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We report the phase and amplitude ultrafast measurement of nonlinear random light by using a heterodyne time-lens technique in its digital time holography configuration (spatial encoding arrangement with hologram observation for recording in single-shot the electric field, SEAHORSE) [1]. We have developed an algorithm in order to compensate the aberrations generally induced by the high order dispersion in time lens devices. This enables an aberration-free single-shot recording of the phase and of the amplitude over a large temporal window (200 ps) with a resolution of the order of 300fs [2]
We apply this new version of the SEAHORSE to investigate the spontaneous (or noise induced) modulation instability (MI) in the anomalous regime of dispersion of single mode fibers. We observe phase and amplitude signatures of Akhmediev breather-like in very good agreement with numerical predictions based on the focusing one-dimensional nonlinear Schrödinger equation. Note that the recording of the amplitude dynamics (without the phase information) had already been observed by using conventional time lens devices [3].
Finally, taking advantage of the phase and amplitude single-shot recording, we compute the inverse scattering transform (nonlinear Fourier transform) of the modulation instability. This allows us to measure for the first time the Weyl’s distribution of the amplitude of the solitons, which has been predicted theoretically in the framework of the inverse scattering transform [4]
[1] A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, Nat.
Photonics 12, 228 (2018).
[2] A. Lebel, A. Tikan, S. Randoux, P. Suret and F. Copie Opt. Lett. 46, 2 (2021)
[3] M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla,
R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, Nat. Commun. 7,
13675 (2016).
[4] A Gelash, D Agafontsev, V Zakharov, G El, S Randoux, P Suret
Phys. Rev. Lett., 123, 23, 234102 (2019)
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