Temporally super-resolved dispersive Fourier transformation spectroscopy

Temporally super-resolved dispersive Fourier transformation spectroscopy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Temporally super-resolved dispersive Fourier transformation spectroscopy Qi Wen, Zhaoyang Wen, Yuan Chen, Bowen Sun, Zhicheng Huang, Ming Yan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6665551/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Dispersive Fourier transformation (DFT) maps the spectrum of an optical pulse into the time domain via chromatic dispersion, enabling real-time, pulse-resolved spectral analysis with a single photodetector. This technique has unlocked new possibilities for single-shot measurements of transient phenomena in physics, photonics, and biological systems. However, its applicability in ultrafast regimes is hindered by temporal aliasing, which arises when pulses are spaced closer than their stretched duration. Here, we introduce temporally super-resolved time-stretch spectroscopy that overcomes this limitation. By storing a sequence of ultrashort pulses—each encoding a unique, non-repetitive spectral event—in an optical cavity and retrieving them sequentially using an asynchronous pulse picker and a DFT oscilloscope, we isolate individual pulses and suppress aliasing. This achieves a three-orders-of-magnitude improvement in temporal resolution. In proof-of-concept experiments, we resolve the spectral evolution of 25 GHz electro-optic comb pulses and distinguish spectra separated by just 3 ps. This technique enables continuous, ps-resolved measurements of non-repetitive spectra and is readily extendable to other DFT-based modalities, including ultrafast microscopy. Spectroscopy Dispersive Fourier transformation spectroscopy time-stretch single-shot measurement Figures Figure 1 Figure 2 Figure 3 Figure 4 Main text The growing demand for ultrafast spectroscopic tools is driven by the need to probe transient phenomena across a wide range of fields, from optoelectronics to molecular physics and biomedical research [ 1 ]. However, traditional spectrometers, which rely on moving components or detector arrays [ 2 – 4 ], are intrinsically slow and insufficient for capturing phenomena on microsecond (µs) and shorter timescales, such as carrier relaxation in semiconductors, phase transitions in materials, and protein dynamics in biological systems [ 5 – 7 ]. While pump-probe techniques resolve ultrafast dynamics on the picosecond (ps) and femtosecond (fs) scales, their stroboscopic nature limits them to periodic or repeatable processes [ 8 – 10 ]. Capturing non-repetitive, transient dynamics—hallmarks of natural systems—demands fast, continuous, single-shot measurement techniques. Dispersive Fourier transformation (DFT) is a real-time technique that exploits the space-time duality between paraxial diffraction and temporal dispersion, enabling measurements of fast, non-repetitive signals [ 11 – 13 ]. Specifically, it leverages chromatic dispersion in a dispersive medium (e.g., a long fiber) to map the spectral content of an optical pulse onto a time-domain waveform. Under sufficient group velocity dispersion—analogous to the far-field (Fraunhofer) regime in spatial optics—the temporal intensity profile of the stretched pulse directly replicates its optical spectrum. This process, often referred to as time-stretching [ 14 – 16 ], results in real-time bandwidth compression, allowing the use of a single detector and high-memory-depth digitizer to record long sequences of transient events—a task that remains challenging for other techniques, such as those employing streak cameras [ 17 , 18 ]. This capability has unlocked new regimes of spectroscopy, enabling discoveries such as optical rogue waves [ 19 ], the onset of mode-locking [ 20 ], and soliton molecule dynamics [ 21 ], and has recently been extended to critical mid-infrared bands for transient chemical sensing [ 22 – 25 ]. When applied to spectroscopy, DFT enables pulse-by-pulse spectral analysis (Fig. 1 a), with temporal resolution set by the pulse spacing [ 11 ], which must exceed the stretched pulse duration to prevent interference from temporal aliasing (Fig. 1 b). At the same time, achieving adequate spectral resolution requires sufficient dispersion to stretch the pulses, imposing a trade-off between temporal and spectral resolution. This compromise, together with technical constraints such as detection bandwidth and Nyquist sampling (see Supplementary Note 1), inherently restricts the temporal resolution of current DFT spectrometers to the nanosecond (ns) scale [ 11 – 25 ]. Breaking this barrier is essential for propelling real-time, single-shot spectral measurement into the ultrafast regime—an urgent need for investigating phenomena such as microcavity dynamics [ 26 – 28 ], catalytic reaction pathways [ 29 ], and ultrafast carrier transport [ 30 ]. In this Letter, we present a temporal-aliasing-free approach to DFT spectroscopic measurement. Our method captures a sequence of non-repetitive events by storing them in an optical cavity and retrieves the spectra in equivalent time using asynchronous time gates and a DFT oscilloscope. This technique achieves a three-order-of-magnitude improvement in temporal resolution, enabling continuous, single-shot measurements of non-repetitive spectra with ps resolution. Critically, resolving dynamic spectra—each comprising hundreds of spectral elements—represents a distinct concept of resolution compared to signal processing or temporal imaging [ 31 ]. Furthermore, the system supports single-shot recording lengths of up to tens of ns, thereby opening new possibilities for ultrafast spectroscopic applications. Figure 1 c illustrates the core concept of our approach, which employs an active optical cavity to store and replicate a cluster of ultrashort pulses—each encoding a spectral event. This transforms transient signals into repetitive ones, enabling equivalent time sampling by a fast, asynchronous pulse picker and subsequent analysis with time-stretching. The pulse-picking process, analogous to time-domain dual-comb sampling [ 32 ], is shown in Fig. 1 d. The pulse clusters repeat with a period of Τ 1 , determined by the cavity round-trip time. Within each cluster, the pulses are separated by ΔΤ, which defines the temporal resolution. The pulse picker is gated at a slightly offset period, Τ 2 , and the offset, Τ 2 -Τ 1 , matches the time interval ΔΤ. This enables automatically selecting a single pulse from each cluster in sequence. Experimentally, such a pulse picker can be implemented using an electro-optic modulator (EOM, Fig. 2 a) or an optical-optical modulator (Fig. 2 b), such as one employing optical parametric amplification (OPA), illustrated in Fig. 2 c. EOMs can create temporal gates of tens of ps using high-speed electronics, while optical gates are much narrower, down to a few ps or even fs [ 33 ], albeit with greater complexity. Here, we demonstrate both schemes as proof of concept. Our first experiment (Fig. 2 a) is based on an erbium-doped fiber amplification cavity and an EOM pulse picker (bandwidth: 40 GHz). The details are provided in Methods and Supplementary Fig. 1. In short, the amplifier provides a gain to compensate intra-cavity loss caused by an optical input-output coupler, single-mode fibers, and a time-delay line (for controlling the cavity length). This cavity has a round-trip period (T 1 ) of 9.3 ns, corresponding to a repetition frequency ( f r ) of 107.8 MHz. The intra-cavity group velocity dispersion is managed to nearly zero for minimizing its temporal and spectral impacts on the pulses injected into the cavity (see simulation results in Supplementary Fig. 2). For testing the cavity, we launch a train of mode-locked pulses (repetition frequency: 1 MHz) into it, yielding duplicated pulses spaced by T 1 = 9.3 ns. By adjusting the EOM’s driving frequency and phase, we synchronize the EO gates with the pulses. The gate width, determined by the electronical driving signal (Supplementary Fig. 3), is ~ 30 ps, which unblocks the mode-locked pulses (pulse width ~ 1 ps). This is crucial to avoid contaminating pulse spectra due to the time-frequency Fourier relationship. We then send the gated pulses to a time-stretch system comprising a 5-km single-mode fiber, a 40-GHz photodetector, and an 8-bit digital oscilloscope (33 GHz bandwidth, 40 GS/s sample rate). The time-stretch data in Fig. 3 a demonstrate good spectral