I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. PRINCIPLE AND EXPERIM...III. EXPERIMENTAL RESULTS...IV. CONCLUSIONREFERENCESOptical frequency combs emerging as a powerful tool in optics are of significant merit in precise measurements of time and frequency.1–31. R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000). https://doi.org/10.1103/physrevlett.85.22642. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). https://doi.org/10.1038/416233a3. J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: From frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003). https://doi.org/10.1109/jstqe.2003.819109 The broad bandwidth, unprecedented frequency accuracy, and spectral resolution of frequency combs have greatly revolutionized optical frequency metrology via a remarkably stable measurement grid provided by the equally spaced comb lines.4,54. S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306, 1318–1324 (2004). https://doi.org/10.1126/science.11023305. N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13, 146–157 (2019). https://doi.org/10.1038/s41566-018-0347-5 As a promising alternative candidate for a miniature frequency comb, soliton microcombs, generated from microresonators pumped by a continuous-wave (CW) laser, have received increasing interest for their less energy consumption, more compact footprint, and complementary metal–oxide–semiconductor compatibility.6–86. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007). https://doi.org/10.1038/nature064017. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011). https://doi.org/10.1126/science.11939688. L. Chang, S. Liu, and J. E. Bowers, “Integrated optical frequency comb technologies,” Nat. Photonics 16, 95–108 (2022). https://doi.org/10.1038/s41566-021-00945-1 Particularly, soliton microcombs provide fully coherent frequency combs and phase-locked femtosecond pulses with ultrahigh repetition rates ranging from tens of GHz to a few THz.9–119. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013). https://doi.org/10.1038/nphoton.2013.34310. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361, eaan8083 (2018). https://doi.org/10.1126/science.aan808311. W. Wang, L. Wang, and W. Zhang, “Advances in soliton microcomb generation,” Adv. Photonics 2, 034001 (2020). https://doi.org/10.1117/1.AP.2.3.034001 These unique properties of soliton microcombs have been utilized in a wide range of system-level applications, such as optical communication,12–1412. P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017). https://doi.org/10.1038/nature2238713. Y. Geng, X. Huang, W. Cui, Y. Ling, B. Xu, J. Zhang, X. Yi, B. Wu, S.-W. Huang, K. Qiu, C. W. Wong, and H. Zhou, “Terabit optical OFDM superchannel transmission via coherent carriers of a hybrid chip-scale soliton frequency comb,” Opt. Lett. 43, 2406–2409 (2018). https://doi.org/10.1364/ol.43.00240614. Y. Geng, H. Zhou, X. Han, W. Cui, Q. Zhang, B. Liu, G. Deng, Q. Zhou, and K. Qiu, “Coherent optical communications using coherence-cloned Kerr soliton microcombs,” Nat. Commun. 13, 1070 (2022). https://doi.org/10.1038/s41467-022-28712-y dual-comb spectroscopy,15,1615. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016). https://doi.org/10.1126/science.aah651616. A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018). https://doi.org/10.1126/sciadv.1701858 ultrafast ranging,17,1817. M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359, 884–887 (2018). https://doi.org/10.1126/science.aao196818. P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018). https://doi.org/10.1126/science.aao3924 ultralow-noise microwave synthesis,19,2019. J. Liu, E. Lucas, A. S. Raja, J. He, J. Riemensberger, R. N. Wang, M. Karpov, H. Guo, R. Bouchand, and T. J. Kippenberg, “Photonic microwave generation in the X- and K-band using integrated soliton microcombs,” Nat. Photonics 14, 486–491 (2020). https://doi.org/10.1038/s41566-020-0617-x20. Q.-F. Yang, Q.