Observing non-repetitive and statistically rare signals that occur on short timescales requires fast real-time measurements that exceed the speed, precision and record length of conventional digitizers. Photonic time stretch is a data acquisition method that overcomes the speed limitations of electronic digitizers and enables continuous ultrafast single-shot spectroscopy, imaging, reflectometry, terahertz and other measurements at refresh rates reaching billions of frames per second with non-stop recording spanning trillions of consecutive frames. The technology has opened a new frontier in measurement science unveiling transient phenomena in nonlinear dynamics such as optical rogue waves and soliton molecules, and in relativistic electron bunching. It has also created a new class of instruments that have been integrated with artificial intelligence for sensing and biomedical diagnostics. We review the fundamental principles and applications of this emerging field for continuous phase and amplitude characterization at extremely high repetition rates via time-stretch spectral interferometry.
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Jalali, B., Solli, D., Goda, K., Tsia, K. & Ropers, C. Real-time measurements, rare events and photon economics. Eur. Phys. J. Special Topics 185, 145–157 (2010).
Taleb, N. N. The Black Swan: The Impact of the Highly Improbable (Random House, 2007).
VanderLugt, A. Optical Signal Processing (Wiley, 2005).
Boyraz, O. & Jalali, B. Demonstration of a silicon Raman laser. Opt. Express 12, 5269–5273 (2004).
Solli, D., Ropers, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450, 1054–1057 (2007).
Akhmediev, N., Ankiewicz, A. & Taki, M. Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373, 675–678 (2009).
Pisarchik, A. N., Jaimes-Reátegui, R., Sevilla-Escoboza, R., Huerta-Cuellar, G. & Taki, M. Rogue waves in a multistable system. Phys. Rev. Lett. 107, 274101 (2011).
Dudley, J. M., Dias, F., Erkintalo, M. & Genty, G. Instabilities, breathers and rogue waves in optics. Nat. Photon. 8, 755–764 (2014).
Akhmediev, N. et al. Roadmap on optical rogue waves and extreme events. J. Opt. 18, 063001 (2016).
Suret, P. et al. Single-shot observation of optical rogue waves in integrable turbulence using time microscopy. Nat. Commun. 7, 13136 (2016).
Mahjoubfar, A., Goda, K., Betts, G. & Jalali, B. Optically amplified detection for biomedical sensing and imaging. J. Opt. Soc. Am. A 30, 2124–2132 (2013).
Bhushan, A., Coppinger, F. & Jalali, B. Time-stretched analogue-to-digital conversion. Electron. Lett. 34, 1081–1082 (1998).
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).
Jalali, B. & Coppinger, F. M. A. Data conversion using time manipulation. US patent US6288659 (2001).
Runge, A. F., Broderick, N. G. & Erkintalo, M. Observation of soliton explosions in a passively mode-locked fiber laser. Optica 2, 36–39 (2015).
Herink, G., Kurtz, F., Jalali, B., Solli, D. & Ropers, C. Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules. Science 356, 50–54 (2017).
Roussel, E. et al. Observing microscopic structures of a relativistic object using a time-stretch strategy. Sci. Rep. 5, 10330 (2015).
Evain, C. et al. Direct observation of spatiotemporal dynamics of short electron bunches in storage rings. Phys. Rev. Lett. 118, 054801 (2017).
Solli, D., Chou, J. & Jalali, B. Amplified wavelength–time transformation for real-time spectroscopy. Nat. Photon. 2, 48–51 (2008).
Saltarelli, F. et al. Broadband stimulated Raman scattering spectroscopy by a photonic time stretcher. Opt. Express 24, 21264–21275 (2016).
Dobner, S. & Fallnich, C. Dispersive Fourier transformation femtosecond stimulated Raman scattering. Appl. Phys. B 122, 278 (2016).
Chen, C. L. et al. Deep learning in label-free cell classification. Sci. Rep. 6, 21471 (2016).
Jalali, B., Chan, J. & Asghari, M. H. Time–bandwidth engineering. Optica 1, 23–31 (2014).
Chan, J. C., Mahjoubfar, A., Chen, C. L. & Jalali, B. Context-aware image compression. PLoS ONE 11, e0158201 (2016).
Asghari, M. H. & Jalali, B. Anamorphic transformation and its application to time–bandwidth compression. Appl. Opt. 52, 6735–6743 (2013).
