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Abstract
Dispersive time stretch has made many ultrafast applications possible owing to its high frame rate, as compared to conventional spectroscopies. By further introducing a converging time lens, this spectroscopy can resolve arbitrary emission spectra within the aperture. However, a spectral resolution of tens of picometers hinders its high-precision application. There are two limitations: the temporal aperture of the acquired signal and the actual acquisition bandwidth. To overcome these restrictions, two approaches were developed. First, a large-aperture time lens, with higher-order dispersion compensation, is used to overcome the fundamental limit of the time–bandwidth product. Second, asynchronous optical sampling, based on two frequency combs, overcomes the technical limit of the acquisition bandwidth. As a result, in this study, time-stretch spectroscopy achieved a 1-pm spectral resolution, 24-nm observation bandwidth, and 1-kHz frame rate. Moreover, it was used to observe some spectral dynamics of the random lasing process and devices with narrow spectral widths. This scheme provides essential improvement for time-stretch spectroscopy to achieve high precision.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultrafast spectral dynamics provides an effective method to gain insight into various physical, chemical, and biological phenomena [1–3]. Compared with conventional mechanical scanning or arrayed detector-based spectroscopy, dispersive time stretch maps the spectral information to the time domain and improves the acquisition frame rate by several orders of magnitude [4–6]. However, in addition to an ultrafast frame rate, high spectral resolution and large observation bandwidth are highly desired for various applications [7]. Achieving high spectral resolution has always been a challenging task because of the time–bandwidth product constraint, especially under a limited acquisition time span [8,9]. Several schemes have been introduced to achieve high spectral resolution, such as coherent optical spectrum analyzer and Brillouin optical spectrum analyzer, which can easily achieve sub-picometer resolution, while several minutes are required to capture the entire spectrum [10,11]. However, dual-comb spectroscopy can solve this problem by achieving sub-picometer resolution and a frame rate in the approximately kilohertz range [12]. Two optical frequency combs, with slightly different repetition rates, beat with each other to down-convert the spectral information to the radio frequency range. However, dual-comb spectroscopy is usually used for absorption spectroscopy rather than arbitrary emission spectroscopy which can obtain the spectrum of any signal, such as amplifying spontaneous emission [13].
By using ultrafast dispersive time stretch, mapping the spectral information to the time domain and acquiring the spectra through a single-pixel detector, dispersive Fourier transformation (DFT) can easily achieve a frame rate in the approximately megahertz range, and it has frequently been applied [14,15]. Similar to dual-comb spectroscopy, DFT is a form of absorption spectroscopy. To circumvent this constraint, a temporal-focusing-mechanism-based parametric spectro-temporal analyzer (PASTA) was introduced [16,17]. Arbitrary waveforms within the aperture of the time lens can be reconstructed into a wavelength-to-time sequence, and a 20-pm resolution and a 58-nm bandwidth under a 10-MHz frame rate have recently been reported [18]. This may be sufficient for most applications, but not for some high-quality (Q) factor devices the resonance spectral width of which can be as short as 1 pm. Moreover, small changes in stress, temperature and humidity may lead to obviously different spectral dynamics [19]. The spectral resolution of the PASTA can be improved in two ways. First, the aperture of the time lens can be enlarged to compress the focusing pulse, which may not be difficult for parametric-mixing-based time lenses, although the effect of higher-order dispersion should be noted [20]. Second, the acquisition bandwidth of the PASTA can be increased. Because the optical pulsewidth can be as narrow as several picoseconds, a hundreds-of-gigahertz bandwidth is almost impossible for conventional photodetectors (PDs) and oscilloscopes [21]. Therefore, to improve the resolution, it is necessary to increase the detection bandwidth and compensate for higher-order dispersion.