reproducibility and strong consistency with the steady-state spectrum measured prior to the mode-locked pulses entering the cavity. The achieved time-stretch spectral resolution is 0.07 nm (Supplementary Note 1). Within the spectral range of 1550–1580 nm, the cavity has a negligible impact on the injection pulse spectrum. Additionally, in our temperature-controlled and vibration-isolated environment, the cavity length (and thus T 1 ) remains effectively constant during fast, single-shot measurements. If needed, the cavity can also be actively stabilized using a phase-lock loop [ 34 ] for long-term operation. To further demonstrate our method, we capture the transient spectral dynamics of 25 GHz pulses (repetition period: 40 ps) generated by an EO comb exhibiting modulation instability (see Methods). Since the cavity can store information only for durations shorter than its round-trip time, we use another EOM to fetch a short segment (~ 6 ns) of the comb pulse train, which is then injected into the cavity. Figure 3 b shows the pulse cluster and its duplicates, measured directly using the fast detector and the oscilloscope, without pulse picking and time stretching. The pulse clusters, separated by T 1 ​ (9.3 ns), exhibit intensity decay with each duplication, like a cavity ring-down process, due to the imbalance between intra-cavity gain and loss. Unsurprisingly, the current electronics, with their limited bandwidth (< 33 GHz), barely resolve the 25 GHz pulses, let alone their individual DFT spectra. In contrast, our pulse-picking scheme isolates single pulses for DFT measurements (Fig. 3 c). In this experiment, the EOM is driven with a period of T 2 ​= T 1 ​+ ΔT, where ΔT = 40 ps​. The time-stretch spectra for the isolated pulses are plotted in Fig. 3 d, showing 18 consecutive events separated by 40 ps. This surpasses the temporal resolving capability of current DFT spectrometers (e.g., a few to tens of ns [ 22 – 25 ]). Even so, the temporal resolution and maximum scan rate of this setup are constrained by the EOM pulse picker's response time (25 ps) and bandwidth (40 GHz). In the second proof-of-concept experiment, we showcase an OPA-based pulse picker that improve temporal resolution to a few ps, enabling a sub-terahertz scan rate. OPA is a second-order nonlinear process that amplifies a signal by transferring energy from a pump beam in a nonlinear crystal, yielding an idler wave to conserve energy and momentum. In this setup (Fig. 2 b), pulses from a mode-locked laser are directed into a set of glass wedges, producing a train of sub-pulses (pulse width: 1 ps) spaced by 3 ps, determined by the wedge thickness. After duplication in the fiber cavity, the sub-pulses are sent to the OPA unit (Fig. 2 c), which features a 20-mm-long chirped-poling lithium niobate (CPLN) crystal. Within the crystal, a single sub-pulse from each cluster is amplified by a pump pulse (center wavelength: 1.03 µm; pulse width: 2 ps; pulse energy: >20 nJ) through the OPA process. Figure 4 a illustrates the intensity contrast between amplified and unamplified pulse clusters (with an extinction ratio of > 20). A zoomed-in view of the selected sub-pulses is shown in Fig. 4 b. We then use the DFT oscilloscope to resolve individual sub-pulse spectra. A recorded time-stretch spectrum is shown in Fig. 4 c, closely matching the initial pulse spectrum (Fig. 4 d) measured with an optical spectrum analyzer at the mode-locked laser output. For comparison, Fig. 4 e presents a typical time-stretch spectrum with strong interference patterns from closely spaced pulses, measured at the output of the wedges. This aligns with the steady-state spectrum (Fig. 4 f) obtained using the optical spectrum analyzer. These results confirm the effectiveness of the OPA-based pulse picker. Consequently, we measure ~ 286 spectral elements (spectral resolution of 0.07 nm at full width of 20 nm) in total with a temporal resolution of 3 ps, nearly three orders of magnitude finer than that allowed by the stretched pulse duration (~ 1.8 ns). The temporal resolution of our scheme is ultimately limited by the signal pulse duration and can be enhanced by using shorter pulses, such as those below 100 fs [ 35 ]. Meanwhile, alternative optical gating methods, such as those leveraging Kerr effects, can further improve the gate extinction ratio, e.g., by exploiting polarization properties [ 36 ]. Importantly, the spectral features, such as molecular absorptions, are encoded in the signal pulses. As long as the optical gate fully overlaps with the signal pulse, these features are preserved (see Supplementary Fig. 4). Finally, our scheme offers an extendable recording length depending on the storage cavity, governed by two key factors: (1) the number of duplications, limited by the balance among intracavity gain, loss, dispersion, and nonlinearity—currently allowing duplication of over 1200 pulses (Supplementary Fig. 5); and (2) the cavity round-trip time (T 1 , typically tens of ns), which can be increased by lengthening cavity, albeit at the expense of added complexity in managing the other parameters. Nonetheless, our approach is well-suited for studies prioritizing temporal resolution over recording length, as transient phenomena in such cases may last only a few ns [ 37 , 38 ]. While the combination of a storage cavity with advanced time-domain techniques, such as time lenses, has been explored in signal processing (e.g., panoramic-reconstruction temporal imaging [ 31 ] to extend recording duration), our work differs by focusing on enhancing temporal resolution beyond the intrinsic limits imposed by pulse dispersion. In summary, we present a time-domain method for ultrafast spectral measurements. Our approach addresses the respective limitations of pump-probe techniques—namely, their inability to measure non-repetitive events—and DFT spectroscopy, which suffer from limited temporal resolution. While recent advances in DFT spectroscopy have focused on enhancing spectral resolution [ 23 ], expanding spectral bandwidth [ 24 ], and extending wavelength coverage [ 25 ], our work uniquely targets temporal resolution. Our approach achieves a temporal resolution nearly three orders of magnitude higher than existing DFT spectrometers (Supplementary Table 1). A comparison of our work with other time-resolved spectroscopic techniques is provided in Supplementary Table 2. In particular, compared to existing ultrafast techniques such as streak cameras, our method achieves three key advances: (1) single-point operation simplifies data acquisition and enables real-time processing, thanks to advances in fast photodetectors and digitizers; (2) an optimized fiber cavity could extend the recording length (e.g., > 1200 events); (3) a long stretching fiber supports high spectral resolution (e.g., picometer-level [ 23 ]), whereas spatial dispersion techniques are fundamentally limited by diffraction. By combining these capabilities, our method will emerge as a promising tool for a broad spectrum of applications. As an ultrafast spectroscopic technique, our method is immediately applicable for characterizing noise, studying optical fluctuations, and uncovering soliton phenomena, such as those occurring in microcavities or within a round-trip period of a mode-locked laser. Its ability to resolve non-repetitive events may provide complementary insights to existing pump-probe techniques, with applications in areas like chemical reaction dynamics [ 39 ], laser-induced plasmas [ 40 ], and phase transitions in materials [ 41 ]. Furthermore, by integrating mature frequency up-conversion techniques [ 23 – 25 ], our approach could extend into the mid-infrared regime for ultrafast molecular fingerprinting, unlocking new possibilities in fundamental physics, biology, and materials science. When combined with spectral-spatial encoding, our method has the potential to transform ultrafast spatial detection, enhancing the temporal resolution of time-stretch imaging [ 42 ]. Methods Laser sources Our experiments use two laser sources. The first is a home-built mode-locked fiber laser based on the nonlinear amplifying loop mirror, emitting sub-ps pulses centered at 1563 nm. A pulse picker (Supplementary Fig. 2) reduces its repetition rate from 80 MHz to 1 MHz to prevent temporal overlap during pulse duplication. This laser validates our time-stretch system in the first experiment and generates high-repetition-rate pulses in the second experiment. The second source is a