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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