Collapse dynamics of super Gaussian beams

1
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
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
p
Gaussian initial condition

• Power P38Pcr for both initial conditions

Why? High power - early stage of collapse Only
SPM
Gaussian
Super-Gaussian
High power can neglect diffraction

• Geometrical optics
• Not due to Fresnel diffraction

Exact solution - depends on initial phase (SPM)
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
• Excellent agreement between theory and
  experiments

Experiment
Simulation
1.3 cm
2.0 cm
Experimental setup

• Water cell
• E13.3 µ
• Image area 0.3mm X 0.3mm

3.0 cm
4.3 cm
SPATIO TEMPORAL SPHERE COLLAPSE PULSE SPLITTING
IN TIME AND SPACE
t0
t0?fil/2

• 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