Optical frequency combs (OFCs) have become increasingly pervasive in recent years, with their advantageous frequency coherence properties enabling significant developments in numerous fields, such as optical communications, spectroscopy, and microwave signal processing. Recent interest in OFC development emphasizes minimizing and mitigating phase noise of individual comb lines for high-quality signal generation, processing, and detection. Cavity-less electro-optic combs and parametric combs are attractive sources for these applications in that they permit flat spectra, tunable tone spacing, and robustness to temperature variations. Although previous research has demonstrated broadband parametric OFC generation, the scaling of the phase noise has not been systematically investigated. Here, we demonstrate a 25 GHz-spacing cavity-less parametric OFC generator and investigate the interaction between electronic and optical noise sources that affect its phase noise and linewidth. In addition, we study the optimal design of a nonlinear amplified loop mirror based pulse shaper with a focus on the impact of pump power on the signal-to-pedestal power ratio, which ultimately influences the spectral flatness and the optical signal-to-noise ratio (OSNR) after the parametric expansion. Notably, we design the OFC using all polarization-maintaining (PM) components, demonstrating the performance of PM highly nonlinear fibers in parametric comb generation. This results in a PM cavity-less comb with <9 dB power variation over 110 nm, >0 dBm power per tone, <10 kHz linewidth, and >23 dB OSNR. These characteristics make it highly desirable for application in communication and signal processing.

Optical frequency combs (OFCs) were originally developed to count optical cycles for frequency metrology.1 Over the past decade, they have significantly expanded their application space into the realms of telecommunications, spectroscopy, and signal processing.2–7 For example, OFCs with a high optical signal-to-noise ratio (OSNR) and narrow linewidths can be exploited as light sources and local oscillators in coherent wavelength division multiplexing (WDM) communication systems to effectively mitigate optical fiber nonlinearities.8–10 Emerging ultra-wideband transmission systems that use the S + C + L bands would benefit from high power and flat-spectrum OFCs to maximize spectral efficiency.11 

Low phase noise and flat-spectrum OFCs have also been found to be the key enabler of coherent light detection and ranging (LiDAR),12 comb-assisted radio frequency (RF) signal processing,4,13 medical spectroscopy,14 and carrier frequency synchronization for microwave systems.15 These emerging applications have motivated the development of OFC generators that emphasize high OSNR, flat spectra, tunable tone spacing, and low phase noise, rather than “over-one-octave” spectral widths as in metrology.16–18 

Cavity-based OFCs, such as mode-locked lasers, resonant cavity electro-optic (EO) combs, and microring resonator-based Kerr combs,19–21 are efficient in producing broad spectral bandwidths but usually output spectra with poor flatness due to the deterministic pulse shapes formed by the cavity. In contrast, cavity-less OFCs, such as gain-switched combs,22,23 cascaded-modulator-based OFCs,24,25 parametric OFCs,26 or combined approaches,16,17 have shown flat spectra over the bandwidth of interest, promising high performance and robust operation for communication and signal processing applications.4,27 For example, previous research has demonstrated the development of fiber-based flat-spectrum combs with >0 dBm per tone and an OSNR (considering 0.1 nm noise bandwidth) exceeding 33 dB over the telecom C-band,26 supporting high spectral efficiency [>64 quadrature amplitude modulation (QAM)] and high capacity (>2 Pb/s) transmission.28 

However, despite the high performance demonstrated by OFC generation schemes thus far, several significant challenges remain to be addressed. First, the existing demonstrated parametric combs are not polarization-maintaining (PM) due to the use of non-PM components, such as standard single-mode fibers (SSMFs) and non-PM highly nonlinear fibers (HNLFs). As a result, optical transceivers or processors based on such OFCs would require active polarization control, adding cost and complexity. Second, recent research shows that the non-PM mixers that generate new optical tones in the parametric comb introduce additional amplitude and phase noise compared to their PM counterparts, which leads to degraded phase noise.29 Finally, although line-by-line linewidth characterization has been performed using the self-heterodyne delay interferometer method (SHDI),30 the scaling of phase noise and the interaction between different origins of noise in an EO comb or an EO-comb-pumped parametric OFC generator have not been investigated. Gaining insight into how noise scales with comb bandwidth is crucial for the comb-based signal processing and digital signal processing (DSP) design in microwave and optical communications. This understanding is particularly relevant for joint phase estimation and phase-coherent nonlinearity mitigation, where phase coherence plays a critical role.8,9,25

