Photonic microwave and RF programmable true time delays for phased array antennas using a soliton crystal Kerr micro-comb source

We demonstrate signicantly improved performance of a microwave true time delay line based on an integrated optical frequency comb source. The broadband micro-comb (over 100 nm wide) features a record low free spectral range of 49GHz, resulting in an unprecedented record high channel number (81 over the C band) – the highest number of channels for an integrated comb source used for microwave signal processing. We theoretically analyze the performance of a phased array antenna and show that this large channel count results in a high angular resolution and wide beam steering tunable range. This demonstrates the feasibility of our approach as a competitive solution towards implementing integrated photonic true time delays in radar and communications systems.

For PAAs, the number of radiating elements determines the beam-width, and so, in order to enhance the angular resolution, a large channel number is required for the TTDL. Typically, discrete lasers arrays [26,[32][33][34] or FBG arrays [24][25] have been employed for multiple TTDL channels, resulting in a signi cant increase in system cost and complexity. In turn, this greatly limits the number of channels in practical systems. Other schemes based on optical frequency combs (OFCs) [6] can mitigate this problem, yet many approaches to generating OFCs, such as those based on cascaded electro-optical (EO) modulators [9,[35][36][37][38][39][40] and Fabry-Perot EO modulators [41], require external radio frequency (RF) sources, which still impose considerable cost and complexity to the TTDL.
On the other hand, OFCs generated by high-Q micro-resonators, termed micro-combs or Kerr combs [42][43][44][45][46][47], offer a new generation of compact, low-cost, and highly e cient multi-wavelength sources, thus bringing about huge possibilities towards achieving high-performance TTDLs. Their advantages include the potential for a large number of channels (wavelengths) and greatly reduced footprint and complexity, resulting in signi cantly improved performance for delay-line structure-based microwave photonic systems.
Recently, [48,49] we demonstrated photonic microwave TTDLs based on an integrated micro-comb source with a free spectral range (FSR) of 200GHz, achieving high performance when applied to PAAs in terms of beam resolution and angular tuning range. In this paper, we signi cantly improve the performance of this device, both in terms of angular resolution and beamwidth, by employing a microcomb source with a 49GHz FSR, thus dramatically increasing the available number of-channels from 21 to 81 over the C-band, which is a record high for integrated comb source-based TTDLs. We experimentally demonstrate an 81-channel true time delay and then calculate the key performance parameters for a phased array antenna based on our device, thus verifying the feasibility and effectiveness of our approach. Figure 1 shows a schematic of the microwave TTDL based on an integrated optical Kerr comb source.

Operation Principle
The TTDL contains two modules: the rst generates the optical micro-comb using an integrated MRR while the second creates replicas of input RF signals at each wavelength followed by weighting and wavelength dependent time delays (i.e., induced by the dispersive medium) using standard optical bres to form the high-channel count TTDL for the phased array antenna.
The MRR used to generate the Kerr optical comb ( Fig. 2(a)) was fabricated on a high-index doped silica glass platform using CMOS compatible processes [42]. First, high-index (n = ~1.7 at 1550 nm) doped silica glass lms were deposited using plasma enhanced chemical vapour deposition (PECVD), and then patterned by deep UV photolithography and subsequently processed via reactive ion etching to form waveguides with exceptionally low surface roughness. Finally, silica (n = ~1.44 at 1550 nm) was deposited via PECVD as an upper cladding. Our device architecture used a vertical coupling scheme where the gap can be controlled via lm growth -a more accurate approach than lithographic techniques [50]. Other advantages of our platform for nonlinear optics include ultra-low linear loss (~0.06 dB cm −1 ), a relatively high nonlinear parameter (~ 233 W −1 km −1 ) and, in particular, negligible nonlinear loss up to extremely high intensities (~25 GW cm −2 ) [42][43][44]. The compact integrated MRR had a radius of ~592 µm with a free spectral range (FSR) of ~0.4 nm, i.e., ~49 GHz, as indicated in Fig. 2(b) and Fig. 2(d). Although micro-combs with smaller FSRs have been reported with whispering-gallery-mode resonators or SiN micro-ring resonators [51,52], our device has the smallest FSR of any micro-comb source that has been used for microwave signal processing. This FSR -a factor of 4 smaller than our previous results [48,49] -enabled up to four times the number of channels (as many as 81 channels) over the C-band. After packaging the device with bre pigtails, the total insertion loss was ~ 1 dB. Due to the ultra-low propagation loss of our platform, the MRR featured a narrow resonance linewidth (Fig. 2(c)) corresponding to a Q factor of ~1.2 million. In order to obtain optimal parametric gain, the MRR was designed to feature anomalous dispersion in the C-band [53].