Mahjoubfar, A., Chen, C. L. & Jalali, B. Design of warped stretch transform. Sci. Rep. 5, 17148 (2015).
Chen, C. L., Mahjoubfar, A. & Jalali, B. Optical data compression in time stretch imaging. PLoS ONE 10, e0125106 (2015).
Jalali, B. & Mahjoubfar, A. Tailoring wideband signals with a photonic hardware accelerator. Proc. IEEE 103, 1071–1086 (2015).
Chou, J., Boyraz, O., Solli, D. & Jalali, B. Femtosecond real-time single-shot digitizer. Appl. Phys. Lett. 91, 161105 (2007).
Goda, K., Tsia, K. & Jalali, B. Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena. Nature 458, 1145–1149 (2009).
Mahjoubfar, A. et al. High-speed nanometer-resolved imaging vibrometer and velocimeter. Appl. Phys. Lett. 98, 101107 (2011).
Wong, T. T., Lau, A. K., Wong, K. K. & Tsia, K. K. Optical time-stretch confocal microscopy at 1 μm. Opt. Lett. 37, 3330–3332 (2012).
Bosworth, B. T. et al. High-speed flow microscopy using compressed sensing with ultrafast laser pulses. Opt. Express 23, 10521–10532 (2015).
Han, Y. & Jalali, B. Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations. J. Lightwave Technol. 21, 3085–3103 (2003).
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).
Kim, J., Park, M. J., Perrott, M. H. & Kärtner, F. X. Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution. Opt. Express 16, 16509–16515 (2008).
Konishi, T., Tanimura, K., Asano, K., Oshita, Y. & Ichioka, Y. All-optical analog-to-digital converter by use of self-frequency shifting in fiber and a pulse-shaping technique. J. Opt. Soc. Am. B 19, 2817–2823 (2002).
Portuondo-Campa, E., Paschotta, R. & Lecomte, S. Sub-100 attosecond timing jitter from low-noise passively mode-locked solid-state laser at telecom wavelength. Opt. Lett. 38, 2650–2653 (2013).
Lonappan, C. K., Madni, A. M. & Jalali, B. Single-shot network analyzer for extremely fast measurements. Appl. Optics 55, 8406–8412 (2016).
Jalali, B., Chan, J. & Mahjoubfar, A. Analog gearbox: a photonic hardware accelerator. In Avionics Vehicle Fiber-Optics Photon. Conf. (AVFOP) 1–2 (IEEE, 2016).
Yegnanarayanan, S., Trinh, P. & Jalali, B. Recirculating photonic filter: a wavelength-selective time delay for phased-array antennas and wavelength code-division multiple access. Opt. Lett. 21, 740–742 (1996).
Solli, D., Gupta, S. & Jalali, B. Optical phase recovery in the dispersive Fourier transform. Appl. Phys. Lett. 95, 231108 (2009).
Buckley, B. W., Madni, A. M. & Jalali, B. Coherent time-stretch transformation for real-time capture of wideband signals. Opt. Express 21, 21618–21627 (2013).
Trebino, R. et al. Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating. Rev. Sci. Instrum. 68, 3277–3295 (1997).
Iaconis, C. & Walmsley, I. A. Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses. Opt. Lett. 23, 792–794 (1998).
Konishi, T., Kato, T. & Goto, H. Waveform reconstruction device, waveform reconstruction system, and waveform reconstruction method. US patent US8886037 (2014).
DeVore, P. T., Buckley, B. W., Asghari, M. H., Solli, D. R. & Jalali, B. Coherent time-stretch transform for near-field spectroscopy. IEEE Photon. J. 6, 1–7 (2014).
Mahjoubfar, A., Chen, C., Niazi, K. R., Rabizadeh, S. & Jalali, B. Label-free high-throughput cell screening in flow. Biomed. Opt. Express 4, 1618–1625 (2013).
Han, Y. & Jalali, B. Continuous-time time-stretched analog-to-digital converter array implemented using virtual time gating. IEEE Trans. Circuits Systems I: Regular Papers 52, 1502–1507 (2005).
Chou, J., Conway, J. A., Sefler, G. A., Valley, G. C. & Jalali, B. Photonic bandwidth compression front end for digital oscilloscopes. J. Lightwave Technol. 27, 5073–5077 (2009).
