Nonlinear relativistic optics in the single-cycle, single-wavelength regime with kilohertz repetition rate

Summary form only given. Laser intensity in the relativistic regime, i.e. > 10/sup 18/ W/cm/sup 2/ for near-IR light, has opened new frontiers in physics. At this intensity, electrons acquire quiver energy greater than, 0.5 MeV, corresponding to the mass-energy of the electron. Their relativistic behavior is dominated by a mass increase and a large ponderomotive force (v /spl times/ B) where v is the quiver velocity of the electrons and B the light magnetic field. The laser-matter interaction in this regime is characterized by the generation of high-energy photons (x-rays and /spl gamma/-rays) and energetic electrons and ion. The latter are accelerated to tens of MeVs by the large forces associated with the v /spl times/ B term. Recently, we have shown that single millijoule pulses in the 10-fs regime (single cycle), focused to 1-/spl mu/m (single wavelength), can produce intensities greater than 10/sup 19/ W/cm/sup 2/ at kilohertz repetition rates. Because of their very short Rayleigh range (/spl sim/1 /spl mu/m) one might think that these pulses would have only limited applications. They would not be useful in electron acceleration, where longer interaction distances are necessary. If the laser numerical aperture (NA) is matched to the NA of a relativistic waveguide (determined by the laser power and the plasma frequency), single-mode propagation of the relativistic pulse over many Rayleigh ranges can be obtained, as in conventional waveguide optics. This is demonstrated by a 2D PIC simulation of laser pulse matching with a plasma slab.