Time- and Position-Dependent Breakdown Volume Calculations to Explain Experimentally Observed Femtosecond Laser-Induced Plasma Properties

Focusing of femtosecond laser pulses in gases can produce different gas breakdown phenomena depending on the focusing conditions: from simple optical breakdown like laser "sparks" to a nonlinear optical breakdown like filamentation. The dynamics of such plasmas after the pulse exposure is dependent on the energy deposited by the laser in the breakdown volume. Using a time- and position-dependent breakdown model, we estimate the breakdown volume and show that the energy deposited by the laser in this breakdown volume determines the characteristics of laser-induced plasma in the post-pulse exposure regime. Experimentally we find that for different focal lengths there exists a threshold value of the energy density beyond which a transition from an ellipsoidal shape to a spherical shape can be observed, followed by a toroidal expansion of the produced plasma. When electron density and electron temperature are expressed as a function of the energy density, deviations from the parabolic dependence on irradiance are observed. They imply additional ionization by multiphoton ionization in the plasma volume that occurs when the peak power of the laser pulse is above the critical power for self-focusing in air. The relevance of this experimental and theoretical study is to prevent undesired self-focusing conditions during material processing, a step toward well-controlled laser-plasma etching without laser ablation.