An asynchronous optical sampling (ASOPS) inspired by dual-comb spectroscopy was introduced to the large-aperture PASTA system to increase the acquisition bandwidth and to achieve high spectral resolution. Two combs with slightly different repetition rates are employed, and one is operated as the pump of the PASTA, whereas another is the sampling pulse [22]. The envelope of their product term is a temporal magnification of the temporal spectrum; thus, the equivalent bandwidth is significantly reduced. In this study, ASOPS was introduced to the PASTA, and the detection bandwidth requirement decreased from hundreds of gigahertz to several megahertz. Meanwhile, higher-order dispersion compensation schemes were adopted to achieve a fine resolution and a large observation bandwidth [23]. As a result, the spectral resolution of the PASTA improved from 20 to 1 pm (2.5 GHz to 125 MHz) with a 1-kHz repetition rate. Based on this improved PASTA, the thermal drift of the resonance peak of a high-Q microring resonator [7] and the random lasing spectral dynamics of an erbium-doped fiber amplifier (EDFA) were experimentally explored. This improved ultrafast spectroscopy may be a powerful tool to explore some physical and chemical phenomena further under extreme conditions.
2. Principle
To overcome the limited resolution of the detection bandwidth, ASOPS was introduced into the PASTA system, as shown in Fig. 1. Two combs with slightly different repetition rates (Δf = f1 – f2) serve as the swept pump of the time lens and the sampling pulse of the ASOPS, respectively. When the first pulse of comb 2 is temporally aligned with comb 1, its neighboring pulse is misaligned by Δt = Δf / (f1 × f2), which is the scanning step of the ASOPS. The temporal spectra of the PASTA are synchronized with comb 1 and remain identical during the ASOPS process with a time period of 1/Δf. To avoid the influence of carrier frequency drift, ASOPS is performed through degenerate four-wave mixing (FWM), as shown in Fig. 1(c). Consequently, the envelope of the newly generated idler is actually the temporally magnified PASTA output, and the magnification ratio is M = f1/Δf. Therefore, the detection bandwidth is reduced to 1/M of the original bandwidth [21]. Finally, the envelope of the idler can be detected by a low-pass PD/filter and acquired by a small-bandwidth oscilloscope, as shown in Fig. 1(e).
Fig. 1. Schematic diagram of ASOPS-based PASTA. (a) The conventional PASTA system with comb 1 serves as the swept pump of the time lens. (b) Comb 2 serves as the sampling pump of ASOPS. (c) For ASOPS, the temporal spectrum is sampled through a nonlinear parametric mixing process. (d) The temporally magnified temporal spectrum is shown on the envelope of a newly generated idler. (e) The envelope is obtained by passing the idler through a low-pass PD/filter.
Although ASOPS can greatly relax the bandwidth requirement for the PASTA system to achieve high resolution, the actual resolution is also greatly affected by the higher-order dispersion, as shown in Fig. 2. In Fourier optics, different spatial frequencies can be focused on the focal plane of a converging lens, whereas the PASTA is its temporal counterpart based on space–time duality [24]. Different wavelengths are focused on different temporal positions. The ideal temporal ray diagram is shown in Fig. 2(a). For the parametric-mixing-based time lens, the focal group delay dispersion (GDD) of Φf is achieved by a swept pump with a GDD of −2Φf (pre-dispersion module) followed by a post-dispersion module with an output GDD of Φo = Φf. When there is higher-order dispersion in the pre-dispersion module only, the parabolic temporal phase modulation becomes a tilted shape (red line). The degraded temporal ray diagram is shown in Fig. 2(b). The focal pulse has single-sideband tailing, which is almost identical to all the wavelength components, and the spectral resolution of the PASTA is degraded. However, when there is higher-order dispersion just in the post-dispersion module, which corresponds to different output GDD for an identical output fiber, only the central wavelength component (green line) is focused, as shown in Fig. 2(c). The pulsewidth of the sideband wavelength components becomes too large to be observed; thus, the observation bandwidth of the PASTA is greatly narrowed. In this work, both a high spectral resolution and a large observation bandwidth are highly desired; thus, higher-order dispersion in the pre-dispersion and post-dispersion modules must be precisely compensated. After dispersion optimization, ASOPS based PASTA can get a spectral resolution on the order of MHz which is comparable to the dual-comb spectroscopy. Compared with dual-comb spectroscopy, as mentioned before, the main advantage of ASOPS based PASTA is that it can measure any emission spectrum. For dual-comb spectroscopy, one or both combs are required to be used as the probe source, which will be modulated by the sample, so as to obtain the absorption spectrum of the sample. Another advantage is that ASOPS based PASTA does not require to lock the carrier envelope offset frequency of the two combs. Only stable repetition rate is needed. At last, ASOPS based PASTA obtains the spectrum in the time domain directly, while dual-comb spectroscopy needs to perform FFT on the temporal signal.