-X. Ji, L. Wu, B. Shen, H. Wang, C. Bao, Z. Yuan, and K. Vahala, “Dispersive-wave induced noise limits in miniature soliton microwave sources,” Nat. Commun. 12, 1442 (2021). https://doi.org/10.1038/s41467-021-21658-7 optical clock,21,2221. S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014). https://doi.org/10.1364/optica.1.00001022. Z. L. Newman, V. Maurice, T. Drake, J. R. Stone, T. C. Briles, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, B. Shen, M.-G. Suh, K. Y. Yang, C. Johnson, D. M. S. Johnson, L. Hollberg, K. J. Vahala, K. Srinivasan, S. A. Diddams, J. Kitching, S. B. Papp, and M. T. Hummon, “Architecture for the photonic integration of an optical atomic clock,” Optica 6, 680–685 (2019). https://doi.org/10.1364/optica.6.000680 astronomical spectrometer calibration,23,2423. E. Obrzud, M. Rainer, A. Harutyunyan, M. H. Anderson, J. Liu, M. Geiselmann, B. Chazelas, S. Kundermann, S. Lecomte, M. Cecconi, A. Ghedina, E. Molinari, F. Pepe, F. Wildi, F. Bouchy, T. J. Kippenberg, and T. Herr, “A microphotonic astrocomb,” Nat. Photonics 13, 31–35 (2019). https://doi.org/10.1038/s41566-018-0309-y24. M.-G. Suh, X. Yi, Y.-H. Lai, S. Leifer, I. S. Grudinin, G. Vasisht, E. C. Martin, M. P. Fitzgerald, G. Doppmann, J. Wang, D. Mawet, S. B. Papp, S. A. Diddams, C. Beichman, and K. Vahala, “Searching for exoplanets using a microresonator astrocomb,” Nat. Photonics 13, 25–30 (2019). https://doi.org/10.1038/s41566-018-0312-3 and quantum key distribution.2525. F. X. Wang, W. Wang, R. Niu, X. Wang, C. L. Zou, C. H. Dong, B. E. Little, S. T. Chu, H. Liu, P. Hao, S. Liu, S. Wang, Z. Q. Yin, D. Y. He, W. Zhang, W. Zhao, Z. F. Han, G. C. Guo, and W. Chen, “Quantum key distribution with on-chip dissipative Kerr soliton,” Laser Photonics Rev. 14, 1900190 (2020). https://doi.org/10.1002/lpor.201900190Among these applications, dual-comb spectroscopy uses asynchronous frequency combs to down-mix the optical comb into the radio frequency domain, allowing for fast and broadband measurements with high-frequency accuracy.2626. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3, 414–426 (2016). https://doi.org/10.1364/optica.3.000414 However, it is substantially limited to the measurement of the absorption spectrum, while the emission spectrum is of great significance in many application scenarios, such as real-time frequency measurement of rapidly tunable CW lasers and spectral monitoring of the modulated signals in optical communication systems.27,2827. F. R. Giorgetta, I. Coddington, E. Baumann, W. C. Swann, and N. R. Newbury, “Fast high-resolution spectroscopy of dynamic continuous-wave laser sources,” Nat. Photonics 4, 853–857 (2010). https://doi.org/10.1038/nphoton.2010.22828. J. M. S. Domingo, J. Pelayo, F. Villuendas, C. D. Heras, and E. Pellejer, “Very high resolution optical spectrometry by stimulated Brillouin scattering,” IEEE Photonics Technol. Lett. 17, 855–857 (2005). https://doi.org/10.1109/lpt.2005.843946 Measurement of the emission spectrum is traditionally implemented by diffraction grating-based optical spectrum analyzers and interferometer-based spectrometers. More recently, leveraging the temporal characteristics of the frequency combs, the emission spectrum can be mapped into the temporal waveform via the optical Fourier transform achieved using the time-lens focusing mechanism, such as the time-resolved spectroscopy based on the time lens.29–3129. C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric spectro-temporal analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep. 3, 2064 (2013). https://doi.org/10.1038/srep0206430. C. Zhang, B. Li, and K. K.-Y. Wong, “Ultrafast spectroscopy based on temporal focusing and its applications,” IEEE J. Sel. Top. Quantum Electron. 