub-signal preserves 1/N of the original sampling points, as shown in Fig. 1(c) (red solid line). The down-converted sub-signal is then detected and processed with low-bandwidth B/($2N$ ) electronics and ADCs in a second sampling stage, as depicted in Fig. 1(d).

In a time-interleaved configuration, the remaining sampling points can be captured and processed in real time in parallel branches. This time-interleaving is achieved by applying an electrical phase shift (${\Delta \mathrm { }\phi }_{k}=\mathrm {(2}\pi k)\mathrm {/}N$ , where k is from 0 to N-1) to the oscillator driving the RM for each branch. This phase shifting eliminates the need for optical delay lines. The bandwidth required for the detectors and signal processing is reduced by a factor of N compared to the original signal. Additionally, in traditional EADCs, the resolution (indicated by signal-to-noise and distortion (SINAD) and effective number of bits (ENOB)) is limited by the input maximum frequency at a certain time jitter [11], [41]. By reducing the input frequency through optical sampling, our method improves the SINAD and ENOB, as we have shown in our previous works [4], [5], [19], [24], [25]. An ENOB (9 dB SINAD) improvement of around 1.5-bit was achieved experimentally for a three-branch PADC when sampling a 14.5 GHz signal with 30 GSa/s. For a nine-branch PADC system, a 2.72-bit (16.37 dB SINAD) improvement was calculated in simulations for sampling a 62.5 GHz signal with 126 GSa/s. This was reflected in the improved measured Q-factor for both signal generation and reception using the proposed method as it has been demonstrated in [19], [24], and [25].

SECTION III. Experimental Setup

The experimental setup, depicted in Fig. 2, illustrates a single branch of the proposed three-branch PADC, as shown in Fig. 1. A wavelength-tunable distributed-feedback (DFB) laser provided the optical single-tone input, delivering 5 dBm of power. The laser’s polarization was adjusted by a polarization controller (PC) before the signal passed through the cascaded RMs chip. Details about the optical chip, manufactured by a multi-project wafer run in AMF Singapore, can be found in [29] and [30]. Each RM features a PN junction operating under a reverse bias configuration with a radius of $10 \mu $ m. The modulation efficiency is 0.85 V.cm, and the EO bandwidth is 18 GHz. The chip’s temperature was adjusted to 22°C with a Peltier element to prevent a resonance drift due to heat.

FIGURE 2.

Schematic illustration of the experimental setup. A single-tone laser from a distributed-feedback laser (DFB) is modulated with the wireless signal-to-be-sampled in the first ring modulator (RM1). The optical sampling and generation of the sinc-pulse sequences are acquired in the second RM (RM2) which is modulated with a single frequency from a radio-frequency oscillator (RFO). (a) Top view of the cascaded integrated RMs with the ground-signal-ground-signal probe (GSGS). (b) Side view of the cascaded integrated RMs. PC: Polarization controller, EDFA: erbium-doped fiber amplifier, OBPF: optical bandpass filter, 99:1: 99% to 1% optical power splitter, OSA: Optical spectrum analyzer, PD: Photodiode, OSC: Oscilloscope.

The electrical wireless signal was modulated onto the optical carrier with the first RM (RM1). In the experiments, simply an analog baseband signal has been used. The signal was generated by an arbitrary waveform generator (AWG). The 7-dBm signal was combined with a voltage bias via a bias Tee and launched into RM1 by a ground-signal-ground-signal (GSGS) probe. Fig. 2(a) shows a top view of the chip, including the connected GSGS probe and optical input/output power probes via grating couplers. A front-side view is also presented in Fig. 2(b).

A 4.5 dBm radio frequency oscillator (RFO) generates a single frequency RF line, which is applied to the second RM (RM2). Therefore, RM2 generates a 3-line, flat frequency comb (SPS with 2 zero-crossings) and simultaneously samples the incoming signal. The optical signal is then amplified using an erbium-doped fiber amplifier (EDFA) to a 10 dBm constant output. This was done to compensate for coupling and insertion losses. The amplified signal was then filtered with a 0.5 nm optical bandpass filter (OBPF) to reduce the amplifier-induced noise. To monitor and measure the optical sampling results, the optical signal is split with a 99:1 optical coupler. The 1% of the power was directed to an optical spectrum analyzer. The remaining signal was detected with a photodiode and recorded in an oscilloscope (OSC). The OSC is synchronized with the AWG and the RFO.