Ng, W., Rockwood, T., Sefler, G. & Valley, G. Demonstration of a large stretch-ratio photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz. IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).
Wong, J. H. et al. Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme. J. Lightwave Technol. 29, 3099–3106 (2011).
Valley, G. C. Photonic analog-to-digital converters. Opt. Express 15, 1955–1982 (2007).
Stigwall, J. & Galt, S. Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretch systems. J. Lightwave Technol. 25, 3017–3027 (2007).
Han, Y., Boyraz, O. & Jalali, B. Ultrawide-band photonic time-stretch A/D converter employing phase diversity. IEEE Trans. Microwave Theory Techniques 53, 1404–1408 (2005).
Fuster, J., Novak, D., Nirmalathas, A. & Marti, J. Single-sideband modulation in photonic time-stretch analogue-to-digital conversion. Electron. Lett. 37, 67–68 (2001).
Fard, A. et al. All-optical time-stretch digitizer. Appl. Phys. Lett. 101, 051113 (2012).
Lonappan, C. K. et al. Time-stretch accelerated processor for real-time, in-service, signal analysis. In IEEE Global Conf. Signal Information Processing 707–711 (2014).
Kitayama, K.-I. & Wada, N. Photonic IP routing. IEEE Photon. Technol. Lett. 11, 1689–1691 (1999).
Wada, N. & Kitayama, K.-I. A 10 gb/s optical code division multiplexing using 8-chip optical bipolar code and coherent detection. J. Lightwave Technol. 17, 1758–1765 (1999).
Ruban, V. et al. Rogue waves—towards a unifying concept?: Discussions and debates. Eur. Phys. J. Special Topics 185, 5–15 (2010).
Wetzel, B. et al. Real-time full bandwidth measurement of spectral noise in supercontinuum generation. Sci. Rep. 2, 882 (2012).
Solli, D., Herink, G., Jalali, B. & Ropers, C. Fluctuations and correlations in modulation instability. Nat. Photon. 6, 463–468 (2012).
Godin, T. et al. Real time noise and wavelength correlations in octave-spanning supercontinuum generation. Opt. Express 21, 18452–18460 (2013).
Dean, R. in Water Wave Kinematics 609–612 (Springer, 1990).
Kharif, C. & Pelinovsky, E. Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B 22, 603–634 (2003).
Gabaix, X., Gopikrishnan, P., Plerou, V. & Stanley, H. E. A theory of power-law distributions in financial market fluctuations. Nature 423, 267–270 (2003).
Anderson, C. The Long Tail: Why the Future of Business is Selling Less of More (Hachette Books, 2006).
Clauset, A., Shalizi, C. R. & Newman, M. E. Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009).
Pisarenko, V. & Rodkin, M. Heavy-Tailed Distributions in Disaster Analysis (Springer Science & Business Media, 2010).
Zhen-Ya, Y. Financial rogue waves. Commun. Theor. Phys. 54, 947–949 (2010).
Birkholz, S., Brée, C., Demircan, A. & Steinmeyer, G. Predictability of rogue events. Phys. Rev. Lett. 114, 213901 (2015).
Cundiff, S. T., Soto-Crespo, J. M. & Akhmediev, N. Experimental evidence for soliton explosions. Phys. Rev. Lett. 88, 073903 (2002).
Soto-Crespo, J. M., Akhmediev, N. & Ankiewicz, A. Pulsating, creeping, and erupting solitons in dissipative systems. Phys. Rev. Lett. 85, 2937–2940 (2000).
Runge, A. F., Broderick, N. G. & Erkintalo, M. Dynamics of soliton explosions in passively mode-locked fiber lasers. J. Opt. Soc. Am. B 33, 46–53 (2016).
Akhmediev, N., Dudley, J. M., Solli, D. & Turitsyn, S. Recent progress in investigating optical rogue waves. J. Opt. 15, 060201 (2013).
Liu, Z., Zhang, S. & Wise, F. W. Rogue waves in a normal-dispersion fiber laser. Opt. Lett. 40, 1366–1369 (2015).
Lecaplain, C. & Grelu, P. Rogue waves among noiselike-pulse laser emission: an experimental investigation. Phys. Rev. A 90, 013805 (2014).
Runge, A. F., Aguergaray, C., Broderick, N. G. & Erkintalo, M. Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers. Opt. Lett. 38, 4327–4330 (2013).
