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The rate equation model considers the interplay of linear absorption, photoionization, avalanche ionization and recombination, traces thermalization and temperature evolution during the laser pulse, and portrays the role of thermal ionization that becomes relevant for T > 3000 K. Modeling of free-electron generation includes recent insights on breakdown initiation in water via multiphoton excitation of valence band electrons into a solvated state at Eini = 6.6 eV followed by up-conversion into the conduction band level that is located at 9.5 eV.
The ability of tracing the temperature evolution enabled us to link the model of laser-induced plasma formation with a hydrodynamic model of plasma-induced pressure evolution and phase transitions that, in turn, traces bubble generation and dynamics as well as shock wave emission. This way, the amount of nonlinear energy deposition in transparent dielectrics and the resulting material modifications can be assessed as a function of incident laser energy. The unified model of plasma formation and bubble dynamics yields an excellent agreement with experimental results over the entire range of investigated pulse durations (femtosecond to nanosecond), wavelengths (UV to IR) and pulse energies.
Fitting data by a model considering breakdown initiation via a solvated electron state yielded an effective Drude electron collision time of 1 fs. Modeling predicts that the threshold continues to decrease up to 1.3 μm but levels out for longer wavelengths. It remains low in the mid IR because wavelength-independent tunneling ionization ensures a constant level of seed electrons for the ionization avalanche even though the influence of multiphoton ionization ceases.
The low breakdown threshold opens promising perspectives for ultrashort-pulsed laser surgery at wavelengths around 1.3 μm and 1.7 μm, which are attractive due to a favorable combination of low scattering and moderate water absorption. The wavelength dependence of the irradiance threshold together with tissue optical data was used to estimate the wavelength dependence of the energy threshold at various cutting depths. For focusing depths up to 200 μm, pulse energies required for surgery are smallest for < 800 nm. However, the energy minimum shifts to wavelengths around 1350 nm for z = 500 μm, and to the region around 1700 nm for z = 1 mm.
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