Experimental Generation of Riemann Waves in Optics: A Route to Shock Wave Control

Abstract

We report the first observation of Riemann (simple) waves, which play a crucial role for understanding the dynamics of any shock-bearing system. This was achieved by properly tailoring the phase of an ultrashort light pulse injected into a highly nonlinear fiber. Optical Riemann waves are found to evolve in excellent quantitative agreement with the remarkably simple inviscid Burgers equation, whose applicability in physical systems is often challenged by viscous or dissipative effects. Our method allows us to further demonstrate a viable novel route to efficiently control the shock formation by the proper shaping of a laser pulse phase. Our results pave the way towards the experimental study, in a convenient benchtop setup, of complex physical phenomena otherwise difficult to access.

Rogue waves and analogies in optics and oceanography

“…Additional experiments coherently exciting higher-order breather solutions of the NLSE further supported this interpretation [58][59][60]. Related experiments extended the study of hydrodynamic analogies in optics even further, reporting controlled shock dynamics [61], and dam-breaking phenomena [62,63].…”

Optical spatial shock waves in nonlocal nonlinear media

“…Eqs. (16) are equivalent to Euler and continuity equations, respectively, for a fluid of speed u, mass density ρ and pressure proportional to ρ 2 . In the reported dynamics, the diffraction, initially of order 2 , starts to play a relevant role in proximity of the wave breaking.…”

“…Dispersive shock waves (DSWs) are rapidly oscillating solutions of hyperbolic partial differential equations that contrast the generation of multivalued regions through the formation of undular bores [1][2][3][4][5][6][7][8][9][10][11]. This class of phenomena was investigated in several physical fields, initially in shallow water waves [12] and ion-acoustic waves [13], then in oceanography [14], pulses propagation in photonic fibers [15,16], Bose-Einstein condensates [17][18][19][20][21][22], quantum liquids [23], photorefractive media [24], plasma physics [25], viscous fluids [26], and diffracting optical beams [5,[27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Experimental observation of the emergence of Peregrine-like events in focusing dam break flows

“…Recent other works have stressed the crucial importance and universality of such structures, especially the Peregrine wave [7,8,9] which can also be detected in deep water and other nonlinear medium governed by the NLSE [10,11]. Normally dispersive fibers have also stimulated experimental research, mainly driven by the interest in the study of dispersive shock waves (DSW) [12] : optical equivalent of undular bores [13], reproduction of dam-breaking problems [14], or the Riemann simple waves [15], have provided recent examples of the insights that can be obtained in the defocusing regime of propagation.…”