In the rst module, CW pump light from a tunable laser source was ampli ed by an erbium-doped bre ampli er (EDFA) to pump the on-chip MRR. Before the MRR, a tunable optical bandpass lter and a polarization controller were employed to suppress the ampli ed spontaneous emission noise and adjust the polarization state, respectively. When the pump wavelength was tuned to one of the resonances of the MRR and the pump power was high enough to provide su cient parametric gain, parametric oscillation in the MRR occurred, ultimately generating a Kerr optical comb with a high degree of equal line spacing [42][43]. In order to avoid resonance drift and maintain the wavelength alignment of the resonances to the pump light, the MRR was mounted on a temperature controlled stage.
In the second module, the generated Kerr comb was directed to a Mach-Zehnder modulator (MZM), where replicas of an input RF signal were produced at each wavelength. The output optical signals from the MZM were delayed by a dispersive SMF, yielding a time delay difference between adjacent channels.
Finally, individual channels were manipulated by a waveshaper, separated by a wavelength division multiplexer (WDM), thus achieving a multichannel RF TTDL based on Kerr combs.
We note that integrated dispersive delays for fully integrated beamforming systems have been achieved recently using promising approaches, including chirped Bragg gratings [54], photonic crystals [55], and low loss silicon nitride waveguides [56].
In PAA systems, optical signals on selected TTDL channels are separately converted into the electrical domain and then sent to an antenna array to drive the radiating elements. Considering that the antenna array is a uniformly spaced linear array with an element spacing of d PAA , the steering angle θ 0 of the PAA can be given as [57] where c is the speed of light in vacuum, and τ is the time delay difference between adjacent radiating elements. From Eq. (1), one can see that the steering angle can be tuned by adjusting τ, i.e., changing the length of the dispersive medium or simply selecting every m th (m = 1, 2, 3, …) TTDL channel as radiating elements. These two approaches for tuning τ offer complementary advantageseither ne tuning steps or a large tuning range, respectivelyand so they can be combined to achieve optimized performance for practical applications. In the latter case, τ = mT, where T is the time delay difference between adjacent channels, which is determined jointly by the frequency spacing of the comb source and the dispersion accumulated in the delay line. Thus, the steering angle is given by And the corresponding array factor (AF) of the PAA can be expressed as [57] where θ is the radiation angle, M is the number of radiating elements, and λ RF is the wavelength of the RF signals. The angular resolution of the PAA is the minimum angular separation at which two equal targets at the same range can be separated, and is determined by the 3-dB beam-width that can be approximated [58] as θ 3dB = 102/M, which in turn greatly decreases with the number of radiating elements (M). Our TTDL, based on an integrated optical comb source, provides a large number of radiating elements for beam steering, resulting in a greatly enhanced angular resolution of the PAA. Compared with existing techniques based on discrete laser diode arrays, our approach features a compact and simpli ed structure, with potentially signi cantly reduced cost and high performance brought about by the large number of delay channels.