To address the above-mentioned challenges, here, we develop an all-PM parametric OFC generator and investigate the scaling of electronic and optical phase noise in the EO comb and EO-seeded parametric comb. The use of all PM components in this comb generator facilitates seamless integration with wavelength demultiplexers and modulators and ensures stable, polarization-independent shaped pulses from the NALM pulse shaper for nonlinear broadening. To optimize the spectral flatness, we designed and optimized a NALM as a pulse shaper,31,32 in which we study the impact of the pump power on the pulse width and pulse signal-to-pedestal ratio as well as the bandwidth of the expanded comb using a PM-HNLF as a nonlinear mixer. Specifically, we investigate the phase noise scaling of the comb using two RF signal generators with distinct phase noise profiles. Through characterization of the line-by-line optical phase noise of both the EO comb and the parametric comb, we demonstrate the critical role of the RF phase noise in determining the phase noise and linewidth of the broadened comb tones. Utilizing an ultra-low noise RF generator minimizes RF-noise-induced linewidth degradation, resulting in a low-noise frequency comb with a linewidth of less than 10 kHz over a spectral range of 110 nm. To the best of our knowledge, this represents the first demonstration of the PM-HNLF-based parametric OFC generator and the first systematic report of the scaling of its optical phase noise and linewidth.

Figure 1(a) shows the schematic diagram of our cavity-less PM OFC generator. Similar configurations have previously been reported using non-PM HNLF as a parametric mixer.26,33 The OFC generator consists of an EO frequency comb generator, a NALM-based pulse shaper, and a PM-HNLF-based nonlinear mixer. All the components and fibers are PM. The EO comb is seeded using a 1 kHz-linewidth continuous-wave (CW) laser emitting 12 dBm at 1550.08 nm. The CW laser is amplified to 27 dBm using PM-fiber amplifier 1 (PM-FA1) before being modulated by cascaded intensity and phase modulators, all driven by phase-synchronized 25 GHz RF signals from the same source to create a 25 GHz-spacing EO comb signal of about 76 tones with a spectral flatness of about 7 dB. In the time domain, this corresponds to a pulse train with a repetition rate of 25 GHz, with each pulse exhibiting a quasi-linear frequency chirp.17,34 The chirped pulses are subsequently compressed to their transform limit using a 48 m PM single-mode fiber [dispersion: 18 ps/(nm km)], yielding a 25 GHz-repetition rate pulse train with a full-width half-maximum (FWHM) pulse width of 470 fs (assuming a Gaussian pulse shape for the main lobe), as indicated by the black autocorrelation curve in Fig. 1(c). To study the impact of RF noise on the OFC’s phase noise, we employed two different RF synthesizers with a distinct phase noise performance, as compared in Fig. 1(b). RF1 is an OEM low-noise frequency synthesizer (SignalCore SC5521A), whose phase noise is shown in black in Fig. 1(b). RF2 [red curve in Fig. 1(b)] is generated using a state-of-the-art low-noise RF synthesizer (Rohde and Schwarz SMA100B), which has ∼10 dB lower phase noise than RF1 in the sub-300 kHz region and more than 30 dB lower phase noise in the >1 MHz region.

FIG. 1.

Comb generation prototype and interim results. (a) PM parametric comb generation scheme. (b) RF phase noise PSD of the two 25 GHz signals: RF1 (black) and RF2 (red). (c) Autocorrelator measurement for the pulses before (black) and after (red) the NALM. CW, continuous wave; PM, polarization maintaining; FA, fiber amplifier; NALM, nonlinear amplifying loop mirror; WDM, wavelength division multiplexing; EDF, erbium-doped fiber; HNLF, highly nonlinear fiber; and OSA, optical spectrum analyzer.

FIG. 1.

Comb generation prototype and interim results. (a) PM parametric comb generation scheme. (b) RF phase noise PSD of the two 25 GHz signals: RF1 (black) and RF2 (red). (c) Autocorrelator measurement for the pulses before (black) and after (red) the NALM. CW, continuous wave; PM, polarization maintaining; FA, fiber amplifier; NALM, nonlinear amplifying loop mirror; WDM, wavelength division multiplexing; EDF, erbium-doped fiber; HNLF, highly nonlinear fiber; and OSA, optical spectrum analyzer.