Fig. 2. Impact of higher-order dispersion on PASTA through a temporal ray diagram: (a) without higher-order dispersion, (b) with higher-order dispersion in the pre-dispersion module, and (c) with higher-order dispersion in the post-dispersion module.
3. Experimental setup
The experimental setup for the dual ASOPS-based PASTA is shown in Fig. 3. The repetition rates of combs 1 and 2 are 91.86 and 91.861 MHz, respectively, with a difference of 1 kHz. The pulse train of comb 1 first passes through a 3 nm bandpass filter (BPF1, centered at 1561.5 nm) and then is stretched by the pre-dispersion module with a group velocity dispersion (GVD) of 3 ns/nm. The time-stretched swept pump (Ep) has a parabolic phase. Together with the input signal (Es), it passes through a 70-m highly nonlinear fiber (HNLF2) to perform the degenerate FWM. The newly generated idler has the relation Ei = Ep2Es*; thus, the parabolic phase is modulated to the input signal as a time lens. After HNLF2, the idler is filtered by BPF2 and focused by the post-dispersion module to realize frequency-to-time mapping and the temporal spectrum. Afterward, the ultrafast temporal spectrum is sampled by comb 2 through ASOPS by passing through 30-m HNLF3. The sampling pulse train of comb 2 is filtered using 5-nm BPF3 (centered at 1561 nm). Finally, the temporal magnified spectrum is acquired using a 125-MHz PD and an oscilloscope.
Fig. 3. Experimental setup of the ASOPS-based PASTA: (a) overall experimental setup, (b) details of the pre-dispersion module, and (c) details of the post-dispersion module (PC: polarization controller; BPF: bandpass filter; EDFA: erbium-doped fiber amplifier; WDM: wavelength-division multiplexer; HNLF: highly nonlinear fiber; TLS: tunable laser source; DCF: dispersion compensation fiber; SMF: single-mode fiber; NZDSF: nonzero dispersion shift fiber).
Owing to the large pump and observation bandwidth, higher-order dispersion in the pre-dispersion and post-dispersion modules significantly degrade the performance of the PASTA. Therefore, it is essential to compensate for higher-order dispersion. For the pre-dispersion module, as shown in Fig. 3(b), the optical phase conjugation (OPC) method is introduced to compensate for the third-order dispersion and maintain a large second-order dispersion, with an 11.4-km dispersion compensation fiber (DCF) and an 80-km single-mode fiber [23]. The zero-dispersion wavelength of HNLF1 is approximately 1554 nm, but those of HNLF2 and HNLF3 are approximately 1561.5 nm. For the OPC process, a continuous-wave (CW) pump is centered at 1554.9 nm, and the pulse signal (comb 1) is filtered by BPF1 centered at 1548.3 nm. Therefore, the newly generated idler, with a GDD of −3840 ps2 (∼3 ns/nm), is located at 1561.5 nm, and it serves as the swept pump of the time lens. For the post-dispersion module, the required GDD (1920 ps2, −1.5 ns/nm GVD) is significantly smaller; thus, a nonzero dispersion shift fiber (NZDSF) is introduced to compensate for the third-order dispersion of the DCF, and a large compensated bandwidth benefits the observation bandwidth [25]. The performance of the higher-order dispersion compensation is shown in Fig. 4 (GDD corresponding to different wavelengths). The variation in GDD for the pre-dispersion module with the OPC compensation scheme is suppressed from 66 to 0.7 ps2 over the wavelength range from 1559 to 1563 nm. For the post-dispersion module with NZDSF, the variation of GDD is suppressed from 150 to 0.8 ps2 over the wavelength range from 1570 to 1600 nm.
Fig. 4. Performance of high-order dispersion compensation: (a) GDD of the pre-dispersion module versus wavelength before (black dots) and after (red triangles) the OPC scheme and (b) GDD of the post-dispersion module versus wavelength before (black dots) and after (red triangles) the introduction of NZDSF.