22, 295–306 (2016). https://doi.org/10.1109/jstqe.2015.247740431. N. Yang, L. Chen, L. Li, Y. Li, C. Zhang, Y. Wang, K. K. Y. Wong, and X. Zhang, “Time-division-multiplexed observation bandwidth for ultrafast parametric spectro-temporal analyzer,” Opt. Express 27, 30441–30448 (2019). https://doi.org/10.1364/oe.27.030441In time-resolved spectroscopy, the frequency-mapped waveform of the emission spectrum can be captured in the time domain via temporal detection with a spectral resolution mainly limited by the detection bandwidth. For a typical detection bandwidth of 40 GHz, the spectral resolution is constrained to around 20 pm in our experiments. The asynchronous optical sampling (ASOPS) method based on two mode-locked fiber combs with slightly different repetition rates is utilized to equivalently increase the detection bandwidth to hundreds of GHz, thereby improving the spectral resolution from 20 to 2 pm.3232. L. Chen, X. Dong, N. Yang, L. Zhang, Z. Lei, C. Zhang, and X. Zhang, “Pure temporal dispersion for aberration free ultrafast time-stretch applications,” J. Lightwave Technol. 39, 5589–5597 (2021). https://doi.org/10.1109/jlt.2021.3085106 However, the increase in resolution comes at the price of a substantial drop in frame rate, from 92 MHz to 4 kHz, which is equal to the difference in the repetition rate of the dual combs. It is worth noting that the arbitrary detuning ASOPS enables improvement in frame rate in pump–probe measurements while maintaining a high spectral resolution.33,3433. L. Antonucci, X. Solinas, A. Bonvalet, and M. Joffre, “Asynchronous optical sampling with arbitrary detuning between laser repetition rates,” Opt. Express 20, 17928–17937 (2012). https://doi.org/10.1364/oe.20.01792834. N. B. Hébert, S. Boudreau, J. Genest, and J.-D. Deschênes, “Coherent dual-comb interferometry with quasi-integer-ratio repetition rates,” Opt. Express 22, 29152–29160 (2014). https://doi.org/10.1364/oe.22.029152 Specifically, two electro-optic combs having quasi-integer-ratio repetition rates have been used to measure absorption features with high resolution and moderate frame rates.35,3635. B. Xu, X. Fan, S. Wang, and Z. He, “Broadband and high-resolution electro-optic dual-comb interferometer with frequency agility,” Opt. Express 27, 9266–9275 (2019). https://doi.org/10.1364/oe.27.00926636. S. Wang, X. Fan, B. Xu, and Z. He, “Fast MHz spectral-resolution dual-comb spectroscopy with electro-optic modulators,” Opt. Lett. 44, 65–68 (2019). https://doi.org/10.1364/ol.44.000065 The scheme based on electro-optic modulators imposes some restrictions on the two combs, such as the relatively low repetition rates set by the injected radio frequency. Obviously, soliton microcombs with a high repetition rate are capable of achieving a higher frame rate in such a dual-comb ASOPS system, which is of great significance for fast and high-resolution time-resolved spectroscopy.

Here, we propose and experimentally demonstrate a hybrid ASOPS-based time-resolved spectroscopy for an emission spectrum with simultaneous high resolution, high frame rate, and wide bandwidth, utilizing optical Fourier transform and a hybrid ASOPS technique based on dual combs having quasi-integer-ratio repetition rates. A mode-locked fiber comb of repetition rate f1 acts as the pump pulse to implement optical Fourier transform based on a time lens while a soliton microcomb of repetition rate f2s ≈ 1000f1 serves as the probe pulse of the hybrid ASOPS technique to implement parallel multi-point sampling in a single time window of the fiber comb, thereby equivalently increasing the acquisition frame rate by nearly 3 orders of magnitude while maintaining a high spectral resolution. As a proof of concept, a tunable CW laser is quantitatively characterized, indicating a resolution of 0.63 pm, a frame rate of 1 MHz, and a bandwidth of 13.6 nm. In addition, the frame rate can be flexibly tuned from 45 kHz to 1 MHz by slightly adjusting the repetition rate of the fiber comb. Finally, we successfully track frequency transients of a linearly scanning laser with a tuning rate as high as 6.2 THz/s. It is believed that such novel hybrid ASOPS-based time-resolved spectroscopy is expected to become one of the most promising and useful techniques of single-shot real-time spectral analysis in various applications.