Close modal

As spectral flatness is one of the key performance requirements, we implemented a NALM to suppress the low-power pedestals that result from the dispersive chirp compression, which can cause significant spectral rippling after the mixing stage and reduce the mixing efficiency. Note that the pedestal can be eliminated if the EO comb stage generates a perfect Gaussian pulse with a linear chirp. Nevertheless, the quasi-linear chirp generated by modulating phase modulators with sinusoidal signals unavoidably introduces pedestals in the time domain. Compared to the passive nonlinear optical loop mirror (NOLM), a NALM offers a higher suppression of the pulses’ pedestals and a lower loss, resulting in a flatter spectrum with a higher OSNR after the parametric mixer stage.

Our NALM is comprised of a 60:40 coupler, a bi-directional erbium-doped fiber amplifier (EDFA), and a 40 m PM-HNLF, labeled as PM-HNLF 1 in Fig. 1(a). The PM-HNLF 1 exhibits a dispersion of −0.5 ps/(nm km) at 1550 nm and zero dispersion wavelength of 1565 nm [a dispersion slope of 0.024 ps/(nm2 km)]. The estimated nonlinear coefficient (effective gamma) is ∼10.5 W−1 km-1. To minimize the residual dispersion originating from fiber pigtails and erbium-doped fiber (EDF), we develop a bi-directional EDFA using a highly doped PM EDF with a peak absorption of 80 dB/m at 1530 nm. Pump 1 consistently outputs 660 mW, while the output power of pump 2 is adjusted to achieve a flat spectral shape after the nonlinear mixing stage. Unlike standard telecommunication EDFA that utilizes standard EDF with a much lower peak absorption of about 5–8 dB/m, the highly doped EDF significantly reduces the length of the EDF and, consequently, the residual dispersion within the loop, resulting in shorter pulse widths and higher pedestal suppression ratios. In addition, due to self-phase modulation (SPM), the output pulses from the NALM undergo further compression. The optical pulse propagating clockwise undergoes SPM in the center of the pulses due to the high peak power, while the pedestals of the pulse do not experience SPM due to the low power. The counterclockwise propagated pulses are not amplified, and therefore, no SPM effect occurs for both the pulse peak and pedestals. After interfered at the coupler, the pedestals are reflected and the center of the pulses passes through the NALM, resulting in an increased signal-to-pedestal power ratio. The NALM output pulse width after PM dispersion compensation fiber (DCF) compression is ∼260 fs and the autocorrelation signal-to-pedestal ratio is 15 dB, shown as the red curve in Fig. 1(c). Here, we use the derived signal-to-pedestal ratio from the autocorrelation traces as an approximate metric for the actual signal-to-pedestal ratio of the pulse. The autocorrelation traces are measured at position ① shown in Fig. 1(a), for the pulse characterization before NALM, and after the isolator and PM-DCF at position ② for the pulse characterization after NALM.

In the final stage, the shaped pulses are amplified to an average power of 33 dBm using a PM booster EDFA (PM-FA2) before pumping a 50 m PM-HNLF, labeled as PM-HNLF 2 in Fig. 1(a). The PM-HNLF 2 has a normal dispersion of −1.3 ps/(nm km) and a zero dispersion wavelength of 1605 nm. To compensate for any residual dispersion introduced by the booster EDFA, we employed a PM-DCF to ensure maximum peak power delivery to the nonlinear mixer. We characterize the comb spectra and OSNR using an optical spectrum analyzer (OSA) with a resolution of 0.02 nm. A 120 pm bandwidth tunable filter was employed to extract individual tones for phase noise characterization. The phase noise of individual comb tones is characterized using a self-homodyne-based phase noise analyzer, and the consequent linewidth is calculated from the phase noise measurement assuming 100 µs observation time.35 

