Propagation into a homogeneous plasma of a laser beam at irradiances higher than 1/500 of the relativistic threshold can result in self-focusing due to the highly sensitive relativistic dependence of the optical constants on laser irradiance. Electron densities slightly less than the relativistic-cutoff densities are required. Simultaneously with the self-focusing, it is also possible to achieve a dielectric increase (swelling) of laser energy density in the plasma that could reach 1/3 of its maximum value. In prepulsed plasmas, generated by Nd-glass-laser pulses of 3 × 10<sup>16</sup> W/cm<sup>2</sup>, relativistic diffraction-limited self-focusing can generate relativistic electron-oscillation energies and hence pair production.
Heinrich Hora, "Theory of relativistic self-focusing of laser radiation in plasmas," J. Opt. Soc. Am. 65, 882-886 (1975)