  The upcoming $10-100$ petawatt laser facilities may deliver laser pulses with
unprecedented intensity of $10^{22}-10^{25}\rm~W cm^{-2}$, which can trigger
various nonlinear quantum electrodynamic processes in plasma. For effective
laser plasma interactions at such high intensity levels, guided laser
propagation is critical. However, this becomes impossible via usual plasma
electron response to laser fields due to electron cavitation by the laser
ponderomotive force. Here, we find that ion response to the laser fields may
effectively guide laser propagation at such high intensity levels. The
corresponding conditions of the required ion density distribution and laser
power are presented and verified by three-dimensional particle-in-cell
simulations. Our theory shall serve as a guide for future experimental design
involving ultrahigh intensity lasers.
