Math colloquium: Jerry Moloney, University of Arizona
Event Description:
Title: Ultrafast intense laser pulse propagation: Dispersion vs nonlinearity dominated physics.
Abstract: In this talk, I will briefly review the early development of the theory of ultrashort pulse (USP) filamentation. The Unidirectional Pulse Propagation equation (UPPE), a pseudo-spectral solver, will be introduced as a robust Maxwell-like full wave propagator that allows long distance propagation of arbitrary vectorial optical waveforms while resolving the underlying optical carrier wave. In limiting cases, propagating USPs, whether dispersion or nonlinearity dominated, can exhibit very different singular behaviors. In the former limit, the respective mathematical descriptions are typically the envelope NLSE-types which exhibit a blow-up singularity at a finite distance. Nonlinearity dominated interactions are best captured by the optical carrier resolved modified Kadomtsev-Petviashili (mKP)) equation, describing optical carrier shock-like singularities. Applications to be discussed will include both near-IR and long wave atmospheric propagation, multifilament generation seeded by a modulational instability, pulse splitting and X-wave generation, exotic Bessel and Airy beams, extended plasma string generation proposed for guiding high voltage discharges, RF and Microwave guiding and lightning deflection.
of Arizona. He is a former Director of the Arizona Center for Mathematical Sciences at
the University of Arizona. He is a Fellow of the Optical Society of America and was
awarded the Alexander von Humboldt Prize in Physics in 2005. He has published m
than 500 papers with more than 30,000 citations and has a current h-index of 91. He co-
authored the book Nonlinear Optics (CRC Press 1992, 2003) with Alan C Newell, edited
the book Nonlinear Optical Materials (The IMA Volumes Institute for Mathematics and
Its Applications, 1998) and co-edited with Andre Bandrauk and Emmanuel Lorin the
book Laser Filamentation: Mathematical Methods and Models (CRM Series in Mathematical
Physics). His research interests include extreme nonlinear optical interactions with
materials including numerical simulation of atmospheric ultrashort pulse propagation,
nonlinear partial differential equations, filamentation in gases and solids, semiconductor
physics applied to lasers and 2D materials and interactions at the nanoscale including plasmonic, dielectric lattices and
metasurfaces.
