Influence of modulation and shape of laser pump pulses on stimulated Brillouin scattering in self-focusing regime in silica S. Mauger 1 , L. Berg´ e 1 , S. Skupin 2,3 1. CEA-DAM, DIF, F-91297 Arpajon, France 2. Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany 3. Friedrich Schiller University, Institute of Condensed Matter Theory and Optics, 07743 Jena, Germany The propagation of powerful nanosecond optical pulses at the wavelength of 355 nm in thick silica windows usually gives rise to Kerr-induced multiple filamentation, which breaks the homogeneity of the energy distribution and can initiate surface or bulk damage. Part of the incident beam is furthermore back-reflected by stimulated Brillouin scattering (SBS), leading to the creation of a Stokes wave which is also source of damage at the front surface of the sample [1,2]. To address this problem, we study the interaction of these two nonlinear effects from coupled envelope equations in full (3+1)-dimensional geometry. Emphasis is put on the influence of the incident pulse spatial profile and of phase or amplitude modulations applied to the pump wave. Indeed, we demonstrated in [3] that an amplitude modulation ∼| cos [m sin (2πν m t )]| with high enough fre- quency ν m and modulation depth m breaks the incident pulse into pulse trains of short periods (typically tens of ps), and inhibits the creation of the acoustic wave. Such a modulation is efficient to avoid front damage, because no backscattered wave is created, the envelope of Gaussian pulses is preserved and the pump wave self-focuses at the classical Marburger distance. However, the major drawback is that the effective average beam power is halved. In contrast, phase modulations ∼ exp [im sin (2πν m t )] preserve the pump power and do suppress the backscat- tered component for low input powers. At high powers far above the self-focusing threshold (P cr = 0.35 MW), however, they contribute to local amplification of both forward and backward components and lead to turbulent dynamics inside the material if the pump bandwidth ∆ν ≃ 2mν m is moderate, e.g., close to 100 GHz (ν m = 2 GHz and m = 21). Recently, we found that a large bandwidth exceeding a critical value, ∆ν cr , depending on the initial intensity, is able to suppress the Brillouin effect at all power levels. This result is exemplified in Fig. 1, which shows the effects of a phase modulation in subcritical and above-critical configurations. Fig. 1 Effects of a phase modulation for the pump power P 1 = 16P cr . (a), (b), (d) and (e) show intensity profiles in the (x, t ) plane at maximum intensity: (a) Pump intensity near the self-focusing point and (b) Stokes wave at the entrance of the sample for a phase modulation with bandwidth ∆ν < ∆ν cr = 630 GHz. (d), (e) Same quantities for ∆ν > ∆ν cr . (c) represents the maximal pump intensity along the propagation axis. The solid curve corresponds to a bandwidth above critical, whereas the dashed curve corresponds to the same modulation with subcritical bandwidth. The spatial profile of the incident beam is also a key parameter in the propagation dynamics. Multifilamentation can indeed be triggered from noisy perturbations and broad (e.g. Supergaussian) spatial distributions undergoing breakup of their edges into small-scaled cells, for which the self-focusing distance is drastically shortened. For instance, with an incident power of 50P cr , a single Gaussian pulse will self-focus at the Marburger distance z c = 8.6 cm whereas a square pulse suffering a 5% random noise will collapse at z c = 3.6 cm due to modulational instabilities. The action of SBS is discussed for such broad pulses. In conclusion, the interplay between self-focusing and stimulated Brillouin scattering strongly depends on the characteristics of the incident pump pulse, i.e., input power, modulation and beam shape. At high powers trigger- ing self-focusing, phase modulations with large enough bandwidths are shown to definitively suppress Brillouin scattering. References [1] R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 1992). [2] G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001), 3rd Ed. [3] S. Mauger et al., “Self-focusing versus stimulated Brillouin scattering of laser pulses in fused silica,” New. J. Phys. 12, 103049 (2010).