Scheduled for Oct. 22 rather than the usual Wednesday.
Gene Wayne, Boston University
Title: "Propagation of ultra-short optical pulses in nonlinear media"
Abstract: I will describe the derivation of a new model equation for the
propagation of very short pulses in nonlinear optics. The nonlinear
Schroedinger equation has been used very successfully to model soliton
propagation in nonlinear optics, but it is based on the assumption that
the pulse length is much longer than the carrier wavelength. Current
experiments on nonlinear pulses violate this assumption so new models
are needed. In addition to the formal derivation of the new model equation
I will discuss some mathematical aspects of the model (its well posedness
and absence of smooth traveling pulse solutions), the numerical comparison
of the new model both with the original nonlinear equation and with the
standard approximation given by the nonlinear Schroedinger equation, and
finally some first steps toward proving that the new model equation gives
an accurate approximation to Maxwell's equation in the short pulse regime.