Time stretch and its applications

Journal name:
Nature Photonics
Year published:
Published online


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.

At a glance


  1. Digitizer bottlenecks and solutions via time stretch.
    Figure 1: Digitizer bottlenecks and solutions via time stretch.

    As the sampling rate of an analog-to-digital converter (ADC) increases, its dynamic range, measured by the effective number of bits (ENOB), reduces. Three factors are responsible for this: comparator ambiguity caused by the limited gain bandwidth of the transistors, sampling error due to the clock jitter (known as aperture jitter), and thermal (Johnson) noise of the electronic components. a, Among these, the comparator ambiguity and the aperture jitter are the dominant performance-limiting factors at high speeds. b, By slowing down the signal, time stretch resolves these issues by suppressing the effect of the aperture jitter and the comparator ambiguity14. c,d, Consider a high-frequency signal being sampled directly by an ADC. A small jitter will cause a significant error in the sampled amplitude (c), whereas if the signal is slowed down by time stretch prior to the sampling, the effect of clock jitter is considerably reduced (d). Also, slowing down the signal relaxes the comparator speed requirements. Time-stretch ADC works on burst data, but also on continuous data using a technique known as virtual time gating49.

  2. Building blocks of a time-stretch system.
    Figure 2: Building blocks of a time-stretch system.

    A photonic time-stretch system consists of four steps. Step 1: an input signal along with the information carried by it is modulated onto the spectrum of wideband ultrashort optical pulses. Step 2: a group delay dispersive element spreads the spectral components in time causing the information modulated onto the spectrum to be slowed down. This relaxes the speed requirement of the ADC and enhances the digitizer performance as described in Fig. 1. Depending on the amount of dispersion used and the optical bandwidth of the input, this dispersive transformation can be in the near- or far-field. The so-called time-stretch dispersive Fourier transform (TS-DFT) occurs in the far-field regime where the amount of dispersion is large enough to satisfy the stationary phase approximation. Step 3: the optical signal is converted to an analog electrical waveform through photodetection, and then digitized by a real-time ADC. Step 4: digital data analysis and classification using artificial intelligence (AI) is performed in a central processing unit (CPU) or a dedicated processor such as a graphics processing unit (GPU). Images: infinite spiral clock, liseykina / iStock / Getty Images Plus; oscilloscope, RaymondAsiaPhotography / Alamy Stock Photo; AI, Alexey Kotelnikov / Alamy Stock Photo; CPU, Petr Bonek / Alamy Stock Photo; GPU, Patrik Slezak / Alamy Stock Photo.

  3. Different dispersion devices.
    Figure 3: Different dispersion devices.

    Group delay dispersion used in time stretch can be experimentally realized using a number of different device designs. a, An optical fibre with internal Raman amplification provides high dispersion combined with net gain. The pump power is gradually transferred to the signal (Stokes wavelength) avoiding noise (low-power) and nonlinear (high-power) regions. EDFA, erbium-doped fibre amplifier. b, Chirped fibre Bragg grating is advantageous at implementing arbitrary group delay profiles. c, A different approach is a recirculating photonic filter using an arrayed waveguide grating in which an arbitrary delay is applied to each spectral channel41. d, Spectral-to-angular-to-temporal mapping (chromomodal dispersion device) exploits the large modal dispersion of a multi-mode waveguide (a fibre or a pair of planar reflectors) to achieve extremely high chromatic dispersion at 800 nm or visible bands where dispersive fibres are not available122. e, Chromomodal dispersion can be extended to synthesize nonlinear group delay profiles using curved reflectors (middle) to warp the spectro-angular profile (from (i) to (ii)), and then radially transform and map this nonlinear profile into angular excitation of the modes of a multi-mode waveguide (iii)28. Panels a,b,d,e adapted from ref. 28, IEEE.

  4. Applications of time stretch.
    Figure 4: Applications of time stretch.

    Blue: photonic time stretch was initially developed to overcome the speed and resolution limitations of high-speed ADCs12 (i) leading to the development of a femtosecond digitizer29 (ii), and later became the foundation of many ultrafast instrumentation techniques in spectroscopy, for example stimulated Raman spectroscopy19, 20 (vii), imaging and microscopy30 (iv), and in the observation of relativistic17 (v) and nonlinear dynamics for example optical rogue waves5 (iii), soliton explosions15 (vi), build-up of mode-locking123 (viii), and internal dynamics of soliton molecules16 (ix). Green: the coherent (full-field) version, which uses phase measurement using interferometry or phase retrieval algorithms to recover the phase of the optical pulses, has enabled record-breaking instruments in laser vibrometry and velocimetry31 (x), quantitative phase imaging and a time-stretch microscope augmented by artificial intelligence for label-free cell classification22 (xii). Orange: the new concept of warped time stretch is opening up opportunities in real-time optical data analytics and data compression26, 27 (xi). Panel (i) shows an eye diagram of 45 Gbps data captured by a 1.5 GHz electronic digitizer after its speed was boosted by 34× using photonic time stretch35. Figure adapted from: (i), ref. 35, (iv), ref. 124, Wiley; (ii), ref. 29, AIP Publishing LLC; (v), ref. 17, (xi), ref. 26, (xii), ref. 22, under a Creative Commons licence (https://creativecommons.org/licenses/by/4.0/); (vi), ref. 15, (vii), ref. 20, OSA; (viii), ref. 123, Macmillan Publishers Ltd; (ix), University of Goettingen; (x), ref. 125, SPIE.


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Author information


  1. Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA

    • Ata Mahjoubfar &
    • Bahram Jalali
  2. California NanoSystems Institute, Los Angeles, California 90095, USA

    • Ata Mahjoubfar &
    • Bahram Jalali
  3. Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, UK

    • Dmitry V. Churkin &
    • Sergei K. Turitsyn
  4. Institute of Automation and Electrometry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia

    • Dmitry V. Churkin
  5. Novosibirsk State University, Novosibirsk 630090, Russia

    • Dmitry V. Churkin &
    • Sergei K. Turitsyn
  6. Universite de Nice - CNRS UMR 7335, Institut Non Lineaire de Nice, 1361 Route des Lucioles 06560, Valbonne, France

    • Stéphane Barland
  7. Dodd Walls Centre for Photonic and Quantum Electronics, Department of Physics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand

    • Neil Broderick
  8. Department of Bioengineering, University of California, Los Angeles, California 90095, USA

    • Bahram Jalali
  9. Department of Surgery, David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA

    • Bahram Jalali

Competing financial interests

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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