In this system, the large time lens aperture (provided by pump pulse in HNLF2) and high temporal sampling resolution (provided by the ASOPS process) ensure the high spectral resolution. But a further improvement is prevented by the limited FWM conversion bandwidth performed in HNLF2 and HNLF3, especially the latter. It should be noted that two approaches have been adopted to eliminate time jitter which is detrimental to the spectral accuracy. For one, the repetition rates of the two combs are locked to two stable radio-frequency sources through phase-locked loops. For another, the dispersion modules used in the system are placed in an incubator to avoid the effect of temperature variation on dispersion.
As we can see, there are three-stage four-wave mixing processes and a large amount of fibers act as the dispersive medium. These can bring significant losses and degrade the signal-to noise ratio of the system. Although averaging can be used to improve the signal-to-noise, it will sacrifice the frame rate of the system meanwhile. One solution is to use long-period fiber grating instead of optical fiber as the dispersive medium. The high-order dispersion can be controlled by suitable grating parameters and the amount of total dispersion can also be fine-tuned by temperature. In this way, a large amount of dispersion can be achieved with a small loss cost, and the structure of the system can be greatly simplified.
4. Results and discussion
Because the ASOPS scheme makes possible a system with a large detection bandwidth, the pulse shape degraded by higher-order dispersion can be experimentally explored, as shown in Fig. 5. When the higher-order dispersion is fully compensated for, a clean and short pulse is observed in both the experiment and simulation, as shown in Figs. 5(a) and (b). However, if there is higher-order dispersion in the post-dispersion module, which results in different output GDD for different wavelength components, the output pulses cannot be fully focused. As Figs. 5(c) and (d) show, the broadening effect differs with the wavelength, and the observation bandwidth is greatly constrained, as shown by the red triangles in Figs. 5(g) and (h). However, if there is higher-order dispersion in the pre-dispersion module, it results in a tilt parabolic phase modulation, and there is a tail on the right side, as shown in Figs. 5(e) and (f). The shapes of the tail remain almost identical when the wavelength changes, and the resolution is degraded from ∼1 to ∼2 pm with an undegraded observation bandwidth, as shown by the blue diamonds in Figs. 5(g) and (h). The experimental and simulation results are highly consistent, and the influence of the higher-order dispersion is also consistent with the aforementioned principle [23].
Fig. 5. Characterization of the output pulse shape with the influence of higher-order dispersion in the pre-dispersion and post-dispersion modules: (a) experiment and (b) simulation demonstration of the output pulse when the higher-order dispersion is fully compensated for, (c) experiment and (d) simulation demonstration of the output pulse when only the higher-order dispersion of the pre-dispersion module is compensated for, (e) experiment and (f) simulation demonstration of the output pulse when only the higher-order dispersion of the post-dispersion module is compensated for, (g) output pulsewidth and corresponding spectral resolution over the observation bandwidth (black dots, red triangles, and blue diamonds correspond to (a), (b), and (c), respectively), and (h) simulation demonstration of (g).
The characterization of PASTA based on ASOPS and the higher-order dispersion compensation scheme is shown in Fig. 6. Its performance with an observation bandwidth from 1528 to 1552 nm is shown in Fig. 6(a), where the signal under test is a scanning CW laser with a 1-nm step, and the segmental spectra are spliced together. The shapes of each pulse are almost identical, although their amplitudes fluctuate owing to the gain spectra of the EDFA and parametric process. Because the period of the PASTA system is ∼11 ns, the non-overlapped single-shot spectral bandwidth is approximately 7.3 nm. The sampled pulsewidth can also reflect the spectral resolution, and the enlarged pulse shape is shown in Fig. 6(b). For the CW signal at 1540 nm, the PASTA output (black dashed line) had a resolution of 14.75 pm, whereas the ASOPS scheme (red solid line) improved it to 1.06 pm. A similar improvement in spectral resolution was also observed over the observation range, and the average spectral resolution was improved from 14 to 1 pm (1.75 GHz to 125 MHz), as shown in Fig. 6(c). Figure 6(d) shows the window of the time lens, which is ∼9 ns over an 11 ns period, and the systematic dynamic range is shown in Fig. 6(e), with a sensitivity of −20 dBm and a dynamic range exceeding 20 dB.
