The imaginary part of the high-harmonic cutoff

Abstract

High-harmonic generation the emission of high-frequency radiation by the ionization and subsequent recombination of an atomic electron driven by a strong laser eld is widely understood using a quasiclassical trajectory formalism, derived from a saddle-point approximation, where each saddle corresponds to a complex-valued trajectory whose recombination contributes to the harmonic emission. However, the classi cation of these saddle points into individual quantum orbits remains a high-friction part of the formalism. Here we present a scheme to classify these trajectories, based on a natural identi cation of the (complex) time that corresponds to the harmonic cuto . This identi cation also provides a natural complex value for the cuto energy, whose imaginary part controls the strength of quantum-path interference between the quantum orbits that meet at the cuto . Our construction gives an e cient method to evaluate the location and brightness of the cuto for a wide class of driver waveforms by solving a single saddle-point equation. It also allows us to explore the intricate topologies of the Riemann surfaces formed by the quantum orbits induced by nontrivial waveforms.Peer ReviewedPostprint (published version

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