commercial electro-optic (EO) comb (WTAS-02, Optocomb) delivering 25 GHz, sub-10 ps pulses at 1555 nm. To demonstrate our method for resolving ultrafast spectral dynamics, we launch the EO comb (>100 mW) into a 100 m-long highly nonlinear fiber (NL1016-C, YOFC), inducing spectral modulation instability. Storage cavity An active fiber cavity ( Fig. 2 ) stores ultrashort pulses and has an effective length of 1.76 m, yielding a 9.3 ns repetition period adjustable via an intra-cavity free-space delay line. The cavity includes an erbium-doped fiber amplifier (EDFA) with tunable gain to offset losses. Optical pulses (<1 mW) enter through a 20:80 2×2 fiber coupler. The net dispersion is nearly zero, achieved by splicing a short dispersion-compensating fiber. All fiber components and fibers are polarization-maintained. Note that the cavity is not actively stabilized but is passively stabilized by placing it inside an incubator on a vibration isolation platform. Electro-optic pulse picker The pulse picker consists of a 40 GHz intensity modulator (IM) (KY-MU-15-DQ-A, Keyang Photonics) driven by a pulse generator (LaseGen), which produces 30 ps electrical pulses triggered by a radio-frequency sine-wave generator (Rohde&Schwarz SMC100A; disciplined by a hydrogen maser). The sine-wave frequency and phase are precisely adjusted to match the corresponding pulses from the storage cavity. Optical parametric amplification (OPA) In the OPA system ( Fig. 2c ), a home-built ytterbium-doped fiber laser (>1 W average power) serves as the pump, while the storage cavity output acts as the signal. The two beams are spatially combined using a dichroic mirror (DMLP1180, Thorlabs) and focused into a 20-mm chirped-poling lithium niobate (CPLN) crystal (Castech) with a coated aspheric lens (focal length: 75 mm). The amplified signal is then collimated with an identical lens and filtered through a band-pass filter (cut-offs at 1450 and 1800 nm), blocking the pump and mid-infrared idler beams. The pump laser’s adjustable repetition period ensures temporal alignment with the signal pulses, which can be verified by monitoring the OPA output on an oscilloscope for missing pulses. Declarations Acknowledgements Financial support by Innovation Program for Quantum Science and Technology (2023ZD0301000). Contributions M.Y. and H.Z. conceived the idea and designed the experiments. Q.W. and Z.W. conducted the experiment and analyzed the data. Z.W build the laser source. M. Y. and Q. W. drafted the manuscript. H.Z. revised the manuscript. All authors provided comments and suggestions for improvements. Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Competing financial interests The authors declare no competing financial interests. Author information Correspondence and requests for materials should be addressed to M.Y. ( [email protected] ) or H.Z. ( [email protected] ) References Maiuri, M., Garavelli, M. & Cerullo, G. Ultrafast spectroscopy: state of the art and open challenges. J. Am. Chem. Soc. 142 , 3–15 (2020). Hashimoto, K. & Ideguchi, T. Phase-controlled Fourier-transform spectroscopy. Nat. Commun. 9 , 4448 (2018). Markmann, S. et al. Frequency chirped Fourier-Transform spectroscopy. Commun. Phys. 6 , 53 (2023). Ariese, F., Meuzelaar, H., Kerssens, M. M., Buijs, J. B. & Gooijer, C. Picosecond Raman spectroscopy with a fast intensified CCD camera for depth analysis of diffusely scattering media. Analyst 134 , 1192-1197 (2009). Zhang, Z., Piatkowski, L., Bakker, H. J. & Bonn, M. Ultrafast vibrational energy transfer at the water/air interface revealed by two-dimensional surface vibrational spectroscopy. Nat. Chem. 3 , 888–893 (2011). Zhang, H. et al. Ultrafast relaxation of lattice distortion in two-dimensional perovskites. Nat. Phys. 19 , 545-550 (2023). Neuweiler, H., Johnson, C. M. & Fersht, A. R. Direct observation of ultrafast folding and denatured state dynamics in single protein molecules. Proc. Natl Acad. Sci. USA 106 , 18569–18574 (2009). Ashoka, A. et al. Extracting quantitative dielectric properties from pump-probe spectroscopy. Nat. Commun. 13 , 1437 (2022). Woutersen, S., Emmerichs, U. & Bakker, H. J. Femtosecond Mid-IR pump-probe spectroscopy of liquid water: evidence for a two-component structure. Science 278 , 658-660 (1997). Kretschmar, M. et al. Compact realization of all-attosecond pump-probe spectroscopy. Sci. Adv. 10 , eadk9605 (2024). Goda, K. & Jalali, B. Dispersive Fourier transformation for fast continuous single-shot measurements. Nat. Photon. 7 , 102-112 (2013). Mahjoubfar, A. et al. Time stretch and its applications. Nat. Photon. 11 , 341-351 (2017). Godin, T. et al. Recent advances on time-stretch dispersive Fourier transform and its applications. Adv. Phys. X 7 , 2067487 (2022). Fard, A. M., Gupta, S. & Jalali, B. Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging. Laser Photon. Rev. 7 , 207–263 (2013). Jiang, Y., Karpf, S. & Jalali, B. Time-stretch LiDAR as a spectrally scanned time-of-flight ranging camera. Nat. Photon. 14 , 14-18 (2020). Coppinger, F., Bhushan, A. & Jalali, B. Photonic time stretch and its application to analog-to-digital conversion. IEEE Trans. Microwave Theory Techniques 47 , 1309–1314 (1999). Yang, C. et al. Hyperspectrally Compressed Ultrafast Photography. Phys. Rev. Lett. 124 , 023902 (2020). Gao, L., Liang, J., Li, C. & Wang, L. V. Single-shot compressed ultrafast photography at one hundred billion frames per second. Nature 516 , 74-77 (2014). Solli, D. R., Ropers, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450 , 1054-1057 (2007). Herink, G., Jalali, B., Ropers, C. & Solli, D. R. Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate. Nat. Photon. 10 , 321-326 (2016). Peng, J., Boscolo, S., Zhao, Z. & Zeng, H. Breathing dissipative solitons in mode-locked fiber lasers. Sci. Adv. 5 , eaax1110 (2019). Kawai, A. et al. Time-stretch infrared spectroscopy. Commun. Phys. 3 , 152 (2020). Hashimoto, K. et al. Upconversion time-stretch infrared spectroscopy. Light Sci. Appl 12 , 48 (2023). Wen, Z. et al. Broadband up-conversion mid-infrared time-stretch spectroscopy. Laser Photon. Rev. 18 , 2300630 (2023). He, L. et al. Long-wavelength infrared upconversion time-stretch spectroscopy. Appl. Phys. Lett. 125 , 071102 (2024). Karpov, M. et al. Dynamics of soliton crystals in optical microresonators. Nat. Phys. 15 , 1071-1077 (2019). Yu, M. et al. Breather soliton dynamics in microresonators. Nat. Commun. 8 , 14569 (2017). Voloshin, A. S. et al. Dynamics of soliton self-injection locking in optical microresonators. Nat. Commun. 12 , 235 (2021). Zaera, F. New advances in the use of infrared absorption spectroscopy for the characterization of heterogeneous catalytic reactions. Chem. Soc. Rev. 43 , 7624–7663 (2014). Guo, Z. et al. Long-range hot-carrier transport in hybrid perovskites visualized by ultrafast microscopy. Science 356 , 59–62 (2017). Li, B., Huang, S.-W., Li, Y., Wong, C. W. & Wong, K. K. Y. Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics. Nat. Commun. 8 , 61 (2017). Coddington, I., Newbury, N. & Swann, W. Dual-comb spectroscopy. Optica 3 , 414-426 (2016). Chen, F. et al. Optically Controlled Femtosecond Polariton Switch at Room Temperature. Phys. Rev. Lett. 129 , 057402 (2022). Ren, X. et al. Dual-comb optomechanical spectroscopy. Nat. Commun. 14 , 5037 (2023). Lesko, D. M. B. et al. A six-octave optical frequency comb from a scalable few-cycle erbium fibre laser. Nat. Photon. 15 , 281-286 (2021). Moroney, N. et al. A Kerr polarization controller. Nat. Commun. 13 , 398 (2022). Heller, G. T., Shukla, V. K., Figueiredo, A. M. & Hansen, D. F. Picosecond Dynamics of a Small Molecule in Its Bound State with an Intrinsically Disordered Protein. J. Am. Chem. Soc. 146 , 2319-2324 (2024). Lin, Y. et al. Excess charge-carrier induced instability of hybrid perovskites. Nat. Commun. 9 , 4981 (2018). Long, D. A. et al. Nanosecond time-resolved dual-comb absorption spectroscopy. Nat. Photon. 18 , 127-131 (2024). Harilal, S. S. et al. Optical diagnostics of laser-produced plasmas. Rev. Mod. Phys. 94 , 035002 (2022). Bretscher, H. M. et al. Ultrafast melting and recovery of collective order in the excitonic insulator Ta2NiSe5. Nat. Commun. 12 , 1699 (2021). Goda, K., Tsia, K. K. & Jalali, B. Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena. Nature 458 , 1145-1149 (2009). Supplementary Tables, Figures, and Note Supplementary Tables, Figures, and Note are not available with this version Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6665551","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":456638296,"identity":"d651eff7-23fc-4374-9752-176b30678cd0","order_by":0,"name":"Qi Wen","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Qi","middleName":"","lastName":"Wen","suffix":""},{"id":456638297,"identity":"e256a123-46ba-431d-a073-9c4ebd6b7e92","order_by":1,"name":"Zhaoyang Wen","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zhaoyang","middleName":"","lastName":"Wen","suffix":""},{"id":456638298,"identity":"789f615c-e501-4369-98cf-7f69b575a697","order_by":2,"name":"Yuan Chen","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yuan","middleName":"","lastName":"Chen","suffix":""},{"id":456638299,"identity":"ba5a8379-0de2-4d35-ba7e-12507e4f66b2","order_by":3,"name":"Bowen Sun","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Bowen","middleName":"","lastName":"Sun","suffix":""},{"id":456638300,"identity":"e6cf46bc-93ae-4ec9-bdf4-72b158e5ff9e","order_by":4,"name":"Zhicheng Huang","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zhicheng","middleName":"","lastName":"Huang","suffix":""},{"id":456638301,"identity":"f5f63f42-2df7-4a1d-b3aa-b810d195be7e","order_by":5,"name":"Ming Yan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYLCCDwUINmMDMToYZxiQqoWZhyQtujOSnz22Mbhjz8De/OwxD4ON7IYDzM8e4NNidiPN3DjH4FliA88xc2MehjTjDQfYzA3wa0kwk84xOJzAIJHDJs3DcDhxwwEeNgn8WtK/SVsYHLZnkH8D0vKfGC05ZtIMBocZGyR4QFoOEKHlzJsyyR6gX9p40swk5xgkG888zGaGX8vx9G0SPyru2POzH34m8abCTrbvePMzvFoYBBJA5AEGNjAPFFTMeNUDAf8BiJZRMApGwSgYBTgBAGIKQqinesZmAAAAAElFTkSuQmCC","orcid":"","institution":"East China Normal University","correspondingAuthor":true,"prefix":"","firstName":"Ming","middleName":"","lastName":"Yan","suffix":""},{"id":456638302,"identity":"06644796-4a2a-4a96-8ac0-8c44803aed10","order_by":6,"name":"Heping Zeng","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Heping","middleName":"","lastName":"Zeng","suffix":""}],"badges":[],"createdAt":"2025-05-14 15:22:42","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6665551/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6665551/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82833746,"identity":"04a195e7-feee-4cf6-bb59-874def1fee6a","added_by":"auto","created_at":"2025-05-15 18:07:58","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1026278,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBasic concepts. a\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Conventional time-stretch spectroscopy resolves spectral events separated by ~ns. \u003cstrong\u003eb\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Spectral fringes arise from closely spaced events below the apparatus’ temporal resolution. \u003cstrong\u003ec\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Temporally super-resolved time-stretch spectroscopy. A pulse cluster comprising ultrashort pulses separated by a time interval ΔT of ~ps is injected into an optical cavity, generating a train of cluster replicas spaced by the cavity round-trip period (T\u003csub\u003e1\u003c/sub\u003e, about tens of ns). \u003cstrong\u003ed\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Equivalent-time sampling using a pulse picker. The \u003cem\u003en\u003c/em\u003e-th pulse in the \u003cem\u003en\u003c/em\u003e-th cluster replica, with \u003cem\u003en\u003c/em\u003e being a positive integer, is selected by an ultrashort pulse picker. This process produces a new pulse train with a period of T\u003csub\u003e2\u003c/sub\u003e = T\u003csub\u003e1\u003c/sub\u003e + ΔT, where T\u003csub\u003e1\u003c/sub\u003e, T\u003csub\u003e2\u003c/sub\u003e ≫ ΔT. Spectral analysis of these pulses using a dispersive Fourier transformation oscilloscope resolves ultrafast events occurring at intervals of ΔT.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6665551/v1/bae5a1b8aeb98d43a5e12906.png"},{"id":82834284,"identity":"e56db68d-33ad-4044-807f-4f7d77848bc0","added_by":"auto","created_at":"2025-05-15 18:15:58","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":212217,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental schematics. a\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Electro-optic pulse picking. \u003cstrong\u003eb\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Optical-optical pulse picking. \u003cstrong\u003ec\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003eSchematic of optical parametric amplification (OPA). Abbreviations: DL, delay line; OC, optical coupler; EDFA, erbium-doped fiber amplifier; EOM, electro-optic modulator; SMF, single-mode fiber; PD, photodetector; Col, collimator; Cir, circulator; DM, dichroic mirror; M, mirror; CPLN, chirped-poling lithium niobate crystal.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6665551/v1/b8222d1ab8c3dbf313c125f8.png"},{"id":82833752,"identity":"d0693411-0255-461c-994a-21ba052d73d3","added_by":"auto","created_at":"2025-05-15 18:07:58","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1463236,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpectral results using electro-optic pulse picking. a\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Comparison of time-stretch (TS) spectra with a steady-state spectrum measured by an optical spectral analyzer (OSA). \u003cstrong\u003eb\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Time-domain signals without pulse picking and time stretching. \u003cstrong\u003ec\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Unstretched pulse sequence detected after pulse picking. \u003cstrong\u003ed\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Spectral dynamics of a pulse sequence exhibiting modulation instability.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6665551/v1/c9def649e3cae5281517f30f.png"},{"id":82834285,"identity":"8c5f6a4b-6273-4dd2-b754-a5191143bd0d","added_by":"auto","created_at":"2025-05-15 18:15:58","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":914446,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTemporal and spectral results of pulse picking via optical parametric amplification. a\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Time-domain pulse trains.The amplified and unamplified pulses are marked with red and black dash boxes, respectively. \u003cstrong\u003eb\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Zoom-in view of the amplified pulses. \u003cstrong\u003ec\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Dispersive Fourier transformed (DFT) spectrum after pulse picking. \u003cstrong\u003ed\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Initial mode-locked laser spectrum measured by a conventional optical spectral analyzer (OSA). \u003cstrong\u003ee\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e Time-stretch spectrumcompared to, \u003cstrong\u003ef\u003c/strong\u003e\u003cem\u003e,\u003c/em\u003e the steady-state spectrum measured without cavity storage and pulse picking.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6665551/v1/82ac9952f7e48eb77e1da75c.png"},{"id":82834975,"identity":"ebcd5c6f-e7ca-4c37-9ab2-bc85b848376c","added_by":"auto","created_at":"2025-05-15 18:31:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4221454,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6665551/v1/2bdd5e3a-8182-462e-bfc5-551631da7657.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eTemporally super-resolved dispersive Fourier transformation spectroscopy\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Main text","content":"\u003cp\u003eThe growing demand for ultrafast spectroscopic tools is driven by the need to probe transient phenomena across a wide range of fields, from optoelectronics to molecular physics and biomedical research [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. However, traditional spectrometers, which rely on moving components or detector arrays [\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], are intrinsically slow and insufficient for capturing phenomena on microsecond (\u0026micro;s) and shorter timescales, such as carrier relaxation in semiconductors, phase transitions in materials, and protein dynamics in biological systems [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. While pump-probe techniques resolve ultrafast dynamics on the picosecond (ps) and femtosecond (fs) scales, their stroboscopic nature limits them to periodic or repeatable processes [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Capturing non-repetitive, transient dynamics\u0026mdash;hallmarks of natural systems\u0026mdash;demands fast, continuous, single-shot measurement techniques.