Ionization, avalanche/multiphoton

In the investigation of non-thermal damage to dielectrics, the Fokker-Planck equation is applied to describe the transient behaviors of electron densities, and to predict the damage threshold fluences for various laser pulse widths ranging from 10 femtoseconds to 10 picoseconds [13]. This model includes the effects of electron avalanche and multiphoton ionization on the generation of electrons. 

Figure 8 Influence of multiphoton and avalanche ionizations on electron number density at different pulse durations [13] for A = 1053 nm and k =10 TW/cm [13]...

The energy of a laser pulse is absorbed by the electrons of the material. The absorption mechanism is different for opaque and transparent samples. Linear absorption is the main contribution in opaque materials (e.g., metals) whereas absorption has to be realized by nonlinear processes in transparent materials (e.g., dielectrics). These nonlinear processes are avalanche and multiphoton ionization [20-25]. After electronic excitation, the energy is transferred to the lattice and heats it up to boiling and/or to vaporization temperature. Then, electrons and lattice are in thermal equilibrium. The transfer time of the electronic energy to the lattice (electron-phonon-relax-ation time) is of the order of picoseconds [26]. 

Recent measurements have shown that laser ablation (or negatively spoken damage) becomes more deterministic when femtosecond laser pulses are applied [22, 23, 40, 41]. This observation is due to the generation of conduction band (seed) electrons by means of multiphoton ionization (MPI). Based on this knowledge, a model for optical breakdown that takes into account avalanche ionization and MPI was developed [40], The temporal behavior of the free electron density in the conduction band n(t) can be described by a rate equation... 

The first term on the right side of Eq. 8 describes the avalanche ionization and the second one the multiphoton ionization. 7(f) is the time-dependent intensity of the laser and a the avalanche coefficient, denotes the /c-pho-ton absorption cross section and k is equal to the smallest number of photons needed to overcome the optical bandgap of the material. Equation 8 demonstrates that the bandgap of a dielectric has a major influence on its ablation efficiency. For an increasing bandgap, the relative weight of the avalanche process is greater than that of MPI. Yet, MPI provides a deterministic seed electron production for the subsequent avalanche process. Therefore, for shorter pulses, the statistical character of the ablation is reduced [42, 43],... 

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