The imaginary part of the high-harmonic cutoff

Emilio Pisanty, Marcelo F Ciappina, Maciej Lewenstein

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11 Scopus citations


High-harmonic generation—the emission of high-frequency radiation by the ionization and subsequent recombination of an atomic electron driven by a strong laser field—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 classification 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 identification of the (complex) time that corresponds to the harmonic cutoff. This identification also provides a natural complex value for the cutoff energy, whose imaginary part controls the strength of quantum-path interference between the quantum orbits that meet at the cutoff. Our construction gives an efficient method to evaluate the location and brightness of the cutoff 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.
Original languageEnglish
JournalJournal of Physics: Photonics
StatePublished - 27 Jul 2020
Externally publishedYes


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