J. Phys. B: At. Mol. Opt. Phys. 32 (1999) 5593–5603. Printed in the UK PII: S0953-4075(99)02799-6
Multiple high-order harmonic generation in the presence of
intense laser and static magnetic fields
X M Tong† and S I Chu
Department of Chemistry, University of Kansas, Lawrence, KS 66045, USA
and
Kansas Center for Advanced Scientific Computing, Lawrence, KS 66045, USA
Received 19 March 1999, in final form 21 October 1999
Abstract. We perform a nonperturbative study of the effect of static magnetic fields on the
multiple high-order harmonic generation (HHG) processes of atomic H in intense pulsed laser fields.
The time-dependent Schr ¨ odinger equation in three spatial dimensions can be solved accurately and
efficiently by means of the recently developed time-dependent generalized pseudospectral method
(Tong X M and Chu S I 1997 Chem. Phys. 217 119). We found that the presence of a static magnetic
field perpendicular to the laser field polarization direction can introduce a second HHG plateau,
allowing significant extension of the cut-off. The high harmonics in the second plateau reach a
maximum enhancement when the cyclotron frequency of the electron is about equal to one half of
the laser frequency. Through a detailed time-frequency wavelet analysis of the HHG spectra, we
have identified a ‘synchrotron radiation’-like new mechanism responsible for the production of the
second plateau.
1. Introduction
Since the early observation of the phenomenon of multiple high-order harmonic generation
(HHG) in rare gas atoms by intense laser fields, there has been much interest in the study of the
nature of this fundamental laser–atom process in the non-perturbative regime, as well as in the
methods for the enhancement of the HHG [1, 2]. Recently the generation of harmonics well
above 100 has been demonstrated by several experiments using high-intensity short-pulse laser
fields [3,4]. The HHG holds promise for the generation of compact coherent light sources in the
x-ray regime in the future. As such, further theoretical study of the mechanisms and coherent
control of the HHG processes is desirable. In this paper, we show that the HHG plateau can
be significantly extended by the addition of a strong static magnetic field perpendicular to the
laser field polarization direction. We also identify the main mechanisms responsible for the
production of the extended plateau.
In the presence of intense laser fields, the HHG spectrum is generally characterized by
the initial decline of the intensity of the lower harmonics, followed by a plateau of many
harmonics of similar intensity and then a sharp cut-off [1, 2]. The HHG may be produced
by either a tunnelling or multiphoton mechanism or a combination of both. A qualitative
indicator of the nature of the process can be obtained by examining the value of the Keldysh
parameter [5], γ = (I
p
/(2U
p
))
1/2
, where U
p
= I/(4ω
2
0
) is the pondermotive energy, I the
laser intensity, ω
0
the laser frequency and I
p
the field-free ionization potential of the atom.
† Present address: Cold trapped ions, JST Int’l Project, Axis Chofu 3F, 1-40-2 Fuda Chofu, Tokyo 182-0024, Japan.
0953-4075/99/235593+11$30.00 © 1999 IOP Publishing Ltd 5593