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Fluctuations and correlations in modulation instability

Nature Photonics volume 6, pages 463–468 (2012)Cite this article

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Abstract

Stochastically driven nonlinear processes are responsible for spontaneous pattern formation and instabilities in numerous natural and artificial systems, including well-known examples such as sand ripples, cloud formations, water waves, animal pigmentation and heart rhythms1,2,3. Technologically, a type of such self-amplification drives free-electron lasers4,5 and optical supercontinuum sources6,7 whose radiation qualities, however, suffer from the stochastic origins8,9,10,11. Through time-resolved observations, we identify intrinsic properties of these fluctuations that are hidden in ensemble measurements. We acquire single-shot spectra of modulation instability produced by laser pulses in glass fibre at megahertz real-time capture rates. The temporally confined nature of the gain physically limits the number of amplified modes, which form an antibunched arrangement as identified from a statistical analysis of the data. These dynamics provide an example of pattern competition and interaction in confined nonlinear systems.

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Figure 1: Capturing modulation instability in single-shot measurements.
Figure 2: Experimental investigation of single-shot modulation instability.
Figure 3: Autocorrelation analysis of experimental single-shot modulation instability spectra.
Figure 4: Analysis of modulation instability in nonlinear optical fibre by numerical simulation.

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Acknowledgements

This work was supported by the National Science Foundation including CIAN ERC, the Defense Advanced Research Project Agency (DARPA/DSO) Physical Intelligence programme and the Deutsche Forschungsgemeinschaft (DFG-ZUK 45/1). D.R.S. thanks B. de La Brea for helpful discussions.

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Authors and Affiliations

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

    D. R. Solli, B. Jalali & C. Ropers

  2. Courant Research Center Physics and Materials Physics Institute, University of Göttingen, Germany

    D. R. Solli, G. Herink & C. Ropers

  3. California NanoSystems Institute (CNSI), Los Angeles, 90095, California, USA

    B. Jalali

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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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Correspondence to D. R. Solli.

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Solli, D., Herink, G., Jalali, B. et al. Fluctuations and correlations in modulation instability. Nature Photon 6, 463–468 (2012). https://doi.org/10.1038/nphoton.2012.126

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