II. PRINCIPLE AND EXPERIMENTAL SETUP

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. PRINCIPLE AND EXPERIM... <<III. EXPERIMENTAL RESULTS...IV. CONCLUSIONREFERENCESThe main schematic view of the ASOPS-based time-resolved spectroscopy is illustrated in Fig. 1(a). The emission spectrum is first converted into the frequency-mapped waveform with a repetition rate equal to that of comb 1 used to implement the optical Fourier transform. Then, comb 2 acts as the probe pulse to sample the periodic temporal waveform producing a duplicate signal with a scaled-up time axis. Conventionally, comb 1 and comb 2 used for ASOPS originate from mode-locked fiber combs. However, in this work, a soliton microcomb is used as the probe pulse for ASOPS to perform the multi-point sampling of the mapped emission spectrum. For a comprehensive understanding, the principles of the conventional and hybrid ASOPA techniques are detailed in Fig. 1(b). In conventional ASOPA, the time-resolved spectrum and the probe pulse have slightly different repetition rates of f1 and f2, respectively. By sampling the emission spectrum one by one using the probe pulse, a high temporal resolution and a relatively low frame rate of Δf = f1 − f2 are obtained. The sampling time step is given by the difference between the two periods and amounts to Δt = t2 − t1.In the right panel of Fig. 1(b), the probe pulse source is replaced by a soliton microcomb with a high repetition rate of f2s ≈ 1000f1. Assuming that there are N soliton pulses in a cycle of the time-resolved spectrum, each one of these solitons asynchronously samples a small segment of the signal, as shown in the gray strip area, so as to realize the parallel multi-point sampling of the time-resolved spectrum, thus equivalently improving the acquisition rate. As a consequence, the sampling results from different soliton pulses are separated by a time interval of t2s equal to the period of the soliton trains. To retrieve the actual output waveform without sacrificing the resolution, a processing algorithm is needed to reconstruct the sampling results with a new time axis. As illustrated in the bottom of Fig. 1(b), the reconstructed waveform features a sampling time step of Δts = N × t2s − t1 and a sampling frame rate of Δfs = N × f1 − f2s. It is worth noting that the repetition rate f1 of the fiber comb is relatively easy to be changed in the range of hundreds of kHz by tuning the optical delay line, and the number N is about one thousand, allowing the actual frame rate Δfs to be flexibly tuned from kHz to MHz. Unlike the conventional ASOPS technique, we deal with the trade-off between resolution and frame rate via a high repetition rate pulse source and achieve a flexibly tunable high frame rate while maintaining high resolution in such hybrid ASOPS-based time-resolved spectroscopy.The main setup consisting of two functional parts is displayed in Fig. 2(a). First, the optical Fourier transform is implemented by a time lens based on degenerate four-wave mixing (DFWM). A home-built mode-locked fiber comb with a repetition rate of 49.02 MHz is stabilized by a phase-locked loop. Before being combined with the input signal by a wavelength division multiplexer (WDM), the fiber comb is sent into the dispersion module1 with a total second-order dispersion of Φ1 = −3840 ps2 (about 3 ns/nm), thereby generating a linearly chirped pulse used as the pump source of the time lens. The time lens is implemented by applying a temporal quadratic phase from FWM with the linearly chirped pump pulse in a 70 m highly nonlinear fiber (HNLF) with a zero-dispersion wavelength of 1561.5 nm. The idler in the L band is chosen out via an optical bandpass filter (BPF1) and sent into dispersion module 2 with a total second-order dispersion of Φ2 = 1920 ps2 (about −1.5 ns/nm). It is worth noting that the focal dispersion Φf of the time lens is half of the input dispersion Φ1, satisfying the time-lens focusing condition (Φf = −Φ2). As a result, the spectrum of the input signal is encoded onto the pulse train with a repetition rate equal to that of the pump pulse. It is emphasized that the third-order dispersion of the two modules is well eliminated to obtain a pure second-order dispersion, thereby significantly improving temporal resolution and measurement bandwidth. A detailed description of module 1 [Fig. 2(b)] shows the optical phase conjugation (OPC) method for eliminating the third-order dispersion.3232. L. Chen, X. Dong, N. Yang, L. Zhang, Z. Lei, C. Zhang, and X. Zhang, “Pure temporal dispersion for aberration free ultrafast time-stretch applications,” J. Lightwave Technol. 