Dynamical rate equation model for femtosecond laser-induced breakdown in dielectrics

Abstract

Experimental and theoretical studies of laser-induced breakdown in dielectrics provide conflicting conclusions about the possibility to trigger ionization avalanche on the subpicosecond time scale and the relative importance of carrier-impact ionization over field ionization. On the one hand, current models based on a single ionizationrate equation do not account for the gradual heating of the charge carriers, which, for short laser pulses, might not be sufficient to start an avalanche. On the other hand, kinetic models based on microscopic collision probabilities have led to variable outcomes that do not necessarily match experimental observations as a whole. In this paper, we present a rate-equation model that accounts for the avalanche process phenomenologically by using an auxiliary differential equation to track the gradual heating of the charge carriers and define the collisional impact rate dynamically. The computational simplicity of this dynamical rate-equation model offers the flexibility to extract effective values from experimental data. This is demonstrated by matching the experimental scaling trends for the laser-induced damage threshold of several dielectric materials for pulse durations ranging from a few fs to a few ps. Through numerical analysis, we show that the proposed model gives results comparable to those obtained with multiple rate equations and identify potential advantages for the development of large-scale, three-dimensional electromagnetic methods for the modeling of laser-induced breakdown in transparent media.

Ion imaging of spatially inhomogeneous nanoplasmas in NaCl particles

“…In step (ii), we used the obtained time-dependent light field inside the particle to calculate the electron density. We used the following rate equation to describe time-dependent quasifree electron density n e (t ) 6,14,16,45,46 where n 0 is the initial electron density (assuming only single ionization of each NaCl unit, n 0 = 1.6 × 10 22 cm −3 ), n a is the time-dependent density of the remaining bound electrons (n a = n 0 − n e ) and ν rec is the recombination rate. Because typical recombination times are longer than pulse durations used in this work, we neglected this contribution (ν rec = 0).…”

Modeling of inhomogeneous heating behavior in ultrafast laser interaction with dielectric–dielectric nanocomposite with band gap contrast

“…For alumina, the lifetime of the conduction band electrons is in the order of magnitude of 100 ps [23], which is much longer than the pulse duration of ultrafast lasers. Thus, this term is commonly omitted for alumina in literature [23][24][25]. For materials with a small elastic constant, such as fused silica and alkali halides, the formation of selftrapped excitons is possible [26].…”

“…Both 𝑚𝑚 𝐶𝐶𝐶𝐶 and 𝑚𝑚 𝑉𝑉𝐶𝐶 are assumed to be equal to the free electron mass 𝑚𝑚 𝑒𝑒 , therefore, 𝑚𝑚 = 𝑚𝑚 𝑒𝑒 2 ⁄ [28]. 𝛥𝛥 is the band gap of the material, 𝑒𝑒 is the electron charge, 𝑒𝑒 is the amplitude of the electric field with 𝑒𝑒 = �2𝐼𝐼 (𝑐𝑐𝜖𝜖 0 𝑛𝑛) ⁄ [24], where, 𝐼𝐼 is the laser intensity, 𝑐𝑐 is the speed of light in vacuum, 𝑛𝑛 is the real part of the refractive index of the material.…”

Delayed-rate equations model for femtosecond laser-induced breakdown in dielectrics

“…Three Appendices gather some of the technical aspects of the model and of its implementation. All calculations are performed using a Python package that we made available online [18].…”