Section for Mathematical Physics
Section for Image Analysis
Abstract: The nonlinear Schrödinger equation (NLS)
describes approximately the dynamics of optical pulse envelopes in the
limit of many oscillations in the carrier wave. In ultra short optical
pulses of order 10 femtoseconds, the number of oscillations is so few that
the validity of the NLS equation is highly questionable. In this case it
is necessary to study the original vector Maxwell equations including nonlinearity
and polarization dynamics. So far investigations have shown that extending
the NLS equation using higher order dispersion and nonlinearities and comparing
to Maxwells equations describes well even ultra short pulses within the
slowly varying envelope approximation. However, in a number of cases also
the extended NLS equation cannot be used. As the magnitude of the dispersion
and nonlinearity depends on the wave number/frequency, waves with different
wave numbers obey different NLS equations. Accordingly, interaction among
ultra short pulses of different wave numbers can only be treated using
the original Maxwell's equations. Blow up observed in quintic NLS equations
may be arrested when investigated in the framework of these original equations.
Interference phenomena and propagation in optical crystals of ultra short
pulses is better modelled by employing the Maxwell's equations. The purpose
of this project is to go beyond the limit of the NLS equation and its extensions
in studies of ultra short nonlinear optical pulses by invoking the first
principle vector Maxwell equations coupled nonlinearily to the Lorenz equations
for the polarization dynamics.
Collaborators:
Funding:
STVF: 172 KKr
Start date: November 2000
End date: November 2001