The experimental setup is shown in Fig. 1(c). A CW laser is amplified and with its polarization state adjusted to pump a nonlinear high Q factor Hydex MRR, which featured a Q factor of over 1.5 million and a free spectral range of ~0.4 nm, or 48.9 GHz. As the detuning between the pump laser and the MRR changed, dynamic parametric oscillation states corresponding to distinctive solutions of the Lugiato-Lefever equation were initiated [44]. We generated soliton crystal micro-combs [45], which were tightly packed solitons circulating in the MRR as a result of a mode crossing (at ~1552 nm in our case), and manifested by the generated distinctive palm-like comb spectrum (Figure 1(b)).

For phase-encoded signal generation, 60 lines of the micro-comb were flattened, using two stages of WaveShapers (Finisar 4000S) to acquire a high link gain and signal-to-noise ratio. This was achieved by pre-flattening the micro-comb lines with the first WaveShaper (WS1) such that the optical power distribution of the wavelength channels roughly matched with the desired channel weights. The second WaveShaper was employed for accurate comb shaping assisted by a feedback loop as well as to separate the wavelength channels into two parts (port 1 and port 2 of the WaveShaper) according to the polarity of the designed binary phase codes. The feedback loop was constructed by reading the optical spectrum with an optical spectrum analyzer and comparing with designed weights to generate an error signal, which was fed back into the second WaveShaper (WS2) to calibrate its loss until the error was below 0.2 dB. Here, we use a Gaussian pulse with a duration of Δ*t* =84 ps, as the RF fragment *f* [*t*]. The input RF pulse was imprinted onto the comb lines, generating replicas across all the wavelength channels. The replicas then went through a ~13 km long spool of standard single mode fiber to progressively delay them, leading to a delay step of ~84 ps between the adjacent wavelength channels that matched with the duration of the RF pulse Δ*t*. Finally, the wavelength channels were separated into two parts according to designed phase codes and sent to a balanced photodetector (Finisar, 40 GHz) to achieve negative and positive replicas for the phase encoding.

By applying designed phase codes during the separation of the wavelength channels, the sine cycles could be π-phase shifted at desired times. The phase-encoded results are shown in Figure 2. The number of Gaussian pulses for each RF segment (denoted by *m*) was reconfigured from 6 to 2, corresponding toreconfigurable sequence lengths (*N*/*m*) ranging from 10 to 30 and phase coding speeds 1/(*m*Δ*t*) ranging from 1.98 to 5.95 Gb/s. The employed phase codes were denoted both by the shaded areas and the stair waveforms (black solid line). This result shows that our photonic phase coder can offer reconfigurable sequence lengths to address the performance tradeoffs between range resolution and system complexity. To acquire a large pulse compression ratio for a high resolution, the sequence length should be maximized, where the number of Gaussian pulses for each RF segment (*m*) should be set to 2. Further, to reduce the complexity and cost of the RF system (such as the number of range gates at the receiver), the sequence length could be reduced by either employing fewer wavelength channels or by increasing *m*. The corresponding optical spectra (Figure 2(a, c, e)) were measured at the output of WaveShaper to show the positive and negative phase codes realized by changing the wavelength channels’ output ports at the WaveShaper. The encoded RF waveforms (Figure 2(b, d, f)) clearly show the flipped phase of the RF segments at the time of negative phase codes, where the number of sine cycles was reconfigured as well according to m. This result also shows that our approach is fully reconfigurable for different phase codes and encoding speeds. We note that higher encoding speeds can be achieved by reducing the duration of the RF fragment and the delay step Δ*t*.