\u003c/p\u003e \u003cp\u003eDispersive Fourier transformation (DFT) is a real-time technique that exploits the space-time duality between paraxial diffraction and temporal dispersion, enabling measurements of fast, non-repetitive signals [\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Specifically, it leverages chromatic dispersion in a dispersive medium (e.g., a long fiber) to map the spectral content of an optical pulse onto a time-domain waveform. Under sufficient group velocity dispersion\u0026mdash;analogous to the far-field (Fraunhofer) regime in spatial optics\u0026mdash;the temporal intensity profile of the stretched pulse directly replicates its optical spectrum. This process, often referred to as time-stretching [\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], results in real-time bandwidth compression, allowing the use of a single detector and high-memory-depth digitizer to record long sequences of transient events\u0026mdash;a task that remains challenging for other techniques, such as those employing streak cameras [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. This capability has unlocked new regimes of spectroscopy, enabling discoveries such as optical rogue waves [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], the onset of mode-locking [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], and soliton molecule dynamics [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], and has recently been extended to critical mid-infrared bands for transient chemical sensing [\u003cspan additionalcitationids=\"CR23 CR24\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhen applied to spectroscopy, DFT enables pulse-by-pulse spectral analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea), with temporal resolution set by the pulse spacing [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], which must exceed the stretched pulse duration to prevent interference from temporal aliasing (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). At the same time, achieving adequate spectral resolution requires sufficient dispersion to stretch the pulses, imposing a trade-off between temporal and spectral resolution. This compromise, together with technical constraints such as detection bandwidth and Nyquist sampling (see Supplementary Note 1), inherently restricts the temporal resolution of current DFT spectrometers to the nanosecond (ns) scale [\u003cspan additionalcitationids=\"CR12 CR13 CR14 CR15 CR16 CR17 CR18 CR19 CR20 CR21 CR22 CR23 CR24\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Breaking this barrier is essential for propelling real-time, single-shot spectral measurement into the ultrafast regime\u0026mdash;an urgent need for investigating phenomena such as microcavity dynamics [\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], catalytic reaction pathways [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], and ultrafast carrier transport [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this Letter, we present a temporal-aliasing-free approach to DFT spectroscopic measurement. Our method captures a sequence of non-repetitive events by storing them in an optical cavity and retrieves the spectra in equivalent time using asynchronous time gates and a DFT oscilloscope. This technique achieves a three-order-of-magnitude improvement in temporal resolution, enabling continuous, single-shot measurements of non-repetitive spectra with ps resolution. Critically, resolving dynamic spectra\u0026mdash;each comprising hundreds of spectral elements\u0026mdash;represents a distinct concept of resolution compared to signal processing or temporal imaging [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Furthermore, the system supports single-shot recording lengths of up to tens of ns, thereby opening new possibilities for ultrafast spectroscopic applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec illustrates the core concept of our approach, which employs an active optical cavity to store and replicate a cluster of ultrashort pulses\u0026mdash;each encoding a spectral event. This transforms transient signals into repetitive ones, enabling equivalent time sampling by a fast, asynchronous pulse picker and subsequent analysis with time-stretching. The pulse-picking process, analogous to time-domain dual-comb sampling [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed. The pulse clusters repeat with a period of Τ\u003csub\u003e1\u003c/sub\u003e, determined by the cavity round-trip time. Within each cluster, the pulses are separated by ΔΤ, which defines the temporal resolution. The pulse picker is gated at a slightly offset period, Τ\u003csub\u003e2\u003c/sub\u003e, and the offset, Τ\u003csub\u003e2\u003c/sub\u003e-Τ\u003csub\u003e1\u003c/sub\u003e, matches the time interval ΔΤ. This enables automatically selecting a single pulse from each cluster in sequence. Experimentally, such a pulse picker can be implemented using an electro-optic modulator (EOM, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) or an optical-optical modulator (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), such as one employing optical parametric amplification (OPA), illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. EOMs can create temporal gates of tens of ps using high-speed electronics, while optical gates are much narrower, down to a few ps or even fs [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], albeit with greater complexity. Here, we demonstrate both schemes as proof of concept.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOur first experiment (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) is based on an erbium-doped fiber amplification cavity and an EOM pulse picker (bandwidth: 40 GHz). The details are provided in Methods and Supplementary Fig.\u0026nbsp;1. In short, the amplifier provides a gain to compensate intra-cavity loss caused by an optical input-output coupler, single-mode fibers, and a time-delay line (for controlling the cavity length). This cavity has a round-trip period (T\u003csub\u003e1\u003c/sub\u003e) of 9.3 ns, corresponding to a repetition frequency (\u003cem\u003ef\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) of 107.8 MHz. The intra-cavity group velocity dispersion is managed to nearly zero for minimizing its temporal and spectral impacts on the pulses injected into the cavity (see simulation results in Supplementary Fig.\u0026nbsp;2).\u003c/p\u003e \u003cp\u003eFor testing the cavity, we launch a train of mode-locked pulses (repetition frequency: 1 MHz) into it, yielding duplicated pulses spaced by T\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;9.3 ns. By adjusting the EOM\u0026rsquo;s driving frequency and phase, we synchronize the EO gates with the pulses. The gate width, determined by the electronical driving signal (Supplementary Fig.\u0026nbsp;3), is ~\u0026thinsp;30 ps, which unblocks the mode-locked pulses (pulse width\u0026thinsp;~\u0026thinsp;1 ps). This is crucial to avoid contaminating pulse spectra due to the time-frequency Fourier relationship. We then send the gated pulses to a time-stretch system comprising a 5-km single-mode fiber, a 40-GHz photodetector, and an 8-bit digital oscilloscope (33 GHz bandwidth, 40 GS/s sample rate). The time-stretch data in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea demonstrate good spectral reproducibility and strong consistency with the steady-state spectrum measured prior to the mode-locked pulses entering the cavity. The achieved time-stretch spectral resolution is 0.07 nm (Supplementary Note 1). Within the spectral range of 1550\u0026ndash;1580 nm, the cavity has a negligible impact on the injection pulse spectrum. Additionally, in our temperature-controlled and vibration-isolated environment, the cavity length (and thus T\u003csub\u003e1\u003c/sub\u003e) remains effectively constant during fast, single-shot measurements. If needed, the cavity can also be actively stabilized using a phase-lock loop [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] for long-term operation.\u003c/p\u003e \u003cp\u003eTo further demonstrate our method, we capture the transient spectral dynamics of 25 GHz pulses (repetition period: 40 ps) generated by an EO comb exhibiting modulation instability (see Methods). Since the cavity can store information only for durations shorter than its round-trip time, we use another EOM to fetch a short segment (~\u0026thinsp;6 ns) of the comb pulse train, which is then injected into the cavity. