Self-waveguiding of relativistic laser pulses in neutral gas channel

We demonstrate that an ultrashort high intensity laser pulse can propagate for hundreds of Rayleigh ranges in a prepared neutral hydrogen channel by generating its own plasma waveguide as it propagates; the front of the pulse generates a waveguide that confines the rest of the pulse. A wide range of suitable initial index structures will support this "self-waveguiding" process; the necessary feature is that the gas density on axis is a minimum. Here, we demonstrate self-waveguiding of pulses of at least $1.5\times10^{17} W/cm^2$ (normalized vector potential $a_0\sim0.3)$ over 10 cm, or $\sim100$ Rayleigh ranges, limited only by our laser energy and length of our gas jet. We predict and observe characteristic oscillations corresponding to mode-beating during self-waveguiding. The self-waveguiding pulse leaves in its wake a fully ionized low density plasma waveguide which can guide another pulse injected immediately following; we demonstrate optical guiding of such a follow-on probe pulse