SECTION IV. Experimental Results

The experiment began by ensuring the proper connection of the RF probe (GSGS) to the chip. This included a quick preliminary characterization of the RMs resonances to select the appropriate DFB based on the laser’s operating wavelength and the RMs resonant frequencies. This was performed with an additive white Gaussian noise (AWGN) input to the cascaded RMs and a 4 GHz resolution optical spectrum analyzer (OSA), as shown in Fig. 3(b). Initially, the reverse bias voltages were set to 0.32 V for RM1 and 1.46 V for RM2. The resulting resonant frequencies are shown by the red curve in Fig. 3(a). Adjusting the bias voltages shifted the resonance, confirming the proper connectivity of the RF probe. When the reverse bias voltages were set to 0.94 V for RM1 and 0.08 V for RM2, the resonant frequencies of both modulators were aligned, as depicted by the blue curve in Fig. 3(a).

FIGURE 3.

Characterization and adjustment of the resonances for the cascaded ring modulators. (a) Measured optical resonance spectra for the cascaded ring modulators using the experimental setup depicted in (b) with an additive white Gaussian noise (AWGN) source and an optical spectrum analyzer (OSA) of 4 GHz resolution. (c) Recorded optical resonance spectra for the cascaded ring modulators using the experimental setup (d) with a distributed-feedback laser (DFB) swept at around 1 GHz and an optical power meter. RM: Ring modulator, PC: Polarization controller. RM1 bias =0.32 V, RM2 bias =1.46 V for separated resonant frequencies (red). RM1 bias =0.94 V, RM2 bias =0.08 V for overlapped resonant frequencies (blue).

Following this, a DFB laser was used as input, with its frequency swept in 1.13 GHz steps (equivalent to 9 pm wavelength steps). The output optical power was measured using an optical power meter, as shown in Fig. 3(d). This was done to achieve a more precise characterization of the resonances and to select the appropriate frequency operating region for the RMs. The separated and overlapped resonances of the RMs are illustrated in Fig. 3(c). The DFB laser’s carrier frequency was then tuned to the yellow-highlighted linear operating region in Fig. 3(c) for the subsequent measurements.

Figure 4 shows the generation of 3-line combs (SPS with 2 zero-crossings) by modulating the second RM subsequently with two different sinusoidal radio frequencies (10 and 20 GHz). This results in a bandwidth of 30 GHz for an RF of 10 GHz (Fig. 4(a) and (b)) and a bandwidth of 60 GHz for an RF of 20 GHz (Fig. 4 (c) and (d)). Please note that for the second measurement, the RM was slightly driven above its 3-dB EO bandwidth of 18 GHz. Hence, a 60 GSa/s sampling rate could be achieved with the proposed three-branch PADC system. With careful optimizations such as bias and power adjustments, a RM can be overdriven beyond its 3-dB EO bandwidth [29], [30], [33], [40].

FIGURE 4.

Measured optical spectrum of the generated phase-locked 3-line frequency comb at a spacing of (a) 10 GHz, and (c) 20 GHz. Measured time domain sinc-pulse sequences form the 3-line comb at a repetition rate of (b) 10 GHz and (d) 20 GHz.

To validate the sampling, a 1 GHz analog sine wave was selected as the signal-to-be-sampled. The signal was sampled by the 10 GHz ($\Delta f$ ) SPS from Fig. 4 (b). Fig. 5(a) shows the measured 1 GHz sine wave along with the original sampling points (red solid lines), the sampled 10 GHz SPS (black solid line), and the obtained sampling points (blue dots). The signal-to-be-sampled was generated with an AWG. The root-mean-square error (RMSE) between the original and obtained sampling points was calculated to be 1.03%.

FIGURE 5.

(a) Sampled 1 GHz sine wave with 3-line OFC at 10 GHz spacing (black solid line), the obtained sampling points (blue dots), and the original 1 GHz sine wave signal-to-be-sampled and sampling points (red solid lines). (b) A zoomed version of the highlighted blue area in (a) with the illustration of other sampling information gathered by shifting the sinc-pulse sequence by 120° (blue dashed line) and 240° (green dashed line) in parallel branches to achieve 30 GSa/s.