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb shows the pulse cluster and its duplicates, measured directly using the fast detector and the oscilloscope, without pulse picking and time stretching. The pulse clusters, separated by T\u003csub\u003e1\u003c/sub\u003e​ (9.3 ns), exhibit intensity decay with each duplication, like a cavity ring-down process, due to the imbalance between intra-cavity gain and loss. Unsurprisingly, the current electronics, with their limited bandwidth (\u0026lt;\u0026thinsp;33 GHz), barely resolve the 25 GHz pulses, let alone their individual DFT spectra.\u003c/p\u003e \u003cp\u003eIn contrast, our pulse-picking scheme isolates single pulses for DFT measurements (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). In this experiment, the EOM is driven with a period of T\u003csub\u003e2\u003c/sub\u003e​= T\u003csub\u003e1\u003c/sub\u003e​+ ΔT, where ΔT\u0026thinsp;=\u0026thinsp;40 ps​. The time-stretch spectra for the isolated pulses are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed, showing 18 consecutive events separated by 40 ps. This surpasses the temporal resolving capability of current DFT spectrometers (e.g., a few to tens of ns [\u003cspan additionalcitationids=\"CR23 CR24\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]). Even so, the temporal resolution and maximum scan rate of this setup are constrained by the EOM pulse picker's response time (25 ps) and bandwidth (40 GHz).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the second proof-of-concept experiment, we showcase an OPA-based pulse picker that improve temporal resolution to a few ps, enabling a sub-terahertz scan rate. OPA is a second-order nonlinear process that amplifies a signal by transferring energy from a pump beam in a nonlinear crystal, yielding an idler wave to conserve energy and momentum. In this setup (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), pulses from a mode-locked laser are directed into a set of glass wedges, producing a train of sub-pulses (pulse width: 1 ps) spaced by 3 ps, determined by the wedge thickness. After duplication in the fiber cavity, the sub-pulses are sent to the OPA unit (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec), which features a 20-mm-long chirped-poling lithium niobate (CPLN) crystal. Within the crystal, a single sub-pulse from each cluster is amplified by a pump pulse (center wavelength: 1.03 \u0026micro;m; pulse width: 2 ps; pulse energy: \u0026gt;20 nJ) through the OPA process. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea illustrates the intensity contrast between amplified and unamplified pulse clusters (with an extinction ratio of \u0026gt;\u0026thinsp;20). A zoomed-in view of the selected sub-pulses is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003eWe then use the DFT oscilloscope to resolve individual sub-pulse spectra. A recorded time-stretch spectrum is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec, closely matching the initial pulse spectrum (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed) measured with an optical spectrum analyzer at the mode-locked laser output. For comparison, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee presents a typical time-stretch spectrum with strong interference patterns from closely spaced pulses, measured at the output of the wedges. This aligns with the steady-state spectrum (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef) obtained using the optical spectrum analyzer. These results confirm the effectiveness of the OPA-based pulse picker. Consequently, we measure\u0026thinsp;~\u0026thinsp;286 spectral elements (spectral resolution of 0.07 nm at full width of 20 nm) in total with a temporal resolution of 3 ps, nearly three orders of magnitude finer than that allowed by the stretched pulse duration (~\u0026thinsp;1.8 ns).\u003c/p\u003e \u003cp\u003eThe temporal resolution of our scheme is ultimately limited by the signal pulse duration and can be enhanced by using shorter pulses, such as those below 100 fs [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Meanwhile, alternative optical gating methods, such as those leveraging Kerr effects, can further improve the gate extinction ratio, e.g., by exploiting polarization properties [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Importantly, the spectral features, such as molecular absorptions, are encoded in the signal pulses. As long as the optical gate fully overlaps with the signal pulse, these features are preserved (see Supplementary Fig.\u0026nbsp;4).\u003c/p\u003e \u003cp\u003eFinally, our scheme offers an extendable recording length depending on the storage cavity, governed by two key factors: (1) the number of duplications, limited by the balance among intracavity gain, loss, dispersion, and nonlinearity\u0026mdash;currently allowing duplication of over 1200 pulses (Supplementary Fig.\u0026nbsp;5); and (2) the cavity round-trip time (T\u003csub\u003e1\u003c/sub\u003e, typically tens of ns), which can be increased by lengthening cavity, albeit at the expense of added complexity in managing the other parameters. Nonetheless, our approach is well-suited for studies prioritizing temporal resolution over recording length, as transient phenomena in such cases may last only a few ns [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. While the combination of a storage cavity with advanced time-domain techniques, such as time lenses, has been explored in signal processing (e.g., panoramic-reconstruction temporal imaging [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] to extend recording duration), our work differs by focusing on enhancing temporal resolution beyond the intrinsic limits imposed by pulse dispersion.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn summary, we present a time-domain method for ultrafast spectral measurements. Our approach addresses the respective limitations of pump-probe techniques\u0026mdash;namely, their inability to measure non-repetitive events\u0026mdash;and DFT spectroscopy, which suffer from limited temporal resolution. While recent advances in DFT spectroscopy have focused on enhancing spectral resolution [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], expanding spectral bandwidth [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], and extending wavelength coverage [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], our work uniquely targets temporal resolution. Our approach achieves a temporal resolution nearly three orders of magnitude higher than existing DFT spectrometers (Supplementary Table\u0026nbsp;1).\u003c/p\u003e \u003cp\u003eA comparison of our work with other time-resolved spectroscopic techniques is provided in Supplementary Table\u0026nbsp;2. In particular, compared to existing ultrafast techniques such as streak cameras, our method achieves three key advances: (1) single-point operation simplifies data acquisition and enables real-time processing, thanks to advances in fast photodetectors and digitizers; (2) an optimized fiber cavity could extend the recording length (e.g., \u0026gt;\u0026thinsp;1200 events); (3) a long stretching fiber supports high spectral resolution (e.g., picometer-level [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]), whereas spatial dispersion techniques are fundamentally limited by diffraction.