Fig. 6. Characterization of ASOPS-based PASTA: (a) spliced observation bandwidth with 1-nm spectral interval, (b) output pulse shape of PASTA system (black dashed line) and ASOPS scheme (red solid line) at 1540 nm, (c) resolution improvement over the observation bandwidth, (d) window size of time lens, and (e) dynamic range performance at different wavelengths.
Because this ASOPS-based PASTA system can achieve a 1-pm resolution and 1-kHz frame rate, which are superior to those of the conventional optical spectrum analyzer (OSA, e.g., Yokogawa AQ6380 with 5-pm resolution and 5-Hz frame rate [26]), it is capable of observing some fast spectral dynamics with fine resolution. In this study, an incidental lasing process of an EDFA was explored when it was operated in the amplified spontaneous emission mode with a high pump current. It was first observed by a conventional OSA (with 10-pm spectral resolution), and some lasing peaks were broadened and degraded, as shown in Fig. 7(a). For comparison, it was also observed by a ASOPS-based PASTA, where the lasing components had a linewidth as low as 1.23 pm, as shown in Fig. 7(b). Moreover, by leveraging the 1-kHz high frame rate, the spectral dynamics of this lasing process can be fully resolved within a certain time span. Figure 7(c) shows that there are multiple modes of lasing simultaneously, and they fail or increase in different oscillation states. Some modes exist for a longer time, whereas others disappear quickly.
Fig. 7. Dynamic spectra of the EDFA lasing process: (a) EDFA lasing spectrum captured by conventional OSA, (b) EDFA lasing spectrum captured by ASOPS-based PASTA, and (c) evolution of the EDFA lasing spectra with a 1-ms interval over a 100-ms window.
Furthermore, this fast and high-resolution spectroscopy can characterize some microdevices, especially those with a high Q factor. A microring resonator with an approximately 106 Q factor was explored, and its microheater can adjust the transmission spectrum with high speed [19]. To explore the transmission spectrum, a mode-lock fiber laser with a 50-MHz repetition rate was introduced as a wideband source. Its mode spacing was considerably smaller than the transmission spectrum. Stationary performance was first characterized by conventional OSA and ASOPS-based PASTA, as shown in Figs. 8(a) and (b), respectively. A significantly narrower linewidth (∼1.45 pm) was captured by the proposed scheme, and this spectral width was matched by the Q factor. To explore its spectral dynamics, a driving voltage was added to adjust the transmission spectrum, as shown in Fig. 8(c). When the driving voltage remained constant at zero (point A), its spectral dynamics over a 100-ms window was recorded, as shown in Fig. 8(d). In addition to the timing jitter fluctuation introduced, the transmission peaks were almost constant. The driving voltage was scanned from 0 to 3 V, and its spectral dynamics at point B over a 100-ms window are displayed in Fig. 8(d). In this case, the transverse-electric (TE) and transverse-magnetic (TM) modes were scanned with slopes of 74 and 71 pm/s, respectively.
Fig. 8. Characterization of a microring resonator through spectral dynamics: (a) transmission spectrum of the microring resonator captured by conventional OSA, (b) transmission spectrum of the microring resonator captured by ASOPS-based PASTA, (c) driving voltage on the microheater of the microring resonator, and (d) and (e) dynamics of the microring resonator transmission spectrum when the driving voltage is constant and when the driving voltage is linearly scanning, respectively.
5. Conclusion
By introducing the ASOPS scheme into the PASTA, ultrafast high-spectral-resolution and large-observation-bandwidth spectroscopy was achieved. Compared with previous works, the two combs with slightly different repetition rates can magnify the time axis and greatly relax the limited bandwidth requirement; therefore, a 1-pm (125-MHz) spectral resolution can be achieved based on a 125-MHz acquisition bandwidth. Moreover, several higher-order dispersion compensation schemes, including OPC and NZDSF, were applied in this work, which are essential as the pump bandwidth and observation bandwidth increase. Finally, this ASOPS-based PASTA system achieved a 1-pm spectral resolution over a 24-nm (7.3 nm non-overlapping) observation bandwidth. Under current configurations, owing to the ASOPS process, the frame rate of the spectroscopy decreases from approximately megahertz to approximately kilohertz; however, if the repetition rate of the sampling comb can be multiplied, e.g., the microring optical frequency comb [27], the actual frame rate can be increased correspondingly. Using this ultrafast spectroscopy, the random lasing spectral dynamics of an EDFA and the thermal drift of the resonance peak of a microring resonator were observed. The technique is useful for the characterization of some ultrafast phenomena in optical devices.