Figure 2 shows the spectra of the first-stage EO comb [Fig. 2(a)] and expanded comb at 0.02 nm resolution [Fig. 2(b)]. Considering a minimum of −1 dBm power per tone, we obtain a 110 nm comb bandwidth spanning from 1500 to 1610 nm, containing 550 tones with a power variation of 9 dB for the expanded parametric comb. Figures 2(c)2(e) display the zoomed-in ranges for the expanded comb around 1520, 1550, and 1582 nm, respectively. A relatively large power variation is observed within the original EO comb bandwidth at 1540 and 1560 nm, which we attribute to the SPM-induced chirp, causing pulse broadening inside the PM-HNLF 2. As the pulses broaden, they overlap with the residual pulse pedestals and cause fast temporal oscillations that lead to spectral ripples within the EO comb bandwidth.31 Since no pedestal spectral components exist outside 1540–1560 nm, no such interference occurs in the generated four wave mixing (FWM) tones.

FIG. 2.

Measured spectrum. (a) Spectrum of the seed EO comb. (b) Expanded spectrum with 0.02 nm resolution. (c)–(e) Spectral insets centered at 1520 , 1550, and 1582 nm, respectively.

FIG. 2.

Measured spectrum. (a) Spectrum of the seed EO comb. (b) Expanded spectrum with 0.02 nm resolution. (c)–(e) Spectral insets centered at 1520 , 1550, and 1582 nm, respectively.

Close modal

Figures 3(a) and 3(b) show the measured linewidth. The black squares and red triangles show the measured linewidth for individual comb tones driven by RF1 and RF2, respectively. In the EO comb measurements shown in Fig. 3(a), the linewidth results are recorded with a 200 GHz interval between 8 tones. Using RF1 signals, the 100 µs linewidth is <4 kHz, while the RF2 signal yields a lower linewidth of less than <2 kHz over the comb bandwidth. Note that the center tone at 1550 nm exhibits the same linewidth using both RF drivers as it is not modulated and, thereby, does not have added RF phase noise.

FIG. 3.

Linewidth measurement. (a) Measured EO comb linewidth for tones with a 200 GHz interval. (b) Measured parametric comb linewidth for tones with an 800 GHz interval with 100 µs observation time using two different RF generators: RF1 (black squares) and RF2 (red triangles).

FIG. 3.

Linewidth measurement. (a) Measured EO comb linewidth for tones with a 200 GHz interval. (b) Measured parametric comb linewidth for tones with an 800 GHz interval with 100 µs observation time using two different RF generators: RF1 (black squares) and RF2 (red triangles).

Close modal

Figure 3(b) shows the measured linewidth of the expanded comb. Using RF1, the linewidth of the expanded comb scales from about 7 kHz in the center of the spectrum to about 40 kHz at the edge of the comb spectrum. The RF2-based parametric comb generator has a significantly improved linewidth, which remains sub-10 kHz over the 110 nm spectral width. As we will show subsequently, this improvement is mainly due to the low phase noise of the first stage EO comb, which is a sum of laser phase noise and the multiplied RF noise in the EO comb generation.

The phase noise of single tone in an EO comb is the sum of the laser phase noise and the multiplied RF phase noise through the modulator. The phase noise of the nth line of an EO comb can be expressed as36–39 
ϕn(t)=ϕl(t)+nϕrf(t),
(1)
where ϕl and ϕrf are the phase noise originating from the laser source and RF oscillator, respectively.

To study how phase noise scales, we measure the phase noise of comb lines and plot the representative results for EO combs driven by RF1 in Fig. 4(a) and RF2 in Fig. 4(b). As the tone order increases, the added RF noise scales with the tone number, while the optical noise from the seed laser remains unchanged. This has resulted in degraded optical phase noise, especially in the high-frequency region (100 kHz to 10 MHz). In the low-frequency range (<100 kHz), the phase noise remains largely the same, indicating that the phase noise of the seed laser dominates in this frequency range. For example, at 10 kHz offset, the phase noise of the EO comb line is around −50 dBc/Hz, which is the same as the PSD value of the laser phase noise. In the 1–10 MHz frequency offset region, the phase noise increase is ∼20 log10(m/n) between the nth and mth tones, where m > n. For instance, in Fig. 4(a), the phase noise of the +8th tone at 1 MHz offset is around −91 dBc/Hz and the +16th tone has a phase noise of −85 dBc/Hz, which indicates that the RF phase noise is the dominated noise in this frequency region. On the contrary, no discernible degradation is observed on the phase noise measurements for the EO comb using RF2 due to the significantly lower RF noise. In this case, the EO comb phase noise is almost equal to the laser phase noise.

