A semi-classical approach for solving the time-dependent Schr\"odinger equation in spatially inhomogeneous electromagnetic pulses

TL;DR

This paper introduces an iterative semi-classical complex trajectory method to solve the time-dependent Schrödinger equation in spatially inhomogeneous electromagnetic fields, validated through numerical comparisons and improved field reconstruction.

Contribution

The paper presents a novel semi-classical approach for inhomogeneous fields, enhancing accuracy over existing methods in solving the Schrödinger equation.

Findings

Validated against ab initio solutions in Coulomb and laser fields

Improved reconstruction of plasmonic infrared fields from photoemission spectra

Demonstrated better accuracy than strong-field approximation methods

Abstract

To solve the time-dependent Schr\"odinger equation in spatially inhomogeneous pulses of electromagnetic radiation, we propose an iterative semi-classical complex trajectory approach. In numerical applications, we validate this method against ab initio numerical solutions by scrutinizing (a) electronic states in combined Coulomb and spatially homogeneous laser fields and (b) streaked photoemission from hydrogen atoms and plasmonic gold nanospheres. In comparison with streaked photoemission calculations performed in strong-field approximation, we demonstrate the improved reconstruction of the spatially inhomogeneous induced plasmonic infrared field near a nanoparticle surface from streaked photoemission spectra.