By incorporating a three-branch ($N=3$ ) PADC system as outlined in Fig. 1, a 30 GSa/s ($3\times \Delta f$ ) sampling rate can be achieved. Fig. 5(b) provides a zoomed-in view of the highlighted section in Fig. 5(a), showing the additional sampling information that would be obtained from a three-branch PADC. This is done by shifting the SPS by 120° (blue dashed line) in a second parallel branch and by 240° (green dashed line) in a third parallel branch. Thus, achieving an overall 30 GSa/s sampling rate (15 times oversampling for the 1 GHz sine wave). If the RMs are not overdriven, the bandwidth of the whole system is restricted by the 3-dB bandwidth of the first RM, since this device has to convert the wireless signal into the optical domain. Therefore, the maximum frequency that can be sampled with our setup is 18 GHz, requiring a sampling rate of 36 GSa/s, and the second RM has to be driven with 12 GHz. Thus, the required 3-dB bandwidth of the second is only 12 GHz ($18\times (2/N))$ which is lower than the first RM.

The orthogonality of the sampling depends on the time shift between the sinc-pulse sequences. This can be precisely controlled and locked to each other by the electrical phase of the sinusoidal oscillator used for optical comb generation. However, as shown in [17] a moderate change of phase does not severely degrade the performance. When receiving an OFDM signal, almost no performance degradation was observed for timing inaccuracies of up to 200 fs. Even with a relatively large timing inaccuracy of 1 ps—equivalent to a phase shift of 0.8% (2.88°) for an 8 GHz RF signal—the Q-factor exhibited a 4 dB penalty, while the EVM penalty increased by 2% compared to the ideal case. Phase shifters with a phase precision of ±0.35° at an 8 GHz frequency are commercially available [17], the resulting SINAD penalty of the sampling would be 0.63 dB. A phase shifter operating between 21 GHz and 30 GHz with a phase error ranging from 0.28° to 0.88° has been demonstrated on a 65 nm CMOS platform [17].

In the next step, a digital non-return-to-zero (NRZ) signal has been tested for sampling. Fig. 6 displays a measured 4 GBd NRZ signal (red curve) modulated on the first RM. The NRZ was sampled with 12 GSa/s (black curve) by the second RM. The sampling points directly follow the 4 GBd NRZ signal with a calculated RMSE of 1.52%. Further parameter optimizations, such as for the bias should reduce the measured RMSE.

FIGURE 6.

Measured time domain trace of a 4 GBd NRZ signal (red) sampled with 12 GSa/s (black). The inset shows a zoom into that graph between 1 and 2 ns.

A higher-level modulation signal was also tested to confirm compatibility. Fig. 7 depicts a measured 2 GBd PAM-4 signal (red curve) again sampled by a 12 GHz SPS (black curve). The sampling points follow the signal-to-be-sampled with an RMSE of 1.31%.

FIGURE 7.

Measured time trace of a 2 GBd PAM-4 signal (red) sampled with 12 GSa/s (black). The inset shows a zoom into that graph between 1 and 2 ns.

The quality of the sampling can be affected by the linearity of the RM through the introduction of certain distortions. Since the second RM is just producing a three- or N-line frequency comb from the sinusoidal input, possible nonlinearities can be very simply compensated. However, for the first RM the transfer from the wireless to the optical signal can be fully affected by the nonlinearity. However, the linearity of RM can be improved by coupling it with a Mach-Zehnder interferometer (MZI), for instance [31], [32], [42]. A high-linearity MZI-assisted ring modulator was demonstrated with a spurious-free dynamic range of 111.3 dB.Hz$^{\mathrm {2/3}}$ for the third-order intermodulation distortion at 1 GHz frequency [42].

Compared to other optical sampling systems based on MZM, for instance, the proposed sampling system is ultra-compact and energy-efficient. However, further investigations are required to compare the energy efficiency with the current generation of COMS based samplers.

SECTION V. Conclusion

In conclusion, a proof-of-concept for a compact and energy-efficient optical sampler was demonstrated, which is designed for receiving high-bandwidth wireless signals. The system utilizes integrated and cascaded RMs, each with a $10~\mu $ m radius, 18 GHz 3-dB EO bandwidth, and 0.85 V.cm modulation efficiency. By aligning the resonant frequencies of the RMs through bias adjustment, a broadband wireless signal was converted to the optical domain, and sub-Nyquist sampling using SPSs was performed. The optical sampler eliminates the need for an external pulse source. It also avoids the aperture jitter associated with traditional electronic sampling circuits. This cascaded RM system offers real-time, high-resolution sampling and processing of high-bandwidth wireless signals. The proposed approach surpasses the current EADCs in bandwidth and signal integrity. It holds promise for advancing compact and energy-efficient real-time wireless communication systems capable of achieving terabit-per-second data rates.