FIG. 4.

EO comb phase noise. (a) Phase noise of the EO comb using RF1, for center tone (black), +8th tone (blue), +16th tone (green), and +32nd tone (orange). (b) Phase noise of the EO comb using RF2 [the same color code mentioned in (a)].

FIG. 4.

EO comb phase noise. (a) Phase noise of the EO comb using RF1, for center tone (black), +8th tone (blue), +16th tone (green), and +32nd tone (orange). (b) Phase noise of the EO comb using RF2 [the same color code mentioned in (a)].

Close modal

Figures 5(a) and 5(b) show the measured phase noise of the expanded comb. The strong RF phase noise from RF1 is further multiplied through the nonlinear parametric process and dominates the phase noise of the expanded comb tones. Using RF2, we obtain a significantly improved phase noise, and the high-order tones (+64, +96, and +128th tones) exhibit a similar linewidth. Interestingly, we observe harmonic peaks, which are multiples of 70 kHz in the expanded comb tones, as shown in both Figs. 5(a) and 5(b). We attribute the harmonic spurs observed in the phase noise measurement to the intensity noise induced by PM-FA2. Notably, its pump driver displays a 70 kHz harmonic tone along with strong low-frequency peaks, as evident in the relative intensity noise (RIN) measurement illustrated in Fig. 5(c). Here, the comparison is drawn between the RIN for the seed laser (represented by the black curve) and the laser amplified by PM-FA2 (depicted by the blue curve). Furthermore, this single tone was multiplied in the nonlinear process, generating high-order harmonics in the phase noise. These added harmonic distortions could be removed by improving the driver electronics and eventually improving the phase noise performance. As the 70 kHz tone is introduced from the current drive of the EDFA pump diode, the intensity noise can be eliminated by using a low-noise pulse amplifier or adding a current filter.

FIG. 5.

Expanded comb noise. (a) Phase noise of the broadened comb using RF1, for center tone (black), +64th tone (blue), +96th tone (green), and +128th tone (orange). (b) Phase noise of the broadened comb using RF2. (c) RIN measurement for the laser (black) and pumped laser (blue).

FIG. 5.

Expanded comb noise. (a) Phase noise of the broadened comb using RF1, for center tone (black), +64th tone (blue), +96th tone (green), and +128th tone (orange). (b) Phase noise of the broadened comb using RF2. (c) RIN measurement for the laser (black) and pumped laser (blue).

Close modal

Previous research showed that the pedestals of the pulses have a significant impact on spectral flatness after the parametric mixer stage.31 The pedestal suppression ratio, which is defined as the power ratio between the peak power of the whole pulse and the peak power of the first side lobe in the time domain auto-correlation results, is employed here as a metric to qualify the quality of the pulse shaping. Although a theoretical analysis has been developed for NALM assuming SPM and a linear bi-directional amplifier gain, its experimental behavior is more complicated due to factors such as the input power-related gain-tilting, amplifier gain saturation, in-loop dispersion and four-wave mixing, and pumping scheme. Here, we experimentally investigate the impact of pump power on the pedestal suppression ratio and its impact on the spectrum and OSNR of the shaped pulses.

Figure 6(a) shows the measurement of the input pulses (gray curve) to the NALM and the output pulses with different total pump powers. The pulse shapes are normalized to their peak power for comparison. The FWHM pulse width entering the NALM is about 470 fs, and the pulse width of the NALM output is about 260 fs regardless of the pump power. Therefore, we can conclude that the pump power has a limited impact on the pulse width. However, a zoomed-in examination of the pedestals, shown as the inset in Fig. 6(a), clearly shows that the pedestal power decreases as the pump power increases from 660 mW (blue) to 940 mW (yellow). The quantified measurements of the pedestal suppression ratio are shown in Fig. 6(b), with the experimental results shown in red solid squares as the pump power increases from 15 to about 22 dB, saturating at 950 mW pump power. The total NALM output power as a function of the pump power is shown in Fig. 6(c). With 10 dBm input power, the NALM becomes transparent with about 700 mw pump power.

FIG. 6.