We also calculated the autocorrelation (Figure 3(a)) of the phase-encoded RF waveforms. As the sequence length varied from 10 to 30, the full width at half-maximum (FWHM) of the compressed pulses varied from 0.52 to 0.17 ns, which corresponds to a pulse suppression ratio rangingfrom 9.7 to 29.6. Meanwhile the peak-to-sidelobe ratio (PSR) also increased with the sequence length from 4.17 to 6.59 dB. These results confirm that the pulse compression ratio of an RF phase-encoded signal is linearly related to its sequence length [46], and that this can be significantly enhanced with our approach by using a larger number of wavelength channels of the microcomb. Figure 3(b) shows calculated examples of the estimated outputs of the range gates, with different distances. Considering an example with a sequence length *N*/*m* = 30, the delay of the matched filters would be 2Δ*t* = 168 ps. The tap coefficients for the *l*th matched filter are *c*[*k*-*l*], where *c*[*k*], *k* = 1, 2,…30, is the employed phase codes. The range resolution of the radar, which is the minimum distance between two resolvable targets, is determined by the delay step (2Δ*t*) of the matched filters, which is given by 2Δ*t* ·*c* = 5 cm, where *c* = 3 × 108 m/s is the speed of RF signals in air. If the distance between the target and radar is *R*, then the delay would be 2*R*/*c*. The range gates would have a maximum output at the lth range gate, *l* = 2*R*/(*c*·2Δ*t*). We note here that this calculation only shows the basic relations between our phase encoder and the radar systems’ performance. Practical radar systems are subject to more complicated trade-offs involving capability versus performance.

For arbitrary waveform generation, 81 lines of the micro-comb were flattened. On the basis of phase encoding, by tailoring the comb lines’ power according to the tap weights arbitrary waveform generation could be achieved. To demonstrate the flexibility of our photonic RF signal generation approach, we designed square waveforms (Figure 4(a-ⅰ)) with a tunable duty cycle ratio ranging from 10–90%. Similarly, sawtooth waveforms (Fig. 4(a-ⅱ)) with a tunable slope ranging from 0.2 to 1 were generated. The received signals were digitally sampled by an 80 GSa/s real-time oscilloscope, with the measured waveforms normalized to the peak intensity. We then demonstrated the frequency-modulated waveform, as shown in Figure 4(b), for which the sign of the frequency modulation (or ‘chirp’) can be programmed to sweep from high to low and then from low to high frequency, which is very difficult to achieve with electronic techniques. We compared the experimental results obtained with the corresponding calculated instantaneous frequency of the designed symmetric concave quadratic chirp, both of which are shown in Figure 4(b-ⅲ,ⅳ).

Compared to electronic means of arbitrary waveform generation, our scheme makes possible RF waveforms with much higher instantaneous bandwidth by simply shortening the time delay and the corresponding optical pulse width. Note that we used a commercial arbitrary waveform generator (Keysight, 65 GSa/s) here to generate the pulse for this proof of principle demonstration. This allowed us to investigate the device performance by, for example, readily changing the pulse width to test the capability of our system to span different frequency ranges for the RF waveform. In practice, however, electronic AWGs are not necessary and can easily be replaced with many other readily available approaches that are simpler, easier and cheaper [47].

The quality and stability of the soliton crystal comb was more than good enough for our experiments. Indeed, the soliton crystal combs have been shown to be stable and reliable enough to support ultrahigh bandwidth communications at 44Terabits/s [48], with extremely high stability over many 10’s of hours. The energy efficiency and noise of our system would be increased further by reducing the loss through the system, for example by achieving higher levels of integration.

There is significant potential for substantially higher levels of integration than the discrete devices used here – ultimately achieving fully monolithically integrated embodiments of our system. The central component of our system, the optical frequency comb source, is already integrated. Further, all of the other components have been demonstrated in integrated form, including on-chip InP spectral shapers [49], highspeed integrated lithium niobate modulators [50], integrated dispersive elements [51], and photodetectors [52]. Finally, many recent advances have been made in reducint the power-consumption of Kerr combs [53] that would greatly reduce the system energy requirements. These results will have a significant impact on the field of microwave photonics, [54–92] particularly that based on micro-combs [93–209] with potential applications even to the mid IR [210–216]