Anisotropic Optical Shock Waves in M-Cresol/Nylon Highly Nonlocal Nonlinearity

Abstract

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.

Third-order Riemann pulses in optical fibers

“…Simple Riemann waves (RWs) are implicit solutions of the inviscid Burgers' equation (IBE), that lies at the basis of fluid dynamics. These waves are of fundamental importance in studying shock wave phenomena occurring not only in hydrodynamics but also in numerous other physical systems [1][2][3][4][5][6][7][8][9][10][11][12]. Interest in RWs arises from the main role played by the IBE, a paradigm nonlinear partial differential equation which is used to model nonlinear and turbulent systems of various complexity, spanning dynamics encountered in e.g.…”