The newly emerging field of Extreme Nonlinear Optics is pushing pulsed laser technology to levels never imagined just a decade ago. Record peak intensities of 10 22 Watts cm 2 have been demonstrated in the laboratory (10 27 Watts cm 2is enough to break down the vacuum and create an electron/positron pair!). In parallel, ultrashort pulse durations have recently been pushed into the attosecond (10 -18 of a second!) regime. More modest femtosecond duration pulses (10 -18 of a second) with peak intensities reaching 10 14 Watts cm 2, are capable of breaking down the main molecular constituents of air (i.e N 2 and O 2) forming critically self-focused light strings that appear to propagate anomalously long distances in the atmosphere. These leave electron-ion plasma channels in their wake that can potentially act as lightning rods and the plasma channels themselves emit burst of THz radiation.

he focus of this talk will be on describing ultrashort pulse propagation models that will allow us to access current and future extreme intensity and ultrashort time interactions with materials. From these models we can seamlessly derive the Nonlinear Schrödinger equation (NLS) and the so-called Nonlinear Envelope (NEE) model of Brabec and Krausz. We will also see that the critical collapse singularity of the 2D NLS equation plays a central role in initiating many of the experimentally observed phenomena. A dramatic manifestation of critical collapse (self-focusing) is the generation of a white light supercontinuum spectrum that spans the entire ultraviolet through visible to far-infrared spectral region. We will see that the generation of this spectrum can be ascribed to a classical 3-wave interaction and its shape is dependent on the dispersion properties of the interacting medium. When a femtosecond duration pulse critically self-focuses in a water cell, the shape of the latter’s spectrum will depend on whether the pulse central wavelength is in the normal (X-Wave) or anomalous (O-Wave) dispersion region of water.