Multiphoton ionization and high-order harmonic generation of He, Ne, and Ar atoms in intense
pulsed laser fields: Self-interaction-free time-dependent density-functional theoretical approach
Xiao-Min Tong* and Shih-I Chu
Department of Chemistry, University of Kansas, and Kansas Center for Advanced Scientific Computing, Lawrence, Kansas 66045
Received 22 December 2000; published 12 June 2001
We present a detailed study of the multiphoton ionization and high-order harmonic generation HHG
processes of rare-gas atoms He, Ne, and Ar in intense pulsed laser fields by means of a self-interaction-free
time-dependent density-functional theory TDDFT recently developed. The time-dependent exchange-
correlation potential with proper short- and long- range potential is constructed by means of the time-dependent
optimized effective potential TDOEP method and the incorporation of an explicit self-interaction-correction
SIC term. The TDOEP-SIC equations are solved accurately and efficiently by the time-dependent generalized
pseudospectral technique. In this study, all the valence electrons are treated explicitly and nonperturbatively
and their partial contributions to the ionization and HHG are analyzed. The results reveal instructive and
qualitatively different behavior from each subshell orbital. Moreover, we found that the HHG yields from Ne
and Ar atoms are considerably larger than that of the He atom in strong fields. Three main factors are identified
for accounting the observed phenomena: a the binding energy of the subshell valence electron, b the
orientation of the valence electron orbital with respect to the electric-field polarization, and c the effect of
multiphoton resonant excitation. In particular, we found that the np
0
valence electrons in Ne and Ar with
lowest binding energies and electron orbital orientation parallel to the electric-field direction, make the domi-
nant contributions to both ionization and HHG processes in sufficiently strong fields.
DOI: 10.1103/PhysRevA.64.013417 PACS numbers: 42.50.Hz, 32.80.Wr, 32.80.Qk, 71.15.Mb
I. INTRODUCTION
The study of atomic and molecular multiphoton and high-
order nonlinear optical processes is a subject of much current
interest and significance in science and technology 1. In
particular, multiple high-order harmonic generation HHG
is one of the most rapidly developing topics in strong-field
atomic and molecular physics. The generation of harmonics
of orders in excess of 300 from rare-gas atoms has been
recently demonstrated by experiments 2–4 using laser
pulses shorter than 20 fs and peak intensity more than
10
14
W/cm
2
. The shortest wavelength generated by the
HHG mechanism to date is about 2.7 nm 2–4, well into the
water window regime. To describe such intense-field pro-
cesses using an ab initio wave-function approach, it is nec-
essary to solve the time-dependent Schro
¨
dinger equations of
many-electron systems, which is well beyond the capability
of current supercomputer technology. One of the successful
approximations being used is the single-active-electron
SAE model with frozen core 5,6. The SAE model has
been applied to the study of HHG of rare-gas atoms in lin-
early polarized LP laser fields involving two spatial di-
mensions, providing useful insights regarding atomic multi-
photon dynamics. However, within the SAE approach, the
electron correlation and the contribution and the role of the
individual spin orbital, particularly those in the valence shell,
cannot be explicitly treated. Indeed the dynamical role of the
individual valence electron to the HHG and multiphoton ion-
ization processes in strong fields has not been thoroughly
studied before. Such a study can provide insights regarding
the detailed quantum dynamics and HHG mechanisms, as
well as the optimal control of strong-field processes. In this
paper we present a quantum study of multiphoton ionization
and HHG processes of rare-gas atoms He, Ne, and Ar by
means of the self-interaction-free time-dependent density-
functional theory TDDFT recently developed 7,8.
It is known that the conventional steady-state DFT and
TDDFT using explicit exchange-correlation ( xc ) energy
functionals, such as those from the local spin-density ap-
proximation LSDA9 and generalized gradient approxi-
mation GGA10–12, contain spurious self-interaction en-
ergy and the xc potentials do not have the proper long-range
Coulombic tail -1/r . As a result, while the total electron
energies of the ground states of atoms and molecules are
rather accurate, the excited and resonance states, as well as
the ionization potentials from the highest-occupied orbital
energies are less satisfactory. For example, the atomic ion-
ization potentials calculated from the conventional DFT ap-
proach using the LSDA or GGA energy functionals are typi-
cally 30 to 50 % too low. Recently, we have presented a
self-interaction-free DFT 13 based on the extension of the
KLI’s Krieger-Li-Iafrate original treatment 14 of the op-
timized effective potential OEP formalism 15,16 along
with the implementation of an explicit self-interaction-
correction SIC term 13,17. Such an OEP/KLI-SIC
method uses only orbital-independent single-particle local
potentials that are self-interaction free and have the proper
short- and long-range ( -1/r ) behavior and is capable of pro-
viding reasonably high accuracy for the excited states and
ionization potentials well within a few percent of the experi-
mental values across the periodic table 18. Further it is
*Present address: ‘‘Cold Trapped Ions’’ Project, ICORP, JST,
Axis Chofu Bdg 3F, 1-40-2 Fuda, Chofu, Tokyo 182-0024 Japan.
Email address: tong@hci.jst.go.jp
PHYSICAL REVIEW A, VOLUME 64, 013417
1050-2947/2001/641/0134178/$20.00 ©2001 The American Physical Society 64 013417-1