Topological Control of Extreme Waves

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed because of the lack of control strategies. We introduce a new concept of nonlinear wave topological control, based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schrödinger equation solutions by the Riemann theta function. We prove it experimentally by reporting the first observation of supervised transitions between extreme waves with different genera, like the continuous transition from dispersive shock to rogue waves. Specifically, we use a parametric time-dependent nonlinearity to shape the asymptotic wave genus. We consider the box problem in a focusing Kerr-like photorefractive medium and tailor time-dependent propagation coefficients, as nonlinearity and dispersion, to explore each region in the state-diagram and include all the dynamic phases in the nonlinear wave propagation. Our result is the first example of the topological control of integrable nonlinear waves. This new technique casts light on dispersive shock waves and rogue wave generation and can be extended to other nonlinear phenomena, from classical to quantum ones. The outcome is not only important for fundamental studies and control of extreme nonlinear waves, but can be also applied to spatial beam shaping for microscopy, medicine, and spectroscopy, and to the broadband coherent light generation.

Marcucci et al. in ArXiv:1908.05212

Our Ising machine in Laser Focus World

August 2019 issue of Laser Focus World reports on our Ising machine in a featured article

Researchers have built the largest photonic Ising machine to date – an optical processor for solving difficult optimization problems by modelin interacting spins via a spatially varying light field

Other web and press release on our Ising machine

Le Scienze : la piu’ grande macchina di calcolo con la luce

Repubblica : la macchina che risolve i problemi alla velocita’ della luce

See also

Super-Duper Ising machine

Perturbation of Transmission Matrices in nonlinear random media

Random media with tailored optical properties are attracting burgeoning interest for applications in imaging, biophysics, energy, nanomedicine, spectroscopy, cryptography, and telecommunications. A key paradigm for devices based on this class of materials is the transmission matrix, the tensorial link between the input and the output signals, that describes in full their optical behavior. The transmission matrix has specific statistical properties, such as the existence of lossless channels, that can be used to transmit information, and are determined by the disorder distribution. In nonlinear materials, these channels may be modulated and the transmission matrix tuned accordingly. Here, the direct measurement of the nonlinear transmission matrix of complex materials is reported, exploiting the strong optothermal nonlinearity of scattering silica aerogel (SA). It is shown that the dephasing effects due to nonlinearity are both controllable and reversible, opening the road to applications based on the nonlinear response of random media.

Adam Fleming, Claudio Conti, and Andrea Di Falco in Annalen Der Physics

Optical Spatial Shock Waves in Nonlocal Nonlinear Media

Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity in temporal pulses transmission and nonlocality in spatial beams propagation. Despite the rich and vast literature on nonlinear waves in optical Kerr media, spatial dispersive shock waves in nonlocal materials deserve further attention for their unconventional properties. Indeed, they have been investigated in colloidal matter, chemical physics and biophotonics, for sensing and control of extreme phenomena.
Here we review the last developed theoretical models and recent optical experiments on spatial dispersive shock waves in nonlocal media. Moreover, we discuss observations in novel versatile materials relevant for soft matter and biology.

Giulia Marcucci et al. in arXiv:1907.02823

See also