Experimental And Theoretical Results
In order to generate the 49 GHz spacing micro-comb, the pump power was boosted up to 30.5 dBm via an EDFA and the wavelength was swept towards the red side. When the detuning between pump wavelength and MRR's resonance became small enough such that the intracavity eld reached a threshold value, modulation instability was initiated, and primary combs arose with a spacing of multiple FSRs. As the detuning was further changed, the parametric gain lobes broadened and secondary comb lines with a spacing equal to the FSR of the MRR were generated by both degenerate and non-degenerate four wave mixing. This nally resulted in a single FSR spaced Kerr optical comb [44,59] (Fig. 2(e)) that was over 100nm wide. A zoom-in view (Fig. 2(f)) indicates that potentially over 400 wavelengths were available for the TTDL. For our experiments, however, the wavelength range was limited to the C-band because of the waveshaper and EDFA, and so this resulted in 81 usable channels, or wavelengths.
While the spectral pro le of our comb was not indicative of operation in the single cavity soliton regime, at the same time the observed stability of the comb spectrum made it clear that we were not operating in the chaotic regime of the Ikeda map [60, 61]. In fact, both the shape and stability of our comb, we believe, are indicative of possible operation in multiple soliton states such as recently reported soliton crystals [62]. Practically speaking, we found that as long as the chaotic states are avoided, the combs generally exhibit su cient stability to feature low enough intensity noise to allow for their effective use in these applications.
The generated comb served as the multi-wavelength source for the TTDL and since the comb spectrum was stable, a waveshaper could be used to shape the comb lines in order to generate desired channel weights. The optical power difference between the comb lines could be compensated for via multi-stage spectral shaping combined with optical ampli cation [20] to meet practical systems' requirements.
Looking to the future, high-conversion-e ciency Kerr combs generated by dark pulses [63] may provide an attractive solution to produce appropriately shaped combs with much higher energy e ciency.
As Fig. 1 shows, the modulated signal after the MZM (EOSPACE) was propagated through ~2.122-km of single mode bre with a dispersion of ~17.4 ps/(nm km), corresponding to a time delay of ~14.8 ps between adjacent wavelength channels. We subsequently employed a Waveshaper (Finisar 4000s) as a wavelength division multiplexer to separate these channels, and then convert them back into the RF domain for PAA applications, thus achieving a high-channel count (up to 81 around the pump wavelength) TTDL with a compact structure.
The RF phase response was characterized by a vector network analyser (Anritsu 37369A), Fig. 3(a)), in which the channel at the central pump wavelength (channel 40) was set as the reference. The time delays corresponding to the measured phase slopes are shown in Fig. 3(b), in which a time delay step of ~14.8 ps/channel can be observed. To evaluate the uniformity of the delay steps between adjacent channels, we t the measured delays with a second-order polynomial function where µ = 1, 2, 3, … , 81, is the channel number, and p 0 , p 1 , p 2 are the t coe cients. As Eq. 4 shows, uniform delay steps correspond to linear τ(µ), while the t curves (p 0 = 6.7687, p 1 = 14.8, p 2 = 0.011878) shown in Fig. 3(b) indicate the appearance of small second-order terms arising from the third-order dispersion (TOD), thus introducing small delay errors in the TTDL (as extracted in the inset). Deviation in the comb wavelength spacing is extremely small (<1MHz), and so any delay errors induced by nonequidistance of the comb lines (<10 -3 fs/step) is negligible.
To investigate key performance parameters of the PAA driven by the micro-comb based TTDL, we calculated the array factors (AFs). Since many factors contribute to the performance of the PAA, such as delay errors, imprecision in channel weights, the number of radiating elements and rapid RF frequency variations, we adopted control variables during the investigation and calculated the AFs by varying only one parameter at a time.
In Fig. 3(c), the AFs are calculated with, and without, delay errors (uniform weights, λ RF = 2.5 cm, d PAA = λ RF / 2, M=81, m=1). As can be seen, the delay errors induced by TOD shift the beam steering angle by 1.54°, and so this must be compensated for when designing the PAA system. We note that TOD compensation in ber has been widely investigated using many approaches, and in our case this can easily be achieved by programming the phase characteristics of the waveshaper.
In Fig. 3(d), the AFs are calculated with generated weights (inset, where the weights of 5 comb lines are supressed for the calculation) and uniform weights (λRF = 2.5 cm, dPAA = λRF / 2, M=81, m=1, T=14.8ps). Both of the AFs calculated this way yield different beam patterns that are each useful for speci c applications. We note that arbitrary beam patterns can be achieved by shaping the channel weights, as we previously reported [48,49].
