Solitonization of the Anderson localization and rogue waves

In a paper published in Optics Express, M. Saleh, C. Conti, and F. Biancalana, report on a new scenario during rogue wave generation. The random intensity profile of an optical pulse fosters Anderson localization of waves that triggers the generation of solitons (the so-called solitonization) and ultimately rogue events. The process also involves event horizons in analogy with black holes. This is a further evidence of the complexity of supercontinuum generation and extreme events in nonlinear fibre optics.

Solitonization of the Anderson localization

Solitons and disorder-induced Anderson states are two apparently unrelated forms of wave localization, the former being due to nonlinearity and the latter to linear disorder.

However, on closer inspection, solitons and disorder induced localized states have similarities: exponential localization, negative eigenvalues, any possible position in space. In the presence of nonlinearity, disorder-induced localizations are expected to have eigenvalue and localization length dependent on power. These states, however, also exist for a negligible nonlinearity: Hence, in the low fluence regime, they are linear Anderson localizations, but at high fluence, they become related to solitons.

In Physical Review A, we analytically and numerically study the process of “solitonization of the Anderson localization,” that is smooth transition from disorder induced to nonlinearity induced wave localization in random media.

Turbulent Transitions in Optical Wave Propagation

In a paper published in Phys. Rev. Lett. , D. Pierangeli, F. Di Mei,  G. Di Domenico, A. J. Agranat, C. Conti, and E. Del Re, report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.

Gamow, Batman and the shocks

Shock generation is a leading topic in nonlinear physics and optics. Shock waves occur whenever one enters highly nonlinear regimes either in time or in space. The origin of the undular bores is among the mysterious dynamics of shock wave generation. The undular bores are the fast oscillations that regularize the wave-breaking after the shock; their features are very difficult to understand theoretically.

A typical phenomenon is the appearance of the Batman ears in the optical intensity when the shock occurs; these “ears” are very pronounced peaks limiting the region of the shock and including undulars bores. Figures above show the Batman ears in the far field of a shock wave genereated in the spatial nonlinear optical propagation. Beyond numerical simulations, we do not have a complete theoretical description of this effect.

In a paper published in Optics Express (arXiv:1601.05796)Maria Chiara Braidotti, Silvia Gentilini, and Claudio Conti show that Gamow vectors of the reversed harmonic oscillator provide a new theoretical tool for the quantitative description of spatial shock waves in nonlocal media. The analytical calculations perfectly reproduce our experiments. This opens a number of possibilities for describing and controlling the shock waves in highly nonlocal and non-instantaneous media. The results also show the validity of the novel theoretical methods inherited by the so-called “time-asymmetric quantum-mechanics.”

The picture above shows the comparison between experiments and the analytically calculated Gamow vectors.

Black holes evaporate, black holes are solitons, solitons evaporate !

The fact that black holes are solitons is not very well known. Abdus Salam and others outlined this issue several years ago. Stephen Hawking predicted that Black Holes evaporate, and this is a quantum effect on classical gravity governed by the highly nonlinear Einstein-Hilbert equations.

Leone Villari, Ewan Wright, Fabio Biancalana and Claudio Conti report on the possibility that all types of classical solitons may evaporate in the quantum regime. A paper in the arXiv contains the theory on the exact quantization of the nonlinear Schroedinger equation: solitons emit a blackbody radiation spectrum at a temperature given by the same formula of Hawking!

This result is intriguing. On one hand, because it represents the first theoretical prediction of the Hawking radiation in a fully nonlinear quantum field theory. The standard Hawking theory relies on the quantization of a linear field in a curved background. The theory may hence provide insights for a true quantum gravity based on the complete quantization of the Einstein-Hilbert equations.

On the other hand, the result is also important because the Hawking radiation from a quantum soliton may furnish a novel highly tunable quantum source with many possible applications.