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Collapse dynamics of super Gaussian beams Gadi Fibich1, Nir Gavish1, Taylor D. Grow2, Amiel A. Ishaaya2, Luat T. Vuong2 and Alexander L. Gaeta2 1 Tel Aviv University, 2 Cornell University Optics Express 14 5468-5475, 2006 BACKGROUND Nonlinear wave collapse is universal to many areas of physics including optics, hydrodynamics, plasma physics, and Bose-Einstein condensates. In optics, applications such as LIDAR and remote sensing in the atmosphere with femtosecond pulses depend critically on the collapse dynamics. Propagation is modeled by the NLS equation 2 iAz (z , x, y )+ Axx + Ayy + A A = 0 The fundamental model for optical beam propagation and collapse in a bulk Kerr medium is the nonlinear Schrödinger equation (NLS). Theory and experiments show that laser beams collapse with a self-similar peak-like profile known as the Townes profile. Until now it was believed that the Townes profile is the only attractor for the 2D NLS. We show, theoretically and experimentally, that laser beams can also collapse with a self-similar ring profile. GAUSSIAN VS SUPER GAUSSIAN BEAMS Super Gaussian initial condition - r4 y 0 = 15e Gaussian Collapse with Townes profile Super Gaussian Collapse with ring profile - r2 y 0 = 15 4 π / 2e Gaussian initial condition • Power P≈38Pcr for both initial conditions Why? High power - early stage of collapse: Only SPM Gaussian High power – can neglect diffraction Super-Gaussian 2 iAz (z , x, y )+ Axx + Ayy + A A = 0 A A0 e , is • Geometrical optics • Not due to Fresnel diffraction Rays Phase SH Exact solution - depends on initial phase (SPM) S A0 z 2 Geometrical optics - Rays perpendicular to phase level sets COLLAPSE DYNAMICS OF SUPER GAUSSIAN BEAMS Theory • High powered super Gaussian input beam • Formation of a ring structure • Ring profile is unstable • Breaks up into a ring of filaments Experimental setup Experiment Simulation 1.3 cm 2.0 cm 3.0 cm 4.3 cm Excellent agreement between theory and experiments • Water cell • E=13.3 μ • Image area: 0.3mm X 0.3mm SPATIO TEMPORAL SPHERE COLLAPSE PULSE SPLITTING IN TIME AND SPACE Propagation of ultrashort laser pulses in a Kerr medium with anomalous dispersion is modeled by the following NLS equation 2 iAz (z, x, y )+ Axx + Ayy - b 2 Att + A A = 0, b2 < 0 • Super Gaussian pulses with anomalous dispersion collapse with a 3D shell-type profile. • Undergo pulse splitting in space and time • Subsequently splits into collapsing 3-D wavepackets. t0 t0+ρfil/2