Comparison between Jacobi-Anger and saddle point methods to treat Above-threshold ionization

TL;DR

This paper compares the Jacobi-Anger and saddle point methods for modeling strong-field ionization, analyzing their accuracy, advantages, and applicability in interpreting photoelectron spectra and momentum distributions under various conditions.

Contribution

It provides a detailed comparison of two analytical approaches within the strong-field approximation, establishing their validity and practical use cases for modeling above-threshold ionization.

Findings

Dipole approximation accurately captures interference structures.

Non-dipole effects cause significant momentum shifts.

Jacobi-Anger expansion offers complete spectral decomposition.

Abstract

We present a detailed comparison of theoretical approaches for modeling strong-field ionization by few-cycle laser pulses. The dipole approximation is shown to accurately capture interference structures in photoelectron spectra, while non-dipole effects introduce significant momentum shifts along the propagation direction. Two complementary analytical methods are used: the Jacobi-Anger expansion provides complete spectral decomposition of transition amplitudes, whereas the saddle-point method efficiently identifies dominant ionization pathways. Through this comparative study within the strong-field approximation framework, we establish validity conditions and practical advantages for each approach. Our results provide guidelines for selecting theoretical methods for advancing the interpretation of strong-field processes. These findings provide a roadmap for interpreting strong-field ionization spectra and momentum distributions, highlighting where non-dipole effects and method choice critically alter predictions.