The propagation of short-pulse lasers through underdense plasmas at ul
tra-high intensities (I greater than or equal to 10(19) W/cm) is exami
ned. The pulse evolution is found to be significantly different than i
t is for moderate intensities. The pulse breakup is dominated by leadi
ng edge erosion and plasma wave wake formation rather than from Raman
forward scattering type instabilities. A differential equation which d
escribes local pump depletion is derived and used to analyze the forma
tion and evolution of the erosion. Pulse erosion is demonstrated with
one dimensional particle in cell (PIC) simulations. In addition, two d
imensional simulations are presented which show pulse erosion along wi
th other effects such as channeling and diffraction. Possible applicat
ions for plasma based accelerators and light sources are discussed. (C
) 1996 American Institute of Physics.