Topological Control of Extreme Nonlinear Waves

Controlling nonlinear optical processes is a significant challenge in photonics. Shock waves, rogue waves and solitons are widespread, from optics to hydrodynamics. Intense research is dedicated to advanced techniques for tailoring extreme waves and finding the conditions to induce transitions between different waves.

We develop a new strategy to supervise, modify and tune a laser beam in third-order nonlinear materials, when light propagation is ruled by the nonlinear Schrödinger equation (NLSE). We denote our approach topological control (TC) [1]. TC is based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the NLSE solutions by the Riemann theta function.

We prove that our method is experimentally realizable in a photorefractive crystal [1]. Specifically, we use the parametric time-dependence of photorefractive nonlinearity to shape the asymptotic wave profile. We tailor propagation coefficients, as nonlinearity and dispersion, to observe all the phases in the nonlinear wave evolution of a rectangular-shaped beam, and to control transitions from shock to rogue waves.

[1] G. Marcucci et al., arXiv:1908.05212, accepted on Nat. Commun.