Soliton gas in optical fiber experiments: nonlinear Fourier transform of the noise-induced modulational instability

Abstract We report the experimental measurement of the density of states (DOS) associated with the soliton gas emerging during the development of the noise-induced modulation instability (MI) in optical fibres. By employing a time-lens-based heterodyne detection technique (SEAHORSE), we reconstruct the complex optical field and compute its nonlinear discrete spectrum within the framework of the inverse scattering transform. Our results show that, at early stages of the MI, the DOS matches the Weyl distribution predicted for an ‘ideal’ critically dense soliton gas, thereby confirming the relevance of the SG description for this nonlinear random wave regime. At larger effective propagation distances, we observe a progressive deformation of the DOS in the complex plane. We compare these observations with numerical simulations of a generalised nonlinear Schrödinger equation that includes losses, third-order dispersion and stimulated Raman scattering (SRS). Our simulations reproduce the main experimental trends and demonstrate that SRS is the dominant mechanism responsible for the spectral deformation. These findings highlight the need to extend the kinetic theory of soliton gas beyond purely integrable evolutions. In particular, our results call for a generalised kinetic equation (or generalised hydrodynamics description) that accounts for weak non-integrable perturbations such as SRS.