Topological control of extreme waves
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, transitions between extreme waves are allowed. However, these have never been experimentally observed because control strategies are still missing. We introduce the new concept of 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 through Riemann theta functions. We demonstrate the concept experimentally by reporting observations of supervised transitions between waves with different genera. Considering the box problem in a focusing photorefractive medium, we tailor the time-dependent nonlinearity and dispersion to explore each region in the state diagram of the nonlinear wave propagation. Our result is the first realization of topological control of nonlinear waves. This new technique casts light on shock and rogue waves generation and can be extended to other nonlinear phenomena.
Nature Communications volume 10, Article number: 5090 (2019)
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.
Review Paper in Advances in Physics X
Terahertz absorption spectroscopy plays a key role in physical, chemical and biological systems as a powerful tool to identify molecular species through their rotational spectrum fingerprint. Owing to the sub-nanometer scale of molecules, radiation-matter coupling is typically dominated by dipolar interaction. Here we show that multipolar rotational spectroscopy of molecules in proximity of localized graphene structures can be accessed through the extraordinary enhancement of their multipolar transitions provided by terahertz plasmons. In particular, specializing our calculations to homonuclear diatomic molecules, we demonstrate that a micron-sized graphene ring with a nano-hole at the core combines a strong near-field enhancement and an inherently pronounced field localization enabling the enhancement of the dipole-forbidden terahertz absorption cross-section of H+2H2+ by 8 orders of magnitude. Our results shed light on the strong potential offered by nano-structured graphene as a robust and electrically tunable platform for multipolar terahertz absorption spectroscopy at the nanoscale.
A. Ciattoni, C. Conti, and A. Marini in Communication Physics
Dispersive shock waves in thermal optical media belong to the third-order nonlinear phenomena, whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the M-Cresol/Nylon mixed solution, to access an extremely-nonlinear highly-nonlocal regime and realize anisotropic shock waves. We prove that a superposition of the Gamow vectors in an ad hoc rigged Hilbert space describes the nonlinear beam propagation beyond the shock point. Specifically, the resulting rigged Hilbert space is a tensorial product between the reversed and the standard harmonic oscillators spaces. The anisotropy turns out from the interaction of trapping and antitrapping potentials in perpendicular directions. Our work opens the way to a complete description of novel intriguing shock phenomena, and those mediated by extreme nonlinearities.
Giulia Marcucci, Phillip Cala, Weining Man, Davide Pierangeli, Claudio Conti, Zhigang Chen in ArXiv:1909.04506
The math of irreversibility
Topological photonic crystal fibers and ring resonators
We study photonic crystal fibers and ring resonators with topological features induced by Aubry- Andre-Harper modulations of the cladding. We find non-trivial gaps and edge states at the interface between regions with different Chern numbers. We calculate the field profile and eigenvalue dispersion by an exact recursive approach. Compared with conventional circular resonators and fibers, the proposed structure features topological protection and hence robustness against symmetry-preserving local perturbations that do not close the gap. These topological photonic crystal fibers sustain strong field localization and energy concentration at a given radial distance. As topological light guiding and trapping devices, they may bring about many opportunities for both fundamentals and applications unachievable with conventional optical devices.
Laura Pilozzi, Daniel Leykam, Zhigang Chen, Claudio Conti in ArXiv:1909.02081
Topological inverse problem by machine learning
Topological cascade laser