# Exit momentum and instantaneous ionization rate of nonadiabatic tunneling ionization in elliptically polarized laser fields

## TL;DR

This paper derives analytical formulas for initial electron momentum and ionization rates during nonadiabatic tunneling in elliptically polarized lasers, revealing momentum offsets and their effects on ionization dynamics.

## Contribution

It introduces new analytical expressions for initial momentum and ionization rate in elliptically polarized fields, accounting for nonadiabatic effects and momentum offsets.

## Key findings

- Nonzero initial momentum offset at tunnel exit in elliptical fields.
- Momentum offsets relate to derivatives of the electric field.
- Ionization rate depends on laser phase and nonadiabatic effects.

## Abstract

Based on the strong-field approximation, we obtain analytical expressions for the initial momentum at the tunnel exit and instantaneous ionization rate of tunneling ionization in elliptically polarized laser fields with arbitrary ellipticity. The tunneling electron reveals a nonzero offset of the initial momentum at the tunnel exit in the elliptically polarized laser field. We find that the transverse and longitudinal components of this momentum offset with respect to the instantaneous field direction are directly related to the time derivatives of the instantaneous laser electric field along the angular and radial directions, respectively. We further show that the nonzero initial momentum at the tunnel exit has a significant influence on the laser phase dependence of the instantaneous ionization rate in the nonadiabatic tunneling regime.