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

## TL;DR

This paper introduces a delayed-rate equations model that accurately predicts femtosecond laser-induced breakdown in dielectrics by tracking plasma density and carrier energy, offering improved physical insight and computational efficiency.

## Contribution

The paper develops a simplified yet accurate delayed-rate equations model that matches complex multiple rate equations with fewer parameters, enhancing understanding and simulation of laser breakdown.

## Key findings

- Model reproduces predictions of multiple rate equations
- Limited free parameters determined by experimental data
- Enables large-scale 3D simulations of laser-induced breakdown

## Abstract

Experimental and theoretical studies of laser-induced breakdown in dielectrics provide conflicting conclusions about the possibility to trigger ionization avalanche on the sub-picosecond time scale and the relative importance of carrier-impact ionization over field ionization. On the one hand, current models based on single ionization-rate equations 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, models based on multiple rate equations that track the carriers kinetics rely on several free parameters, which limits the physical insight that we can gain from them. In this paper, we develop a model that overcomes these issues by tracking both the plasma density and carriers' mean kinetic energy as a function of time, forming a set of delayed rate equations that we use to match the laser-induced damage threshold of several dielectric materials. In particular, we show that this simplified model reproduces the predictions from the multiple rate equations, with a limited number of free parameters determined unambiguously by fitting experimental data. A side benefit of the delayed rate equations model is its computational efficiency, opening the possibility for large-scale, three-dimensional modelling of laser-induced breakdown of transparent media.