Graduate School in Nonlinear Science
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
FEMTO SECOND PULSES IN THE MAXWELL-LORENTZ SYSTEM
by Mads Peter Sørensen
Informatics and Mathematical
Modelling (IMM)
Technical University of Denmark
Building 321
2800 Kgs. Lyngby, Denmark
MIDIT-seminar 505
Thursday, January 31, 2002, 15.00 h
at IMM, Bldg. 305, Room 018, DTU
Abstract:
The Maxwell equations coupled to a single
Lorentz oscillator and with instantaneous Kerr nonlinearity
are investigated. The
existence of soliton-type solutions in the Schrödinger
regime or light bullets containing few optical cycles together with
dark solitons are illustrated numerically. Envelope collapse regimes
of the Schrödinger equation are compared to the full system
and an arrest mechanism is clearly identified
when the spectral width of the initial pulse broadens beyond the
applicability of the asymptotic behavior. We show that beyond certain
threshold the carrier wave steepens into an infinite gradient
similarly to the canonical Majda-Rosales weakly dispersive system.
The weak dispersion in general cannot prevent the wave
breaking with instantaneous or delayed nonlinearities.
Lagrangian and Hamiltonian formulations of the equations are determined.
From Lie point symmetries admitted by the equations
four conservation laws are obtained. The symmetries are used to
obtain classical similarity solutions. In particular
we have found a remarkable kink shaped optical travelling wave solution.
Its stability has been assessed by numerical simulations. For
typical physical parameter values the kink width is of order 10th
of femtoseconds in strongly nonlinear optical polymers.