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Title: Role of the Coulomb singularity in high-order harmonic generation

Abstract

High-order harmonic generation (HHG) from a single hydrogen atom is studied analytically and numerically in the regime of small Keldysh parameter. The HHG spectra from different Coulomb-like model potentials, such as soft-core and/or one-dimensional (1D) potentials are compared to the three-dimensional (3D) Coulomb potential. It is shown, using analytic arguments, that the famous plateau in the HHG spectrum owes its existence to the Coulomb singularity, whereas soft-core potentials give spectra that fall off exponentially with increasing frequency. The idea is demonstrated numerically on a 3D soft-core potential that has the same long-range asymptotic behavior and ground-state energy as hydrogen. In addition, a number of widely used 1D Coulomb-like potentials are discussed. It is shown that in order that a 1D potential be a reasonable substitute for the 3D Coulomb potential, it must have a cusp singularity. A specific potential satisfying this criterion is proposed.

Authors:
;  [1];  [2]
  1. Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 USA (United States)
  2. ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 (United States)
Publication Date:
OSTI Identifier:
20786336
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063411; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; COULOMB FIELD; GROUND STATES; HARMONIC GENERATION; HYDROGEN; ONE-DIMENSIONAL CALCULATIONS; PHOTON-ATOM COLLISIONS; POTENTIAL ENERGY; SINGULARITY; SOFT-CORE POTENTIAL; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Gordon, Ariel, Kaertner, Franz X., and Santra, Robin. Role of the Coulomb singularity in high-order harmonic generation. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Gordon, Ariel, Kaertner, Franz X., & Santra, Robin. Role of the Coulomb singularity in high-order harmonic generation. United States. doi:10.1103/PHYSREVA.72.0.
Gordon, Ariel, Kaertner, Franz X., and Santra, Robin. Thu . "Role of the Coulomb singularity in high-order harmonic generation". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786336,
title = {Role of the Coulomb singularity in high-order harmonic generation},
author = {Gordon, Ariel and Kaertner, Franz X. and Santra, Robin},
abstractNote = {High-order harmonic generation (HHG) from a single hydrogen atom is studied analytically and numerically in the regime of small Keldysh parameter. The HHG spectra from different Coulomb-like model potentials, such as soft-core and/or one-dimensional (1D) potentials are compared to the three-dimensional (3D) Coulomb potential. It is shown, using analytic arguments, that the famous plateau in the HHG spectrum owes its existence to the Coulomb singularity, whereas soft-core potentials give spectra that fall off exponentially with increasing frequency. The idea is demonstrated numerically on a 3D soft-core potential that has the same long-range asymptotic behavior and ground-state energy as hydrogen. In addition, a number of widely used 1D Coulomb-like potentials are discussed. It is shown that in order that a 1D potential be a reasonable substitute for the 3D Coulomb potential, it must have a cusp singularity. A specific potential satisfying this criterion is proposed.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}