Abstract
The combined effects of tunnel ionization of gases on laser frequency upshift, defocusing, and ring formation are considered self-consistently. A high-intensity short pulse laser causes rapid tunnel ionization of a gas. The increasing plasma density leads to a decreasing refractive index, modulating the phase of the laser as it propagates and causing frequency upshift and supercontinuum generation. For laser intensity profile peaking on axis, the tunnel ionization produces a minimum of refractive index on axis, thus defocusing the laser. The defocusing reduces the ionization rate and frequency upshift. As the laser propagates over a Rayleigh length its trailing portion develops a ring shape distribution due to stronger defocusing of rays on axis than the off-axis rays, as seen in a recent experiment.
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