Boosting and Taming Wave Breakup in Second Harmonic Generation

Raphaël Jauberteau,Vincent Couderc,Tigran Mansuryan,Katarzyna Krupa,Fabio Baronio,Sahar Wehbi,Stefan Wabnitz,Benjamin Wetzel,Alessandro Tonello

doi:10.3389/fphy.2021.640025

Abstract

Modulation instability is a universal phenomenon that can be found in a wide variety of nonlinear systems where, in the presence of a noise seed, peaks of random intensities can be generated. Several dynamical systems admit exact solutions in the form of breathers or solitons on a finite background. The vast majority of soliton studies has been restricted so far to one-dimensional systems. In contrast, the occurrences of localized structures in fully spatiotemporal systems has been only sporadically explored. In this work, we experimentally study the conditions for the wave-breaking of spatially extended optical beams in the process of second harmonic generation. Whenever the pump energy of the picosecond-long fundamental beam reaches a critical level, the beam shape at the second harmonic in a KTP crystal breaks into small filaments. These filaments exhibit extreme local intensity peaks, and their statistical distribution can be modified by the input energy of the fundamental beam. Moreover, by analyzing similar wave-breaking dynamics in a PPLN crystal in the presence of a higher nonlinear quadratic response, we observe that the spatial beam breaking may even gradually vanish as the laser intensity grows larger, leading to a spatial reshaping into a smooth and wider beam, accompanied by a substantial broadening of its temporal spectrum.

Highlights

A wide class of nonlinear systems exhibits Modulation Instability (MI): the onset stage of the nonlinear dynamics of MI leads to an exponential growth of periodic perturbations [1]
As can be seen in panels (a–c) of Figure 2, for input intensities close to 0.11 GW/cm2, we observed a spatial focusing of the SH beam: its diameter at 1/e2 dropped from 320 μm down to 50 μm
Panels (d–f) of Figure 2 show that, when increasing the pump intensity IFF above 1 GW/cm2, we observed a breakup of the SH beam into a seemingly random pattern of tightly focalized light filaments

Summary

Introduction

A wide class of nonlinear systems exhibits Modulation Instability (MI): the onset stage of the nonlinear dynamics of MI leads to an exponential growth of periodic perturbations [1]. MI has been largely studied in single mode optical fibers in the presence of dispersion and Kerr nonlinearity, and solitons on a finite background take the form of pulses (in the time domain) evolving along the fiber [2, 3]. In this work we focus our attention on a wider class of higher-dimensional nonlinear systems that involve spatially extended optical beams, whose combined spatial and temporal instabilities are expected to stimulate a host of further studies on nonlinear waves. Wave-breaking, a mechanism of disintegration of optical beams or temporal pulses, has been extensively studied in nonlinear optics. In materials with cubic (Kerr) nonlinearity, there are two principal mechanisms of wave breaking, namely, MI and gradient catastrophe (GC): they appear in Boosting and Taming Wave Breakup either the focusing or the defocusing regime, respectively. In materials with quadratic nonlinearities the MI and GC processes may even coexist [4]

Methods

Results

Conclusion