Ponderomotive self-focusing of a short laser pulse under a plasma density ramp

The ponderomotive self-focusing of a short laser pulse in an underdense plasma under a plasma density ramp is analyzed. The pulse may acquire a minimum spot size due to the ponderomotive self-focusing. Beyond the focus, the nonlinear refraction starts weakening, and the spot size of the laser pulse increases, resulting in an oscillatory self-focusing and defocusing behavior of the beam with the propagation distance. In order to minimize the defocusing, we introduce a localized upward plasma density ramp. Due to the upward plasma density ramp, the laser beam retains a minimum spot size. Self-focusing becomes stronger with a mild ripple as the propagation distance increases. The conditions for the ponderomotive self-focusing for suitable parameters of the laser beam and the plasma are determined. The plasma density ramp of the considered type may be observed in gas jet plasma experiments.