Nonlinear optics above the power threshold for relativistic self-focusing

Due to recent advances in laser technology, there is much current interest in the nonlinear optical interactions of high-intensity and ultrashort duration laser pulses with plasmas. In these interactions, electrons are accelerated by plasma waves, which are driven by the displacement of plasma electrons by the longitudinal ponderomotive force of the laser light. Due to their greater mass, the ions remain stationary during an electron oscillation period, providing an electrostatic restoring force. The oscillating electrons thus create regions of net positive and negative charge. This forms an electrostatic wakefield that propagates with the laser pulse at nearly the speed of light, which can trap and accelerate electrons. It is shown that the field gradient of a plasma wave exceeds that of an RF linac by four orders of magnitude and accelerates a picosecond bunch of electrons in a low-emittance beam. We also demonstrate electron acceleration over distances exceeding the Rayleigh range, which currently limits the acceleration length of laser-plasma accelerators. At high-laser power, the index of refraction of a Gaussian beam in a plasma varies significantly with the radius. Under these conditions, the plasma acts like a positive lens and focuses the beam (relativistic self-focusing). When this effect balances diffraction, relativistic self-guiding occurs, which is found to increase the laser propagation distance, decrease the electron beam divergence, and increase the energy of the accelerated electrons. Due to the enormous pressure exerted radially by the self-focused laser pulse on the plasma, a hollow density cavity is observed to form in the wake of the laser pulse along the laser axis. This density channel is shown to act as a waveguide, capable of guiding a second collinear intense laser pulse well beyond the Rayleigh range. These results are relevant not only to nonlinear optics and compact ultrahigh-gradient electron accelerators, but to astrophysics, the fas- -ignitor concept for inertial confinement thermonuclear fusion, advanced high-resolution medical X-ray sources, and ultrafast science.