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To solve the time-dependent Schr\"odinger equation in spatially inhomogeneouspulses of electromagnetic radiation, we propose an iterative semi-classicalcomplex trajectory approach. In numerical applications, we validate this methodagainst ab initio numerical solutions by scrutinizing (a) electronic states incombined Coulomb and spatially homogeneous laser fields and (b) streakedphotoemission from hydrogen atoms and plasmonic gold nanospheres. In comparisonwith streaked photoemission calculations performed in strong-fieldapproximation, we demonstrate the improved reconstruction of the spatiallyinhomogeneous induced plasmonic infrared field near a nanoparticle surface fromstreaked photoemission spectra.

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