Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate

Journal name:
Nature Photonics
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Published online


Mode-locked lasers have enabled some of the most precise measurements ever performed, from attosecond time-domain spectroscopy to metrology with frequency combs. However, such extreme precision belies the complexity of the underlying mode-locking dynamics. This complexity is particularly evident in the emergence of the mode-locked state, an intrinsically singular, non-repetitive transition. Many details of mode-locking are well understood, yet conventional spectroscopy cannot resolve the nascent dynamics in passive mode-locking on their natural nanosecond timescale, the single pulse period. Here, we capture the pulse-resolved spectral evolution of a femtosecond pulse train from the initial fluctuations, recording ∼900,000 consecutive periods. We directly observe critical phenomena on timescales from tens to thousands of roundtrips, including the birth of the broadband spectrum, accompanying wavelength shifts and transient interference dynamics described as auxiliary-pulse mode-locking. Enabled by the time-stretch transform, the results may impact laser design, ultrafast diagnostics and nonlinear optics.

At a glance


  1. The buildup of femtosecond mode-locking in real time.
    Figure 1: The buildup of femtosecond mode-locking in real time.

    a, In Kerr-lens mode-locking, one of many picosecond fluctuations develops into a stable femtosecond pulse train. These initial fluctuations are induced by moving an intracavity prism. b, Left: The mode-locking transition is detected with a fast photodiode and a real-time oscilloscope. Middle (experimental data) and right (schematic): The recorded time series is segmented with respect to the roundtrip time and displays the transition to the mode-locked state (single pulse). Before mode-locking, picosecond fluctuations typically persist for several thousand roundtrips. c, Left: Single-shot spectral information is obtained via insertion of a dispersive element, the time-stretch dispersive Fourier transform (TS-DFT). Middle (experimental data) and right (schematic): Before mode-locking, the data represent the timing of picosecond fluctuations stemming from a narrow bandwidth. The TS-DFT yields complete spectral information for the emerging femtosecond pulse and the dominant picosecond fluctuation. As sketched in the schematic (right, grey area), the wavelength scale applies to these features. Rapid spectral broadening and femtosecond pulse formation occur over a few hundred roundtrips. RT, roundtrip (scale bars).

  2. Three transitions from quasi-c.w. to mode-locked operation.
    Figure 2: Three transitions from quasi-c.w. to mode-locked operation.

    ac, Each plot contains a subset of 3,500 continuously recorded single-shot spectra (38.5 µs time interval). The wavelength scale applies to the mode-locked state and its precursor, as sketched in Fig. 1. In the first stage, multiple picosecond fluctuations traverse the cavity while the bandwidth of a single picosecond pulse increases moderately over 300–400 roundtrips. Following this phase, nonlinear broadening develops rapidly and a femtosecond pulse forms within 200 roundtrips. d, Cut lines from the data set in c, indicating the normalized power of the decaying background picosecond fluctuations (green) and the growing dominant fluctuation (blue). The spectral evolution is evaluated by means of the FWHM of the emerging dominant fluctuation (red). Multiple stages of rapid spectral broadening begin at the maxima of the power oscillation, indicated by grey arrows. In between, the spectral broadening process slows and can pause momentarily (grey shaded area).

  3. Long-term and short-term views of the mode-locking transition.
    Figure 3: Long-term and short-term views of the mode-locking transition.

    a, Larger section of the data set from Fig. 2c, consisting of 340,000 single-shot spectra (3.74 ms). The wavelength scale applies to the mode-locked state and its precursor, as sketched in Fig. 1. b, Oscillatory power of a picosecond fluctuation (blue) that evolves to the single femtosecond laser pulse (horizontal cut from a, along blue arrow). Corresponding information from the transition in the data set in Fig. 2a is also shown (green). For comparison, the grey line shows the evolving fluctuation for mode-locking start-up without a substantial auxiliary pulse. c, Close-up of the data from a, revealing the interference pattern. d, Starting from a nearly constant value before mode-locking, the detected total energy per roundtrip (blue) overshoots the mode-locked value during the rapid phase of spectral broadening (FWHM, red) due to increased gain. Simultaneously, the beat frequency follows the laser relaxation oscillation and reaches a steady-state frequency of 8 MHz.


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  1. IV. Physical Institute – Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany

    • G. Herink,
    • C. Ropers &
    • D. R. Solli
  2. Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA

    • G. Herink,
    • B. Jalali &
    • D. R. Solli


All authors were closely involved in this study and contributed to the ideas, realization of the experiments, data analysis and interpretation, and writing of the paper.

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