Solli, D. R., Ropers, C. & Jalali, B. Active control of rogue waves for stimulated supercontinuum generation. Phys. Rev. Lett. 101, 233902 (2008).
Runge, A. F., Aguergaray, C., Broderick, N. G. & Erkintalo, M. Raman rogue waves in a partially mode-locked fiber laser. Opt. Lett. 39, 319–322 (2014).
Descloux, D. et al. Spectrotemporal dynamics of a picosecond OPO based on chirped quasi-phase-matching. Opt. Lett. 40, 280–283 (2015).
Akhmediev, N., Ankiewicz, A. & Soto-Crespo, J. Multisoliton solutions of the complex Ginzburg–Landau equation. Phys. Rev. Lett. 79, 4047–4051 (1997).
Ortaç, B. et al. Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser. Opt. Lett. 35, 1578–1580 (2010).
Soto-Crespo, J. M., Grelu, P., Akhmediev, N. & Devine, N. Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs. Phys. Rev. E 75, 016613 (2007).
Chen, W.-C., Chen, G.-J., Han, D.-A. & Li, B. Different temporal patterns of vector soliton bunching induced by polarization-dependent saturable absorber. Opt. Fiber Technol. 20, 199–207 (2014).
Chouli, S. & Grelu, P. Soliton rains in a fiber laser: an experimental study. Phys. Rev. A 81, 063829 (2010).
Chouli, S. & Grelu, P. Rains of solitons in a fiber laser. Opt. Express 17, 11776–11781 (2009).
Bao, C., Xiao, X. & Yang, C. Soliton rains in a normal dispersion fiber laser with dual-filter. Opt. Lett. 38, 1875–1877 (2013).
Niang, A., Amrani, F., Salhi, M., Grelu, P. & Sanchez, F. Rains of solitons in a figure-of-eight passively mode-locked fiber laser. Appl. Phys. B 116, 771–775 (2014).
Huang, S. et al. Soliton rains in a graphene-oxide passively mode-locked ytterbium-doped fiber laser with all-normal dispersion. Laser Phys. Lett. 11, 025102 (2013).
Kelleher, E. & Travers, J. Chirped pulse formation dynamics in ultra-long mode-locked fiber lasers. Opt. Lett. 39, 1398–1401 (2014).
Churkin, D. et al. Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers. Nat. Commun. 6, 7004 (2015).
Donovan, G. M. Dynamics and statistics of noise-like pulses in modelocked lasers. Physica D 309, 1–8 (2015).
Krejcik, P. et al. Commissioning the new LCLS X-band transverse deflecting cavity with femtosecond resolution. In Proc. Int. Beam Instrumentation Conf. 308–311 (2013).
Chan, J., Mahjoubfar, A., Asghari, M. & Jalali, B. Reconstruction in time-bandwidth compression systems. Appl. Phys. Lett. 105, 221105 (2014).
Goda, K. et al. High-throughput single-microparticle imaging flow analyzer. Proc. Natl Acad. Sci. USA 109, 11630–11635 (2012).
Xing, F. et al. A 2-GHz discrete-spectrum waveband-division microscopic imaging system. Opt. Commun. 338, 22–26 (2015).
Avila, K. et al. The onset of turbulence in pipe flow. Science 333, 192–196 (2011).
Tarasov, N., Sugavanam, S. & Churkin, D. Spatio-temporal generation regimes in quasi-CW Raman fiber lasers. Opt. Express 23, 24189–24194 (2015).
Wabnitz, S. Optical turbulence in fiber lasers. Opt. Lett. 39, 1362–1365 (2014).
Horowitz, M. & Silberberg, Y. Control of noiselike pulse generation in erbium-doped fiber lasers. IEEE Photon. Technol. Lett. 10, 1389–1391 (1998).
Zhao, L., Tang, D., Cheng, T., Tam, H. & Lu, C. 120nm bandwidth noise-like pulse generation in an erbium-doped fiber laser. Opt. Commun. 281, 157–161 (2008).
Kobtsev, S., Kukarin, S., Smirnov, S., Turitsyn, S. & Latkin, A. Generation of double-scale femto/pico-second optical lumps in mode-locked fiber lasers. Opt. Express 17, 20707–20713 (2009).
North, T. & Rochette, M. Raman-induced noiselike pulses in a highly nonlinear and dispersive all-fiber ring laser. Opt. Lett. 38, 890–892 (2013).
