Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion

Abstract

Abstract. In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.

Experimental generation of optical flaticon pulses

“…Extreme waves are also well known to occur in shallow waters, e.g., the run-up of a tsunami toward the coast [13]. Once again, similar phenomena have been recently predicted to occur in nonlinear optical fibers with normal GVD [14,15].…”

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

“…Specifically, we consider an optical pulse envelope propagating in a fiber featuring strong nonlinearity and weak (normal) dispersion. In this regime, the NLSE is known to reduce to a 2 × 2 conservation law ruling wave propagation in shallow water (or isentropic gas dynamics), the so-called nonlinear shallow water equations [5,[18][19][20]. Here we go further and demonstrate that, by suitably shaping the temporal profile of the pulse phase, we are able to experimentally generate RWs and control their breaking dynamics.…”

“…Let us now consider the transformation of an arbitrary optical pulse into a Riemann wave A RW ðz; TÞ. To produce a RW, it is necessary to introduce an instantaneous frequency profile (chirp [10]) that is a scaled replica of the amplitude (or, in other words, the phase derivative is proportional to its amplitude) [19,20]. In the particular case where a Riemann pulse (with duration T 0 and peak power P 0 ) propagates in a fiber with normal dispersion (β 2 > 0), such that the dispersion length L D ¼ T 2 0 =β 2 is much longer than the nonlinear length L NL ¼ ðγP 0 Þ −1 , the proportionality relation between the amplitude and chirp is preserved during propagation so that A RW ðz; TÞ ¼ jA RW ðz; TÞje ∓i2 ffiffiffiffiffiffi ffi…”

“…More importantly, under these conditions [18], the evolution of the pulse amplitude (and chirp) in the fiber, which is described by the NLSE, can be well approximated until the shock point by the IBE [20], namely,…”

“…In the IBE framework, the shock develops from the action of both nonlinearity and dispersion on the specifically prepared Riemann pulse, thus enabling a versatile and controlled shock formation. Indeed, the propagation of a Riemann pulse corresponds to a particular case of purely unidirectional energy flow [20], whose parametric representation can be readily obtained by the method of characteristics [2,4]. For the IBE evolution, the characteristic lines T Ci (mapping the energy flow direction) extend from certain given points T i (at z ¼ 0) and can be analytically calculated for any arbitrary input pulse A RW ð0; TÞ:…”