Abstract
Optical breakdown by ultrashort laser pulses in dielectrics presents an efficient method to deposit laser energy into materials that otherwise exhibit minimal absorption at low laser intensities. During optical breakdown, a high density of free electrons is formed in the material, which dominates energy absorption, and, in turn, the material removal rate during ultrafast laser-material processing. Classical models assume spatially uniform electron population and constant laser intensity in the focal region, which results in a time-dependent expressions only, i.e., the rate equations, to predict electron evolution induced by nanosecond and picosecond pulses. For femtosecond pulses, however, the small spatial extent of the pulse requires that the pulse propagation be considered, which results in inhomogeneous plasma and localized electron formation during optical breakdown. In this work, a femtosecond breakdown model is combined with the classical rate equations to determine both time- and position-dependent electron density during femtosecond optical breakdown in water. The model exhibits good agreement when compared with experimental results. For other transparent or moderately absorbing dielectric media, the model also shows promise for determining the time- and position-dependent electron evolution induced by ultrashort laser pulses. Another interesting result is that the maximum electron density formed during femtosecond-laser-induced optical breakdown can exceed the conventional limit imposed by the plasma frequency.
