Tsunamis may be the best-known form of extreme wave, but nonlinear interactions between waves lead to numerous other types. To bring some order into this extreme-wave zoo, one can associate different types with different topologies. For example, dispersive shock waves can have the same topology as a sphere, whereas rogue waves have a double-ring topology. Yet, conversion between different kinds of extreme waves has remained elusive. Now, Giulia Marcucci and colleagues have exploited the topological properties to control such transitions, using optical waves as a testbed.
For nonlinear waves, the topological genus corresponds to the number of oscillating phases. This number changes while the wave propagates, and for light it is also linked to the initial beam waist. In numerical simulations and experiments, adjusting the beam waist then allowed the controlled transition from shock waves to Akhmediev breathers to Peregrine solitons at specific detection times.