Modelling of optical breakdown in dielectrics including thermal effects relevant for nanosecond pulses and sequences of ultra-short laser pulses

The role of morphology and coupling of gold nanoparticles in optical breakdown during picosecond pulse exposures

“…Although the model by Boulais et al [ 31 ] is complete and can be used for arbitrarily shaped objects and plasmon-coupled nanoparticles it does not include the thermal ionization of the aqueous medium. Thermal ionization plays an important role for short pulses (picoseconds and nanoseconds) and ultrashort (femtoseconds) pulse sequences [ 28 , 36 ]. The model also does not include the size corrected dielectric function of gold [ 3 ].…”

“…1 ). The plasma rate equation [ 28 ], based on the full Keldysh theory for multiphoton ionization [ 54 ], the tunneling effect, avalanche ionization, thermal ionization [ 28 , 36 ], diffusion, and recombination losses and photo-thermal emission (PTE) [ 30 ] of hot electrons from the gold surface, was solved to determine the dynamics of the free-electron plasma density in the vicinity of the nanoparticle. The parameters for plasma theory are those described by Linz et al [ 28 ] and Bulgakova et al [ 30 ].…”

“…The thermal ionization in water starts to play a significant role in the production of free electrons when the temperature in the focal volume of the laser is above 5000 K [ 28 , 36 ], and large free-electron densities are already achieved by multiphoton and cascade ionization. On the other hand, thermal ionization also plays a role during repeated sequences of ultrashort laser pulses, when the time delay between pulses is of the order of the thermalization time of the electron plasma energy [ 36 ]. Thermal ionization also partially depletes the density of bound electrons in the valence band and reduces the rate of multiphoton and impact ionization [ 28 ].…”

“…LIOB occurs when the optical breakdown threshold, which is in the range of about 10 11 –10 13 W/cm 2 , is surpassed in the focal region of the laser beam [ 34 – 35 ]. For nanosecond pulses [ 28 ] or ultrashort pulse sequences separated by times of the order of the free-electron energy thermalization time [ 36 ], LITB is a significant source of seed electrons, ρ seed , which is required to initiate the avalanche ionization [ 28 ], when the temperature of the medium increases above approx. 5000 K. LITB starts with linear absorption and thermal ionization of the aqueous medium and continues with non-linear avalanche ionization.…”

Wavelength dependence of nanosecond and femtosecond optical breakdown in water: Theoretical analysis

“…Heating occurs through collision losses of free electrons , and recombination and is counteracted by heat diffusion out of the focal volume. For sufficiently high temperatures, the electron energy distribution reaches across the band gap into the conduction band, and we consider electrons with E > E gap as thermally ionized [3]. As breakdown criterion, we used a critical electron density P er = 10 2 ' em" that corresponds for fs pulses to a temperature rise leading to bubble formation and for ns pulses to aT-rise causing plasma luminescence, as experimentally observed .…”