Third-order Riemann pulses in optical fibers.

Domenico Bongiovanni,Zhili Li,Benjamin Wetzel,Stefan Wabnitz,Roberto Morandotti,Zhigang Chen,Yi Hu

doi:10.1364/oe.411736

Abstract

We introduce the concept of third-order Riemann pulses in nonlinear optical fibers. These pulses are generated when properly tailored input pulses propagate through optical fibers in the presence of higher-order dispersion and Kerr nonlinearity. The local propagation speed of these optical wave packets is governed by their local amplitude, according to a rule that remains unchanged during propagation. Analytical and numerical results exhibit a good agreement, showing controllable pulse steepening and subsequent shock wave formation. Specifically, we found that the pulse steepening dynamic is predominantly determined by the action of higher-order dispersion, while the contribution of group velocity dispersion is merely associated with a shift of the shock formation time relative to the comoving frame of the pulse evolution. Unlike standard Riemann waves, which exclusively exist within the strong self-defocusing regime of the nonlinear Schrödinger equation, such third-order Riemann pulses can be generated under both anomalous and normal dispersion conditions. In addition, we show that the third-order Riemann pulse dynamics can be judiciously controlled by a phase chirping parameter directly included in the initial chirp profile of the pulse.

Highlights

Simple Riemann waves (RWs) are implicit solutions of the inviscid Burgers’ equation (IBE), that lies at the basis of fluid dynamics
We introduce a new class of optical RWs, namely third-order Riemann pulses (TRPs), and study these optical wave-packets in the context of nonlinear optical fiber propagation
We have introduced the concept of TRPs in the context of nonlinear fiber optics and investigated analytically and numerically their properties under different propagation conditions

Summary

Introduction

Simple Riemann waves (RWs) are implicit solutions of the inviscid Burgers’ equation (IBE), that lies at the basis of fluid dynamics. A strong defocusing condition is typically reached for short pulses featuring high power (and usually exhibiting a large bandwidth), in a wavelength range where the dispersion is low (i.e., generally close to the fiber zero-dispersion wavelength (ZDW)) In this regime, the ability to neglect the effects associated with higher-order dispersion terms can become questionable, and one may wonder whether similar RW solutions can still retain analogous physical properties. The dynamics of TRPs originate from the interplay between higher-order dispersion effects and Kerr nonlinearity Their nonlinear evolutions exhibit progressive steepening with constant peak intensity and subsequent shock wave formation, with similar general dynamics yet different characteristics and behaviors when compared with previously studied standard RWs. Guided by our theoretical analysis, we perform numerical studies demonstrating the formation of TRPs by judiciously shaping an initial optical pulse before its injection into the fiber. We highlight a way to approximately control the TRPs, where the shock point can be tuned by acting appropriately on a phase term imprinted onto the initial optical pulse, without modifying the physical parameters of the fiber system

Theory

Third-order Riemann pulses at the zero-dispersion wavelength

Optical control of third-order Riemann pulses

Findings

Conclusion