39, 5589–5597 (2021). https://doi.org/10.1109/jlt.2021.3085106 The spectrum component from 1547 to 1551 nm is filtered out from the fiber comb by BPF3 and propagates through a dispersion compensating fiber (DCF) before being combined with a CW laser at 1555 nm via another WDM. The two signals are launched together into the 100 m HNLF with the zero-dispersion wavelength of 1555 nm for the degenerate FWM process, as displayed at the top of Fig. 2(g). Subsequently, the generated idler from 1559 to 1563 nm is filtered out by BPF4 and used as the chirped pump pulse of the time lens. In the combination of DCF and single mode fiber (SMF), the second-order dispersion is accumulated while the third-order dispersion is eliminated owing to the temporal complex conjugation process, favoring the realization of larger linear dispersion. For simplicity, the third-order dispersion elimination in module 2 [Fig. 2(c)] is implemented by directly combining DCF and non-zero dispersion shift fiber (NZDSF).Second, the soliton microcomb is generated in a four-port integrated high-index doped silica micro-ring resonator (MRR) with a free spectral range (FSR) of 48.971 GHz and a loaded Q-factor of about 2.05 × 106.37,3837. W. Wang, W. Zhang, Z. Lu, S. T. Chu, B. E. Little, Q. Yang, L. Wang, and W. Zhao, “Self-locked orthogonal polarized dual comb in a microresonator,” Photonics Res. 6, 363–367 (2018). https://doi.org/10.1364/prj.6.00036338. W. Wang, Z. Lu, W. Zhang, S. T. Chu, B. E. Little, L. Wang, X. Xie, M. Liu, Q. Yang, L. Wang, J. Zhao, G. Wang, Q. Sun, Y. Liu, Y. Wang, and W. Zhao, “Robust soliton crystals in a thermally controlled microresonator,” Opt. Lett. 43, 2002–2005 (2018). https://doi.org/10.1364/ol.43.002002 Two CW lasers (NKT Basik E15 with 1 kHz linewidth) at 1553 and 1550 nm are both amplified to 2 W using erbium-doped fiber amplifiers (EDFA) and serve as the pump and auxiliary laser, respectively, which are counter-coupled into the MRR via a standard eight-channel fiber array with a coupling loss of 2 dB per facet [Fig. 2(d)]. Benefitting from the thermal compensation implemented by the auxiliary laser, the single soliton state can be stably excited through the coordinated tuning of the pump laser wavelength and the temperature of the MRR. More details of the experimental setup and the soliton generation process can be found elsewhere.39–4439. Z. Lu, W. Wang, W. Zhang, S. T. Chu, B. E. Little, M. Liu, L. Wang, C.-L. Zou, C.-H. Dong, B. Zhao, and W. Zhao, “Deterministic generation and switching of dissipative Kerr soliton in a thermally controlled micro-resonator,” AIP Adv. 9, 025314 (2019). https://doi.org/10.1063/1.508012840. Y. Zhao, L. Chen, W. Wang, R. Wang, H. Hu, X. Wang, C. Zhang, W. Zhang, and X. Zhang, “Repetition rate multiplication control of micro-combs assisted by perfect temporal Talbot effect,” APL Photonics 5, 046102 (2020). https://doi.org/10.1063/1.513959941. X. Wang, P. Xie, W. Wang, Y. Wang, Z. Lu, L. Wang, S. T. Chu, B. E. Little, W. Zhao, and W. Zhang, “Program-controlled single soliton microcomb source,” Photonics Res. 9, 66–72 (2021). https://doi.org/10.1364/prj.40861242. Y. Zhao, L. Chen, C. Zhang, W. Wang, H. Hu, R. Wang, X. Wang, S. T. Chu, B. Little, W. Zhang, and X. Zhang, “Soliton burst and bi-directional switching in the platform with positive thermal-refractive coefficient using an auxiliary laser,” Laser Photonics Rev. 15, 2100264 (2021). https://doi.org/10.1002/lpor.20210026443. Z. Lu, H.-J. Chen, W. Wang, L. Yao, Y. Wang, Y. Yu, B. E. Little, S. T. Chu, Q. Gong, W. Zhao, X. Yi, Y.-F. Xiao, and W. Zhang, “Synthesized soliton crystals,” Nat. Commun. 