\u003c/p\u003e \u003cp\u003eBy combining these capabilities, our method will emerge as a promising tool for a broad spectrum of applications. As an ultrafast spectroscopic technique, our method is immediately applicable for characterizing noise, studying optical fluctuations, and uncovering soliton phenomena, such as those occurring in microcavities or within a round-trip period of a mode-locked laser. Its ability to resolve non-repetitive events may provide complementary insights to existing pump-probe techniques, with applications in areas like chemical reaction dynamics [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], laser-induced plasmas [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], and phase transitions in materials [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Furthermore, by integrating mature frequency up-conversion techniques [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], our approach could extend into the mid-infrared regime for ultrafast molecular fingerprinting, unlocking new possibilities in fundamental physics, biology, and materials science. When combined with spectral-spatial encoding, our method has the potential to transform ultrafast spatial detection, enhancing the temporal resolution of time-stretch imaging [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eLaser sources\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eOur experiments use two laser sources. The first is a home-built mode-locked fiber laser based on the nonlinear amplifying loop mirror, emitting sub-ps pulses centered at 1563 nm. A pulse picker (Supplementary Fig. 2) reduces its repetition rate from 80 MHz to 1 MHz to prevent temporal overlap during pulse duplication. This laser validates our time-stretch system in the first experiment and generates high-repetition-rate pulses in the second experiment. The second source is a commercial electro-optic (EO) comb (WTAS-02, Optocomb) delivering 25 GHz, sub-10 ps pulses at 1555 nm. To demonstrate our method for resolving ultrafast spectral dynamics, we launch the EO comb (\u0026gt;100 mW) into a 100 m-long highly nonlinear fiber (NL1016-C, YOFC), inducing spectral modulation instability.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStorage cavity\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAn active fiber cavity (\u003cstrong\u003eFig. 2\u003c/strong\u003e) stores ultrashort pulses and has an effective length of 1.76 m, yielding a\u0026nbsp;9.3\u0026nbsp;ns repetition period adjustable via an intra-cavity free-space delay line. The cavity includes an erbium-doped fiber amplifier (EDFA) with tunable gain to offset losses. Optical pulses (\u0026lt;1 mW) enter through a 20:80 2×2 fiber coupler. The net dispersion is nearly zero, achieved by splicing a short dispersion-compensating fiber. All fiber components and fibers are polarization-maintained. Note that the cavity is not actively stabilized but is passively stabilized by placing it inside an incubator on a vibration isolation platform.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eElectro-optic pulse picker\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe pulse picker consists of a 40 GHz intensity modulator (IM) (KY-MU-15-DQ-A, Keyang Photonics) driven by a pulse generator (LaseGen), which produces 30 ps electrical pulses triggered by a radio-frequency sine-wave generator (Rohde\u0026amp;Schwarz SMC100A; disciplined by a hydrogen maser). The sine-wave frequency and phase are precisely adjusted to match the corresponding pulses from the storage cavity.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOptical parametric amplification (OPA)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the OPA system (\u003cstrong\u003eFig. 2c\u003c/strong\u003e), a home-built ytterbium-doped fiber laser (\u0026gt;1 W average power) serves as the pump, while the storage cavity output acts as the signal. The two beams are spatially combined using a dichroic mirror (DMLP1180, Thorlabs) and focused into a 20-mm chirped-poling lithium niobate (CPLN) crystal (Castech) with a coated aspheric lens (focal length: 75 mm). The amplified signal is then collimated with an identical lens and filtered through a band-pass filter (cut-offs at 1450 and 1800 nm), blocking the pump and mid-infrared idler beams. The pump laser’s adjustable repetition period ensures temporal alignment with the signal pulses, which can be verified by monitoring the OPA output on an oscilloscope for missing pulses.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFinancial support by Innovation Program for Quantum Science and Technology (2023ZD0301000).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM.Y. and H.Z. conceived the idea and designed the experiments. Q.W. and Z.W. conducted the experiment and analyzed the data. Z.W build the laser source. M. Y. and Q. W. drafted the manuscript. H.Z. revised the manuscript. All authors provided comments and suggestions for improvements.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting financial interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing financial interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor information\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to M.Y. ([email protected]) or H.Z. ([email protected])\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMaiuri, M., Garavelli, M. \u0026amp; Cerullo, G. Ultrafast spectroscopy: state of the art and open challenges. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e\u003cstrong\u003e142\u003c/strong\u003e, 3\u0026ndash;15 (2020).\u003c/li\u003e\n\u003cli\u003eHashimoto, K. \u0026amp; Ideguchi, T. Phase-controlled Fourier-transform spectroscopy. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e9\u003c/strong\u003e, 4448 (2018).\u003c/li\u003e\n\u003cli\u003eMarkmann, S.\u003cem\u003e et al.\u003c/em\u003e Frequency chirped Fourier-Transform spectroscopy. \u003cem\u003eCommun. Phys.\u003c/em\u003e\u003cstrong\u003e6\u003c/strong\u003e, 53 (2023).\u003c/li\u003e\n\u003cli\u003eAriese, F., Meuzelaar, H., Kerssens, M. M., Buijs, J. B. \u0026amp; Gooijer, C. Picosecond Raman spectroscopy with a fast intensified CCD camera for depth analysis of diffusely scattering media. \u003cem\u003eAnalyst\u003c/em\u003e\u003cstrong\u003e134\u003c/strong\u003e, 1192-1197 (2009).\u003c/li\u003e\n\u003cli\u003eZhang, Z., Piatkowski, L., Bakker, H. J. \u0026amp; Bonn, M. Ultrafast vibrational energy transfer at the water/air interface revealed by two-dimensional surface vibrational spectroscopy. \u003cem\u003eNat. Chem.\u003c/em\u003e\u003cstrong\u003e3\u003c/strong\u003e, 888\u0026ndash;893 (2011).\u003c/li\u003e\n\u003cli\u003eZhang, H.\u003cem\u003e et al.\u003c/em\u003e Ultrafast relaxation of lattice distortion in two-dimensional perovskites. \u003cem\u003eNat. Phys.\u003c/em\u003e\u003cstrong\u003e19\u003c/strong\u003e, 545-550 (2023).\u003c/li\u003e\n\u003cli\u003eNeuweiler, H., Johnson, C. M. \u0026amp; Fersht, A. R. Direct observation of ultrafast folding and denatured state dynamics in single protein molecules. \u003cem\u003eProc. Natl Acad. Sci. USA\u003c/em\u003e\u003cstrong\u003e106\u003c/strong\u003e, 18569\u0026ndash;18574 (2009).\u003c/li\u003e\n\u003cli\u003eAshoka, A.\u003cem\u003e et al.\u003c/em\u003e Extracting quantitative dielectric properties from pump-probe spectroscopy. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e13\u003c/strong\u003e, 1437 (2022).\u003c/li\u003e\n\u003cli\u003eWoutersen, S., Emmerichs, U. \u0026amp; Bakker, H. J. Femtosecond Mid-IR pump-probe spectroscopy of liquid water: evidence for a two-component structure. \u003cem\u003eScience\u003c/em\u003e\u003cstrong\u003e278\u003c/strong\u003e, 658-660 (1997).\u003c/li\u003e\n\u003cli\u003eKretschmar, M. et al. Compact realization of all-attosecond pump-probe spectroscopy. \u003cem\u003eSci. Adv.\u003c/em\u003e\u003cstrong\u003e10\u003c/strong\u003e, eadk9605 (2024).\u003c/li\u003e\n\u003cli\u003eGoda, K. \u0026amp; Jalali, B. Dispersive Fourier transformation for fast continuous single-shot measurements. \u003cem\u003eNat. Photon.\u003c/em\u003e\u003cstrong\u003e7\u003c/strong\u003e, 102-112 (2013).\u003c/li\u003e\n\u003cli\u003eMahjoubfar, A.\u003cem\u003e et al.\u003c/em\u003e Time stretch and its applications. \u003cem\u003eNat. Photon. \u003c/em\u003e\u003cstrong\u003e11\u003c/strong\u003e, 341-351 (2017).\u003c/li\u003e\n\u003cli\u003eGodin, T. \u003cem\u003eet al.\u003c/em\u003e Recent advances on time-stretch dispersive Fourier transform and its applications. \u003cem\u003eAdv. Phys. X\u003c/em\u003e\u003cstrong\u003e7\u003c/strong\u003e, 2067487 (2022).\u003c/li\u003e\n\u003cli\u003eFard, A. M., Gupta, S. \u0026amp; Jalali, B. Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging. \u003cem\u003eLaser Photon. Rev.\u003c/em\u003e\u003cstrong\u003e7\u003c/strong\u003e, 207\u0026ndash;263 (2013).\u003c/li\u003e\n\u003cli\u003eJiang, Y., Karpf, S. \u0026amp; Jalali, B. Time-stretch LiDAR as a spectrally scanned time-of-flight ranging camera. \u003cem\u003eNat. Photon.\u003c/em\u003e\u003cstrong\u003e14\u003c/strong\u003e, 14-18 (2020).\u003c/li\u003e\n\u003cli\u003eCoppinger, F., Bhushan, A. \u0026amp; Jalali, B. Photonic time stretch and its application to analog-to-digital conversion. \u003cem\u003eIEEE Trans. Microwave Theory Techniques\u003c/em\u003e\u003cstrong\u003e47\u003c/strong\u003e, 1309\u0026ndash;1314 (1999).\u003c/li\u003e\n\u003cli\u003eYang, C.\u003cem\u003e et al.