Threshold of femtosecond laser-induced damage in transparent materials

The rate at which conduction-band electrons (CBE) absorb laser energy is calculated by both the quantum mechanical and the classical methods. Here fused silica irradiated with a 780-nm femtosecond-pulse laser is used as an example. It is found that the rate obtained by the quantum mechanical method is about one-third of that by the classical method, and it is much less than the direct-current limit. In the flux-doubling model, the avalanche rate in fused silica is 4 I  ps-1 obtained by the quantum mechanical method, while it is about 13.7 I  ps-1 by the classical method, where the laser intensity I is in units of TW cm-2. The differential equation of the evolution of CBE density is solved numerically, and it is found that the combination of CBE–hole recombination, CBE diffusion and initial CBE density (<1013 cm-3) is not important. The dependence of avalanche breakdown threshold on laser-pulse duration is presented. The threshold calculated by the quantum mechanical method agrees well with experimental results, while the threshold obtained by the classical method differs greatly from the experiments.