In Fig. 3 (e), AFs are calculated as as M increases from 4 to 81 (uniform weights, λ RF = 2.5 cm, d PAA = λ RF / 2, m=1, T=14.8ps), where we see that the corresponding 3dB beamwidth θ 3dB signi cantly decreases from 26.8° to 1.2°, matching well with the prediction θ 3dB = 102/M, as shown in Fig. 3(f). Compared with previous results based on a 200GHz-FSR Kerr comb [49], the much larger channel number provided by the 49GHz-FSR Kerr comb signi cantly improves beam resolution for the PAA by more than a factor of four.
To achieve a tunable beam steering angle, every m th (m = 1, 2, 3, …) wavelength of the TTDL can be selected by using the waveshaper. As well, the time delay (τ ) between the radiating elements could be varied with a step size of T. As shown in Fig. 4(a), with 6 radiating elements (M=6), as m varies from 1 to 15, a large tuning range from -69.7° to 72.9° can be achieved. We note that tuning by selecting every m th wavelength is practical in our case because of the large number of channels. The beamwidth ( ∼m ) and steering angle tuning range (∼ 1/m ) represent a trade-off in practical systems. To re ect the relationships between those parameters, in Fig. 4(b-e), we present AFs of PAAs with varying m and M, where M = ⌊Channel Number / m ⌋. Considering the practical requirements for beam steering, M can be set to 3 at least, and thus for the 21-channel PAA based on the 200GHz-FSR Kerr comb [49], m could reach 7 at most, while for the 81-channel PAA based on the 49 GHz-FSR Kerr comb, m could reach as much as 27. Fig. 4(b-c) shows the corresponding M, θ 3dB and θ 0 as a function of m. As can be seen, on the one hand, the 49GHz FSR Kerr comb enables a much larger M as m varies, thus leading to a signi cantly smaller θ 3dB and greatly enhanced angular resolution (Fig. 4(d)). On the other hand, ner tuning steps (from 1.0° to 14.7°) as well as a larger tuning range (142.7°) of the beam steering angle θ 0 are available due to the larger m (Fig. 4(e)).
Given the practical requirements in beamwidth and steering angle tuning range, optimized sets of m and M can be clearly identi ed from these calculations. Further, the beam steering angle can be improved in terms of both tuning step and tuning range by employing dispersion tunable media [32,34] in addition to varying the number of TTDL channels.
Moreover, the PAA can also achieve a wide instantaneous RF bandwidth without beam squint (variation in beam steering angle with RF frequency). Based on the proposed TTDL, as indicated in Fig. 4(f), the beam steering angle θ 0 remains 20.7° while the RF frequency varies from 2 GHz to 17 GHz (with uniform weights, d PAA = 1.25 cm, m=1, M=81,T=14.8ps). As a result, due to our large number of channels, the PAA features greatly enhanced angular resolution, large instantaneous bandwidth, and a wide tunable range of the beam steering angle. This approach is applicable to a wide range of wavelengths even outside the telecom band to the mid IR.
[64-70] Soliton crystal microcombs have been extremely successful at a wide range of microwave and RF functions.

Conclusion
We demonstrate a high channel count (81 over the C-band) TTDL based on an integrated optical frequency comb source. A broadband Kerr comb with a large number of comb lines was generated by an on-chip MRR with an FSR of 49 GHz, which was employed as a high-quality multi-wavelength source for the TTDL. Compared with traditional approaches, the size, complexity and, ultimately, the cost of the system can be greatly reduced. The large channel number of the TTDL resulted in a PAA with a calculated high angular resolution and wide tuning range of the beam steering angle. The enhancement in performance matches well with theory, con rming the feasibility of our approach as a promising solution towards implementing highly recon gurable TTDLs for microwave photonic signal processing functions.

Declarations
Competing interests: The authors declare no competing interests.