Pulse analysis. (a) Pulse before NALM (gray); pulses after NALM with different EDFA pump powers of 660 mW (blue), 760 mW (red), and 940 mW (yellow); the inset shows the zoomed-in view of the pedestals of the pulses. (b) Autocorrelation peak-to-pedestal ratio for different pump powers. (c) Power after NALM for different pump powers.

FIG. 6.

Pulse analysis. (a) Pulse before NALM (gray); pulses after NALM with different EDFA pump powers of 660 mW (blue), 760 mW (red), and 940 mW (yellow); the inset shows the zoomed-in view of the pedestals of the pulses. (b) Autocorrelation peak-to-pedestal ratio for different pump powers. (c) Power after NALM for different pump powers.

Close modal

Two representative spectra of the NALM’s outputs are plotted in Figs. 7(a) and 7(b), for 660 and 940 mW pump powers, respectively, to show the impact of pump power on the optical spectra. Although the pulse widths remain the same, a broader spectrum is clearly observed with a higher pump power due to the greater in-loop power, which leads to a stronger nonlinear expansion in the clockwise propagation of the short pulses. This has also resulted in significantly enhanced OSNR in the short (1520–1540 nm) and long (1560–1580 nm) wavelength regions, which are generated by the clockwise-propagated pulses. This enhanced nonlinearity has also led to the reduction in the pedestal power due to the interference at the output of the NALM, resulting in a smaller power fluctuation and an average OSNR of 33 dB in the 1540–1560 nm wavelength region, which is 5 dB greater than the 660 mW pump power spectrum. The Gaussian-like spectra lead to a flatter spectrum after the parametric mixer stage, as shown in Fig. 7(e). The spectrum in gray shows the expanded spectrum with the NALM operating at 660 mW pump power, and the orange spectrum shows the expanded comb pumped by the NALM operating at 940 mW pump power [refer to Fig. 2(b) for the detailed spectrum]. The comb with a higher pump power provides a broader and flatter spectrum. By optimizing the NALM, we reduced the power variation in the 1520–1560 nm by 5 dB. A 90 nm bandwidth, 10 dB flatness comb with an average OSNR of more than 25 dB is achieved.

FIG. 7.

Spectrum analysis. (a) NALM output spectrum with a single pump power of 660 mW. (b) NALM output spectrum with a pump power of 760 mW. (c) Expanded output spectrum with a pump power of 660 mW (gray) and spectrum with a pump power of 940 mW (orange).

FIG. 7.

Spectrum analysis. (a) NALM output spectrum with a single pump power of 660 mW. (b) NALM output spectrum with a pump power of 760 mW. (c) Expanded output spectrum with a pump power of 660 mW (gray) and spectrum with a pump power of 940 mW (orange).

Close modal

In conclusion, we have demonstrated the first PM-HNLF-based parametric comb generator, achieving a 25 GHz-spaced frequency comb spanning more than 110 nm over 1500–1610 nm. Our phase noise and linewidth analysis clearly indicates that electronic noise should be minimized for high-power performance OFC generators, providing guidance for low-noise EO comb and parametric comb designs. We discuss the optimization of a practical NALM for pulse shaping, providing new insights into how to optimize OSNR and spectrum flatness in a parametric comb system. The PM design in conjunction with the high OSNR, high power, <9 dB spectrum flatness, and <10 kHz linewidth across the whole spectrum region would benefit applications such as optical transceivers and interferometry.

The authors acknowledge the EPSRC ORBITS (Grant No. EP/V051377/1) and BBSRC (Grant No. BB/X005100/1) projects and Royal Society (Grant No. RGS/R1/221215) for their funding and technical support. Y. Luo acknowledges the National Natural Science Foundation of China (Grant No. 62102343). A. Heidt acknowledges funding by the Swiss National Science Foundation (Grant No. PCEFP2_181222).

The authors have no conflicts to disclose.

Yijia Cai: Conceptualization (supporting); Formal analysis (equal); Investigation (equal); Validation (lead); Writing – original draft (equal); Writing – review & editing (equal). Ronit Sohanpal: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). Yuan Luo: Funding acquisition (equal); Project administration (supporting); Resources (equal); Writing – review & editing (supporting). Alexander M. Heidt: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Software (equal); Writing – review & editing (supporting). Zhixin Liu: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are openly available in UCL Research Data Repository at http://doi.org/10.5522/04/24449050.

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