Collapse dynamics of super Gaussian beamsGadi Fibich1, Nir Gavish1, Taylor D. Grow2, Amiel A. Ishaaya2, Luat T. Vuong2 and Alexander L. Gaeta2

1 Tel Aviv University, 2 Cornell UniversityOptics Express 14 5468-5475, 2006

BACKGROUND

GAUSSIAN VS SUPER GAUSSIAN BEAMS

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.

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.

( ) 2, , 0z xx yyiA z x y A A A A+ + + =

Propagation is modeled by the NLS equation

Gaussian Super-Gaussian

COLLAPSE DYNAMICS OF SUPER GAUSSIAN BEAMS

SPATIO TEMPORAL SPHERE COLLAPSEPULSE SPLITTING IN TIME AND SPACE

( ) 2

2 2, , 0, 0z xx yy ttiA z x y A A A A Ab b+ + - + = <

Experimental setup

2

0 0,isA A e S A z

( ) 2, , 0z xx yyiA z x y A A A A+ + + =

High power – can neglect diffraction

Why?High power - early stage of collapse: Only

SPM

RaysPhase SH

•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.

Propagation of ultrashort laser pulses in a Kerr medium with anomalous dispersion is modeled by the following NLS equation

• Water cell • E=13.3 μ• Image area: 0.3mm X 0.3mm

Exact solution - depends on initial phase (SPM)

1.3 cm 2.0 cm

3.0 cm 4.3 cm

Geometrical optics - Rays perpendicular to phase level sets

Gaussian

Collapse with Townes profile

Super GaussianCollapse with ring profile

Theory•High powered super Gaussian

input beam•Formation of a ring structure•Ring profile is unstable•Breaks up into a ring of filaments

Excellent agreement between theory and experiments

Experiment Simulation

t0 t0+ρfil/2

4

0 15 rey -=Super Gaussian initial condition

24

0 15 / 2 rey -=Gaussian initial condition

• Power P≈38Pcr for both initial conditions

•Geometrical optics•Not due to

Fresnel diffraction

π