Suzuki, M., Ganeev, R. A., Yoneya, S. & Kuroda, H. Generation of broadband noise-like pulse from Yb-doped fiber laser ring cavity. Opt. Lett. 40, 804–807 (2015).
Kalaycioğlu, H., Akçaalan, Ö., Yavaş, S., Eldeniz, Y. & Ilday, F. Burst-mode Yb-doped fiber amplifier system optimized for low-repetition-rate operation. J. Opt. Soc. Am. B 32, 900–906 (2015).
Andral, U. et al. Fiber laser mode locked through an evolutionary algorithm. Optica 2, 275–278 (2015).
Lecaplain, C., Grelu, P., Soto-Crespo, J. & Akhmediev, N. Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser. Phys. Rev. Lett. 108, 233901 (2012).
Liu, M. et al. Dissipative rogue waves induced by long-range chaotic multi-pulse interactions in a fiber laser with a topological insulator-deposited microfiber photonic device. Opt. Lett. 40, 4767–4770 (2015).
Sugavanam, S., Tarasov, N., Wabnitz, S. & Churkin, D. V. Ginzburg–Landau turbulence in quasi-CW Raman fiber lasers. Laser Photon. Rev. 9, L35–L39 (2015).
Chen, S., Soto-Crespo, J. M. & Grelu, P. Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence. Opt. Express 22, 27632–27642 (2014).
Chen, S., Soto-Crespo, J. M. & Grelu, P. Watch-hand-like optical rogue waves in three-wave interactions. Opt. Express 23, 349–359 (2015).
Chen, S. et al. Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering. Phys. Rev. A 92, 033847 (2015).
Raich, U. in CAS CERN Accelerator School: Ion Sources (ed. Bailey, R.) 503–514 (CERN, 2013).
Saeys, Y., Van Gassen, S. & Lambrecht, B. N. Computational flow cytometry: helping to make sense of high-dimensional immunology data. Nat. Rev. Immunol. 16, 449–462 (2016).
Adam, J., Mahjoubfar, A., Diebold, E. D., Buckley, B. W. & Jalali, B. Spectrally encoded angular light scattering. Opt. Express 21, 28960–28967 (2013).
Lei, M., Zou, W., Li, X. & Chen, J. Ultrafast FBG interrogator based on time-stretch method. IEEE Photon. Technol. Lett. 28, 778–781 (2016).
Solli, D. R. & Jalali, B. Analog optical computing. Nat. Photon. 9, 704–706 (2015).
Asghari, M. H. & Jalali, B. Edge detection in digital images using dispersive phase stretch transform. J. Biomed. Imaging 2015, 687819 (2015).
Ilovitsh, T., Jalali, B., Asghari, M. H. & Zalevsky, Z. Phase stretch transform for super-resolution localization microscopy. Biomed. Opt. Express 7, 4198–4209 (2016).
Diebold, E. D. et al. Giant tunable optical dispersion using chromo-modal excitation of a multimode waveguide. Opt. Express 19, 23809–23817 (2011).
Herink, G., Jalali, B., Ropers, C. & Solli, D. Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate. Nat. Photon. 10, 321–326 (2016).
Jalali, B., Soon-Shiong, P. & Goda, K. Breaking speed and sensitivity limits: real-time diagnostics with serial time-encoded amplified microscopy. Optik Photonik 5, 32–36 (2010).
Mahjoubfar, A. et al. 3D ultrafast laser scanner. SPIE Proc. 8611, 86110N (2013).
Goda, K., Solli, D. R., Tsia, K. K. & Jalali, B. Theory of amplified dispersive Fourier transformation. Phys. Rev. A 80, 043821 (2009).
We are grateful to S. Bielawski at Universite des Sciences et Technologies de Lille, France for invaluable discussions on electron-beam diagnostics. We are also thankful to D. Solli at UCLA for helpful comments. The work at UCLA was partially supported by the Office of Naval Research (ONR) Multidisciplinary University Research Initiatives (MURI) on Optical Computing and by NantWorks, LLC.
B.J. is a co-founder of Time Photonics, the manufacturer of RogueScope, a single-shot spectrometer based on the time-stretch technique.
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Mahjoubfar, A., Churkin, D., Barland, S. et al. Time stretch and its applications. Nature Photon 11, 341–351 (2017). https://doi.org/10.1038/nphoton.2017.76
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