Funding
National Key Research and Development Program of China (2019YFB2203102); National Natural Science Foundation of China (61735006, 61927817, 62075072).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007). [CrossRef]
2. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009). [CrossRef]
3. H. Chen, N. Yang, C. Qin, W. Li, B. Wang, T. Han, C. Zhang, W. Liu, K. Wang, H. Long, X. Zhang, and P. Lu, “Real-time observation of frequency Bloch oscillations with fibre loop modulation,” Light: Sci. Appl. 10(1), 48 (2021). [CrossRef]
4. D. Derickson, Fiber Optic, Test and Measurement (Prentice Hall, 1998).
5. A. B. Shafer, L. R. Megill, and L. A. Droppleman, “Optimization of the Czerny–Turner spectrometer,” J. Opt. Soc. Am. 54(7), 879–887 (1964). [CrossRef]
6. A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017). [CrossRef]
7. H. Zhou, B. Xiao, N. Yang, S. Yuan, S. Zhu, Y. Duan, L. Shi, C. Zhang, and X. Zhang, “Real-time observation of the thermo-optical and heat dissipation processes in microsphere resonators,” Opt. Express 29(2), 2402–2410 (2021). [CrossRef]
8. C. Zhang, X. Wei, M. E. Marhic, and K. K. Y. Wong, “Ultrafast and versatile spectroscopy by temporal Fourier transform,” Sci. Rep. 4(1), 5351 (2015). [CrossRef]
9. B. Li, S. W. Huang, Y. Li, C. W. Wong, and K. K. Y. Wong, “Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics,” Nat. Commun. 8(1), 61 (2017). [CrossRef]
10. APEX, Optical complex spectrum analyzer, https://www.apex-t.com/optical-complex-spectrum-analyzer-ap268x-series/.
11. Aragon photonics, Brillouin optical spectrum analyzer, https://aragonphotonics.com/bosa-optical-spectrum-analyzer/.
12. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016). [CrossRef]
13. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010). [CrossRef]
14. D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008). [CrossRef]
15. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013). [CrossRef]
16. 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(1), 2064 (2013). [CrossRef]
17. 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(3), 295–306 (2016). [CrossRef]
18. 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(21), 30441–30448 (2019). [CrossRef]
19. W. Wang, L. Wang, and W. Zhang, “Advances in soliton microcomb generation,” Adv. Photonics 2(03), 1 (2020). [CrossRef]
20. C. Zhang, X. Wei, and K. K. Y. Wong, “Performance of parametric spectro-temporal analyzer (PASTA),” Opt. Express 21(26), 32111–32122 (2013). [CrossRef]
21. X. Dong, X. Zhou, J. Kang, L. Chen, Z. Lei, C. Zhang, K. K. Y. Wong, and X. Zhang, “Ultrafast time-stretch microscopy based on dual-comb asynchronous optical sampling,” Opt. Lett. 43(9), 2118–2121 (2018). [CrossRef]
22. H. Zhang, H. Wei, X. Wu, H. Yang, and Y. Li, “Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling,” Opt. Express 22(6), 6597–6604 (2014). [CrossRef]
23. 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(17), 5589–5597 (2021). [CrossRef]
24. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994). [CrossRef]
25. L. Zhang, L. Chen, Z. Lei, Y. Duan, C. Zhang, and X. Zhang, “Calibration-free time-stretch optical coherence tomography with large imaging depth,” Opt. Lett. 44(17), 4135–4138 (2019). [CrossRef]
26. Yokogawa, Optical spectrum analyzer, https://tmi.yokogawa.com/solutions/products/optical-measuring-instruments/optical-spectrum-analyzer/aq6380-optical-spectrum-analyzer/.
27. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011). [CrossRef]