12, 3179 (2021). https://doi.org/10.1038/s41467-021-23172-244. H. Hu, R. Wang, W. Wang, L. Chen, Y. Zhao, X. Wang, C. Zhang, W. Zhang, and X. Zhang, “Ultrafast dynamic RF-spectrum investigation of soliton microcombs,” APL Photonics 7, 046104 (2022). https://doi.org/10.1063/5.0084279 Typical optical spectrum of a single soliton state is overlaid by a characteristic sech2-shaped envelope, as highlighted by the red line in Fig. 2(e). The inset shows the comb spectrum from 1556 to 1563 nm, which is filtered out and shaped by a wavelength selective switch (WSS) to form a transform-limited sech2-shaped temporal pulse used as the probe for ASOPS. The full-width-at-half-maximum (FWHM) pulse width is measured by a commercial autocorrelator at different dispersion values [Fig. 2(f)]. By setting the dispersion value to 0.6 ps/nm, the measured autocorrelation trace with a sech2-fitted envelope is shown in the inset, indicating an FWHM pulse width of 880 fs. Finally, the probe and the frequency-mapped waveform are sent together into the 30 m HNLF with the zero-dispersion wavelength of 1561.5 nm to perform the hybrid ASOPS based on DFWM, wherein the phase information is eliminated by the square law detection of the idler field. Subsequently, the idler is extracted from the DFWM spectrum using another BPF2 in the C band and is then detected by a 40 GHz bandwidth photodetector and a 59 GHz bandwidth oscilloscope (Keysight DSAZ594A). Considering a CW laser at 1540 nm as the input signal, the typical FWM spectra corresponding to the realization of optical Fourier transform and hybrid ASOPS are shown in Fig. 2(g), middle and lower panels, respectively.

III. EXPERIMENTAL RESULTS AND DISCUSSIONS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. PRINCIPLE AND EXPERIM...III. EXPERIMENTAL RESULTS... <<IV. CONCLUSIONREFERENCESAs a preliminary test, a CW laser at 1545 nm is measured and reconstructed to characterize the spectral resolution. The original sampled waveform [left panel of Fig. 3(a)] and the reconstructed waveform [right panel of Fig. 3(a)] are obtained at a frame rate of 1 MHz. A sampling time step per point of 420 fs ensures five points in a single sample for accurate reconstruction of the time-resolved pulse. The inset is the zoom-in view of the mapped pulse, indicating an FWHM pulse width of 1.25 ps extracted from the Gaussian fitting, as highlighted by the red line. According to the wavelength-to-time relation (1.5 nm/ns), the spectral resolution is calculated as 1.25/1.5 ≈ 0.83 pm. The measurement is also repeated for two CW lasers at 1545 and 1546 nm with a frame rate at 0.98 MHz, showing spectral resolutions of 0.88 and 0.98 pm, respectively [Fig. 3(b)]. The reason for the slight difference in resolution between the two measurements is believed to be that the change in the polarization of the input signal impacts the FWM conversion efficiency. In addition, the slight deviation in frame rate mainly results from the drifting of the microcomb repetition rate, since the fiber comb with a phase-locked loop features a stable repetition rate. By stabilizing the average soliton power via a feedback loop, the microcomb repetition frequency fluctuates in a small range of about 10 kHz. As mentioned above, flexible tunability of frame rate is implemented by fine-tuning the repetition rate of the fiber comb in a range of about 300 kHz via an optical delay line. Figure 3(c) shows four typical measured results and corresponding low-pass filtering envelopes at the frame rate of 1 MHz, 0.5 MHz, 111 kHz, and 45 kHz, respectively. The corresponding spectral resolutions extracted from the reconstructed waveforms are 0.93, 0.95, 0.91, and 0.97 pm, respectively, thereby indicating that the spectral resolution remains virtually unchanged at different frame rates. It should be emphasized that achieving a more stable frame rate as low as several kHz imposes a more stringent requirement on the stability of the microcomb repetition rate. There are several approaches to further stabilizing the soliton microcomb repetition rate, such as the Pound–Drever–Hall locking method and the dual-pump thermal compensation scheme assisted by the sideband-based auxiliary light.45,4645. K. Nishimoto, K. Minoshima, T. Yasui, and N. Kuse, “Thermal control of a Kerr microresonator soliton comb via an optical sideband,” Opt. Lett. 47, 281–284 (2022). https://doi.org/10.1364/ol.44832646. J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018). https://doi.org/10.1103/PhysRevLett.121.063902In addition, the maximum achievable frame rate depends on the mapped pulse width and the sampling time step according to the sampling principle, as demonstrated by the above measurement of a CW laser at 1545 nm.To quantify the measurement bandwidth of the system, a tunable CW laser is measured from 1528 to 1552 nm with a tuning step of 1 nm. The single frame of each measurement is plotted together to intuitively manifest the spectral measurement range, as shown in Fig. 4(a), where the time interval is about 1 µs corresponding to a frame rate of 1 MHz. The wavelengths in spectral ranges beyond 1528 and 1552 nm are not characterized and are mainly constrained by the FWM conversion bandwidth as shown in the three spectra in Fig. 2(g). A non-uniform wavelength responsivity is mainly attributed to the unbalanced gain of the erbium-doped fiber amplifiers (EDFA) and the variation conversion efficiency of FWM in different spectral ranges. Nevertheless, a 3-dB bandwidth of about 20 nm is achieved, and the envelope of the wavelength-dependent responsivity can be utilized to calibrate the measurement results to precisely reconstruct the spectral shape of the input signal in practical applications. It should be noted that the maximum observation bandwidth in a single measurement is confined to 13.6 nm set by the time window of 20.4 ns according to the wavelength-to-time relation (1.5 nm/ns). Likewise, the reconstructed waveforms are also illustrated in the same way [Fig. 4(b)]. The spectral resolution results extracted from the Gaussian fitting of the reconstructed waveforms from 1528 to 1552 nm are displayed in Fig. 4(c), showing an overall resolution below 1 pm and the highest resolution of 0.63 pm at 1550 nm. In addition, the measurement dynamic range is characterized to be about 25 dB by changing the input power of the CW laser [Fig. 4(d)]. The results at different wavelengths verify that the sensitivity of the spectroscopic system is about −25 dBm limited by the FWM conversion efficiency and the minimum input power requirement of the EDFA before the photodetector. The use of on-chip waveguides with high nonlinear coefficients and low-noise EDFAs is expected to improve the FWM conversion efficiency, thereby increasing the sensitivity of the time-resolved spectroscopy.As a demonstration of the proposed time-resolved spectroscopy in applications, dynamic spectral tracking of a rapidly tuning laser (New Focus Velocity TLB-6700) is implemented at a measurement frame rate of about 0.95 MHz. As a reference, a fixed-frequency laser at 1545 nm is combined with the linearly chirped laser, and both lasers serve as the input signal. Figure 5(a) shows the voltage signal applied to the tunable laser and the reconstructed spectrum depicted in a 3D spectro-temporal pattern. The measured wavelength interval between the two CW lasers and their linear fitting are plotted vs scanning time in a time window of about 0.4 ms, as shown by the blue dots and red line in the upper panel of Fig. 5(b), where a frequency linear chirp of 6.2 THz/s is inferred. A zoom-in view of the measured wavelength interval at 1.33 ms is given in the lower panel of Fig. 5(b). The step-like results of the wavelength interval are attributed to the ability to distinguish two CW lasers closely spaced in frequency. A wavelength step of about 0.26 pm represents the minimum resolvable wavelength interval between the two CW lasers. To display more details, three typical frames of the original waveform and reconstructed spectrum at different times are depicted in Fig. 5(c). The extracted wavelength intervals at 1.42, 1.51, and 1.60 ms are 29.65, 34.14, and 38.99 pm, respectively. It is obvious that the sampled waveform of the scanning laser gradually shifts to the left in the time window as the wavelength increases. Moreover, the waveform moves from the right end to the left end only in a small wavelength range of about 9 pm. The reason is that the soliton microcomb divides the period of the fiber comb into thousands of segments, where each segment is equal to a period of the soliton microcomb and is scaled up to the sampling period. The sampled waveform shifts across a whole frame period when the laser is scanned over 13.6 pm, corresponding to a time window of 20.4 ps, the period of the soliton microcomb. Therefore, the fitted envelopes of the two sampled waveforms corresponding to the two lasers can be used to extract a more precise wavelength interval of 0.26 pm.To measure the emission spectrum of a light source, different spectroscopic methods have been experimentally demonstrated, such as microcomb-based vernier spectroscopy and frequency comb ptychoscopy.47,4847. Q.