Single-shot reconstruction of spectral amplitude and phase in a fiber ring cavity at a 80 MHz repetition rate

Analysis of laser radiation using the Nonlinear Fourier transform

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Mathematical approaches for simultaneous characterisation of localized and extended fields in optical signals are not well developed. Here, the authors demonstrate the application of the Nonlinear Fourier transform approach based on the Zakharov-Shabat spectral problem for the analysis of fibre laser radiation.

Dynamics of Turing and Faraday instabilities in a longitudinally modulated fiber-ring cavity

We experimentally investigate the round-trip-to-round-trip dynamics of the modulation instability spectrum in a passive fiber-ring cavity presenting an inhomogeneous dispersion profile. By implementing a real-time spectroscopy technique, we are able to record successive single-shot spectra, which display the evolution of the system toward a stationary state. We find that the two instability regimes (Turing and Faraday) that compete in this kind of inhomogeneous cavity not only differ by their characteristic frequency but also by their dynamical behavior. The dynamic transition between those two regimes of instability is also presented.