\u003c/em\u003e Hyperspectrally Compressed Ultrafast Photography. \u003cem\u003ePhys. Rev. Lett.\u003c/em\u003e\u003cstrong\u003e124\u003c/strong\u003e, 023902 (2020).\u003c/li\u003e\n\u003cli\u003eGao, L., Liang, J., Li, C. \u0026amp; Wang, L. V. Single-shot compressed ultrafast photography at one hundred billion frames per second. \u003cem\u003eNature\u003c/em\u003e\u003cstrong\u003e516\u003c/strong\u003e, 74-77 (2014).\u003c/li\u003e\n\u003cli\u003eSolli, D. R., Ropers, C., Koonath, P. \u0026amp; Jalali, B. Optical rogue waves. \u003cem\u003eNature\u003c/em\u003e\u003cstrong\u003e450\u003c/strong\u003e, 1054-1057 (2007).\u003c/li\u003e\n\u003cli\u003eHerink, G., Jalali, B., Ropers, C. \u0026amp; Solli, D. R. Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate. \u003cem\u003eNat. Photon.\u003c/em\u003e\u003cstrong\u003e10\u003c/strong\u003e, 321-326 (2016).\u003c/li\u003e\n\u003cli\u003ePeng, J., Boscolo, S., Zhao, Z. \u0026amp; Zeng, H. Breathing dissipative solitons in mode-locked fiber lasers. \u003cem\u003eSci. Adv.\u003c/em\u003e\u003cstrong\u003e5\u003c/strong\u003e, eaax1110 (2019).\u003c/li\u003e\n\u003cli\u003eKawai, A.\u003cem\u003e et al.\u003c/em\u003e Time-stretch infrared spectroscopy. \u003cem\u003eCommun. Phys.\u003c/em\u003e\u003cstrong\u003e3\u003c/strong\u003e, 152 (2020).\u003c/li\u003e\n\u003cli\u003eHashimoto, K.\u003cem\u003e et al.\u003c/em\u003e Upconversion time-stretch infrared spectroscopy. \u003cem\u003eLight Sci. Appl\u003c/em\u003e\u003cstrong\u003e12\u003c/strong\u003e, 48 (2023).\u003c/li\u003e\n\u003cli\u003eWen, Z. \u003cem\u003eet al.\u003c/em\u003e Broadband up-conversion mid-infrared time-stretch spectroscopy. \u003cem\u003eLaser Photon. Rev. \u003c/em\u003e\u003cstrong\u003e18\u003c/strong\u003e, 2300630 (2023).\u003c/li\u003e\n\u003cli\u003eHe, L.\u003cem\u003e et al.\u003c/em\u003e Long-wavelength infrared upconversion time-stretch spectroscopy. \u003cem\u003eAppl. Phys. Lett.\u003c/em\u003e\u003cstrong\u003e125\u003c/strong\u003e, 071102 (2024).\u003c/li\u003e\n\u003cli\u003eKarpov, M.\u003cem\u003e et al.\u003c/em\u003e Dynamics of soliton crystals in optical microresonators. \u003cem\u003eNat. Phys.\u003c/em\u003e\u003cstrong\u003e15\u003c/strong\u003e, 1071-1077 (2019).\u003c/li\u003e\n\u003cli\u003eYu, M.\u003cem\u003e et al.\u003c/em\u003e Breather soliton dynamics in microresonators. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e8\u003c/strong\u003e, 14569 (2017).\u003c/li\u003e\n\u003cli\u003eVoloshin, A. S.\u003cem\u003e et al.\u003c/em\u003e Dynamics of soliton self-injection locking in optical microresonators. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e12\u003c/strong\u003e, 235 (2021).\u003c/li\u003e\n\u003cli\u003eZaera, F. New advances in the use of infrared absorption spectroscopy for the characterization of heterogeneous catalytic reactions. \u003cem\u003eChem. Soc. Rev.\u003c/em\u003e\u003cstrong\u003e43\u003c/strong\u003e, 7624\u0026ndash;7663 (2014).\u003c/li\u003e\n\u003cli\u003eGuo, Z. \u003cem\u003eet al.\u003c/em\u003e Long-range hot-carrier transport in hybrid perovskites visualized by ultrafast microscopy. \u003cem\u003eScience\u003c/em\u003e\u003cstrong\u003e356\u003c/strong\u003e, 59\u0026ndash;62 (2017).\u003c/li\u003e\n\u003cli\u003eLi, B., Huang, S.-W., Li, Y., Wong, C. W. \u0026amp; Wong, K. K. Y. Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e8\u003c/strong\u003e, 61 (2017).\u003c/li\u003e\n\u003cli\u003eCoddington, I., Newbury, N. \u0026amp; Swann, W. Dual-comb spectroscopy. \u003cem\u003eOptica\u003c/em\u003e\u003cstrong\u003e3\u003c/strong\u003e, 414-426 (2016).\u003c/li\u003e\n\u003cli\u003eChen, F.\u003cem\u003e et al.\u003c/em\u003e Optically Controlled Femtosecond Polariton Switch at Room Temperature. \u003cem\u003ePhys. Rev. Lett.\u003c/em\u003e\u003cstrong\u003e129\u003c/strong\u003e, 057402 (2022).\u003c/li\u003e\n\u003cli\u003eRen, X.\u003cem\u003e et al.\u003c/em\u003e Dual-comb optomechanical spectroscopy. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e14\u003c/strong\u003e, 5037 (2023).\u003c/li\u003e\n\u003cli\u003eLesko, D. M. B.\u003cem\u003e et al.\u003c/em\u003e A six-octave optical frequency comb from a scalable few-cycle erbium fibre laser. \u003cem\u003eNat. Photon.\u003c/em\u003e\u003cstrong\u003e15\u003c/strong\u003e, 281-286 (2021).\u003c/li\u003e\n\u003cli\u003eMoroney, N.\u003cem\u003e et al.\u003c/em\u003e A Kerr polarization controller. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e13\u003c/strong\u003e, 398 (2022).\u003c/li\u003e\n\u003cli\u003eHeller, G. T., Shukla, V. K., Figueiredo, A. M. \u0026amp; Hansen, D. F. Picosecond Dynamics of a Small Molecule in Its Bound State with an Intrinsically Disordered Protein. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e\u003cstrong\u003e146\u003c/strong\u003e, 2319-2324 (2024).\u003c/li\u003e\n\u003cli\u003eLin, Y.\u003cem\u003e et al.\u003c/em\u003e Excess charge-carrier induced instability of hybrid perovskites. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e9\u003c/strong\u003e, 4981 (2018).\u003c/li\u003e\n\u003cli\u003eLong, D. A.\u003cem\u003e et al.\u003c/em\u003e Nanosecond time-resolved dual-comb absorption spectroscopy. \u003cem\u003eNat. Photon.\u003c/em\u003e\u003cstrong\u003e18\u003c/strong\u003e, 127-131 (2024).\u003c/li\u003e\n\u003cli\u003eHarilal, S. S.\u003cem\u003e et al.\u003c/em\u003e Optical diagnostics of laser-produced plasmas. \u003cem\u003eRev. Mod. Phys.\u003c/em\u003e\u003cstrong\u003e94\u003c/strong\u003e, 035002 (2022).\u003c/li\u003e\n\u003cli\u003eBretscher, H. M.\u003cem\u003e et al.\u003c/em\u003e Ultrafast melting and recovery of collective order in the excitonic insulator Ta2NiSe5. \u003cem\u003eNat. Commun.\u003c/em\u003e\u003cstrong\u003e12\u003c/strong\u003e, 1699 (2021).\u003c/li\u003e\n\u003cli\u003eGoda, K., Tsia, K. K. \u0026amp; Jalali, B. Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena. \u003cem\u003eNature\u003c/em\u003e\u003cstrong\u003e458\u003c/strong\u003e, 1145-1149 (2009).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Supplementary Tables, Figures, and Note","content":"\u003cp\u003eSupplementary Tables, Figures, and Note are not available with this version\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Dispersive Fourier transformation, spectroscopy, time-stretch, single-shot measurement","lastPublishedDoi":"10.21203/rs.3.rs-6665551/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6665551/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDispersive Fourier transformation (DFT) maps the spectrum of an optical pulse into the time domain via chromatic dispersion, enabling real-time, pulse-resolved spectral analysis with a single photodetector. This technique has unlocked new possibilities for single-shot measurements of transient phenomena in physics, photonics, and biological systems. However, its applicability in ultrafast regimes is hindered by temporal aliasing, which arises when pulses are spaced closer than their stretched duration. Here, we introduce temporally super-resolved time-stretch spectroscopy that overcomes this limitation. By storing a sequence of ultrashort pulses\u0026mdash;each encoding a unique, non-repetitive spectral event\u0026mdash;in an optical cavity and retrieving them sequentially using an asynchronous pulse picker and a DFT oscilloscope, we isolate individual pulses and suppress aliasing. This achieves a three-orders-of-magnitude improvement in temporal resolution. In proof-of-concept experiments, we resolve the spectral evolution of 25 GHz electro-optic comb pulses and distinguish spectra separated by just 3 ps. This technique enables continuous, ps-resolved measurements of non-repetitive spectra and is readily extendable to other DFT-based modalities, including ultrafast microscopy.\u003c/p\u003e","manuscriptTitle":"Temporally super-resolved dispersive Fourier transformation spectroscopy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-15 18:07:54","doi":"10.21203/rs.3.rs-6665551/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"cf5ab2ea-97d6-43f8-a40f-f6fdd7baca3e","owner":[],"postedDate":"May 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":48535075,"name":"Spectroscopy"}],"tags":[],"updatedAt":"2025-05-15T18:07:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-15 18:07:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6665551","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6665551","identity":"rs-6665551","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}