-F. Yang, B. Shen, H. Wang, M. Tran, Z. Zhang, K. Y. Yang, L. Wu, C. Bao, J. Bowers, A. Yariv, and K. Vahala, “Vernier spectrometer using counterpropagating soliton microcombs,” Science 363, 965–968 (2019). https://doi.org/10.1126/science.aaw231748. D. J. Benirschke, N. Han, and D. Burghoff, “Frequency comb ptychoscopy,” Nat. Commun. 12, 4244 (2021). https://doi.org/10.1038/s41467-021-24471-4 Microcomb-based vernier spectroscopy has been used to measure the spectra of multi-line lasers, which, in combination with a tunable laser, enables precise measurement of absorption spectra. However, the acquisition speed is limited by the repetition rate offset between the two locked soliton microcombs. Furthermore, the frequency comb ptychoscopy is a high-resolution multiheterodyne technique that can reconstruct the spectrum of nearly any complex source to high resolution; for example, the resolution is up to 6.8 kHz, but the measurement time is 40 ms, corresponding to a relatively low measurement frame rate of 25 kHz. Compared to the spectroscopic techniques mentioned above, the proposed time-resolved spectroscopy based on a time-lens focusing mechanism and hybrid ASOPS is theoretically capable of measuring the spectrum of the arbitrary radiation source, which enables the improvement of both spectral resolution and frame rate at the same time. It should be emphasized that the small time window of the soliton microcombs is not suitable for a broad bandwidth spectrum to be temporally stretched without spectral overlap, thereby hindering the direct combination of soliton microcombs and time-lens focusing mechanism in ultrafast time-resolved spectroscopy. That is the reason for using the hybrid ASOPS technique in this work.

IV. CONCLUSION

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ChooseTop of pageABSTRACTI. INTRODUCTIONII. PRINCIPLE AND EXPERIM...III. EXPERIMENTAL RESULTS...IV. CONCLUSION <<REFERENCES

In this paper, we have proposed and experimentally demonstrated a hybrid ASOPS-based time-resolved spectroscopy to implement the high spectral resolution, high frame rate, and wide bandwidth simultaneously. Benefitting from the high repetition rate of a soliton microcomb, parallel multi-point sampling of the frequency-mapped waveform generated by the radiation signal under test is realized to equivalently improve the acquisition rate without sacrificing the resolution. As a proof-of-concept experiment, a tunable CW laser acts as the input signal to characterize the performance in terms of resolution, frame rate, and bandwidth. After delicately optimizing the dispersion parameter and reconstruction algorithm, the ASOPS-based time-resolved spectroscopy features a spectral resolution of 0.63 pm, a frame rate of 1 MHz, a bandwidth of 13.6 nm, and a dynamic range of 25 dB. Furthermore, the frame rate is flexibly tuned from 45 kHz to 1 MHz, which can be further reduced to a few kHz by improving the repetition rate stability of the soliton microcomb. Finally, to further demonstrate the capability of the system, a rapidly scanning laser with a frequency linear chirp of 6.2 THz/s is monitored in real time. It is believed that in combination with a fine tunable CW laser, the system also enables fast and high-resolution measurement of the absorption spectrum. The efforts to further optimize the system should be made in terms of the repetition rate stability of the two combs and the measurement dynamic range. The proposed time-resolved spectroscopy based on a chip-scale soliton microcomb has promise for widespread applications in sensing and ultrafast spectroscopy.