  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.
