A filament forms through a balance of self-focusing (Kerr effect) and plasma self-defocusing. The heat generated as the electron-ion recombine produces a cylindrical shock wave behind which a low-density channel is formed. High-energy UV filaments are used to study the shock wave by shadowgraphy. The shock is seen to start supersonic, before transitioning after microseconds to a constant velocity acoustic wave. Computational models of the gas-dynamics evolution are presented that agree with a well known empirical formula for shockwave velocity, as well as with experimental observations. We determine the profile of induced changes to the refractive index of air due to these thermal effects. We then simulate a vortex filament creating a parabolic index of refraction that can serve as a waveguide for successive filaments.
The challenge of guiding or deflecting a laser beam in a disturbed medium involves careful
consideration of various nonlinear interactions of light with air and their transient response. A
light filament provides a high intensity region in space that maintain its shape for propagation
lengths longer than the Rayleigh range. The possibility to use this light channel for coupling
optical, teraherz and radio frequency had been spurring researches in this field.
We present the contribution of transient nonlinear response of the medium on light propagation.
The nonlinear interaction of ultrashort pulses with air leaves a spatial distribution of ionized medium
that evolves into an equilibrium plasma. The light pulse has left the medium it ionized before the
plasma has reached equilibrium. Therefore, the reaction of the medium onto the filament involves
a transient evolution of the ensemble of ions and electrons that follow deterministic trajectories
under the influence of the light field. Other nonlinear interactions such as molecular alignment
also have a time dependent response. The relative influence of the plasma and molecular motion
is modified by focusing conditions. The standard focusing of light into air combines the nonlinear
Kerr focusing with the desired linear focusing of the optics. A focusing through a sharp pressure
gradient made by an aerodynamic window enhances the pointing stability of the laser beam. The
effect of transient response of the medium driven by nonlinear interaction of ultrashort pulse on
the guided beam will be discussed.
Various models of filamentation in air are presented and the remaining theoretical challenges are pointed out. Means to extend the range of filaments are reviewed and proposed. Filaments offer promise of guiding electrical discharges over large gaps. Experiments of UV filament induced discharge are presented.
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