Field ionization in short and extremely intense laser pulses

TL;DR

This paper investigates field ionization under extremely intense, short laser pulses using analytical and numerical methods, proposing new approximations and formulas applicable to simulations of laser-matter interactions.

Contribution

It introduces two novel approximations for solving the time-dependent Schrödinger equation and derives a simple ionization rate formula for the barrier-suppression regime.

Findings

Derived ionization rate in strong fields

Validated approximations with numerical simulations

Proposed a practical formula for simulations

Abstract

Modern laser systems are able to generate short and intense laser pulses ionizing matter in the poorly explored barrier-suppression regime. Field ionization in this regime is studied analytically and numerically. For analytical studies, both the classical and the quantum approaches are used. Two approximations to solve the time-dependent Schr\"odinger equation are proposed: the free electron approximation, in which the atomic potential is neglected, and the motionless approximation, in which only the external field term is considered. In the motionless approximation, the ionization rate in extremely strong fields is derived. The approximations are applied to several model potentials and are verified using numeric simulations of the Schr\"odinger equation. A simple formula of the ionization rate both for the tunnel and the barrier-suppression regimes is proposed. The formula can be used, for example, in particle-in-cell codes for simulations of the interaction of extremely intense laser fields with matter.