When gases are irradiated by laser fields of intensity greater
than 10^13 Watts/cm^2, one observes light emission at frequencies that are
multiples of the laser frequency (the harmonics). Under certain
conditions, harmonics in excess of 100th order may be observed, which
is radiation in the extreme ultraviolet (EUV) or soft x-ray region
of the spectrum. When such
high harmonics are produced, they tend to be roughly as intense as the
third or fifth harmonic (e.g. as shown in the figure below). At present,
high harmonic generation provides the brightest known source of EUV
radiation, and may soon become a practical and economical for routine
laboratory use.
The mechanism of high harmonic generation is still not understood in detail.
It involves the cooperative response of the atomic medium to radiation, at
a high order of nonlinearity. The response of individual atoms to the
driving field is a key aspect of the generation process. We are engaged
in computations of this response by numerical solution of the time dependent
Schroedinger equation.
Harmonic radiation must be generated by atomic electrons in the vicinity
of the nucleus, since free electrons only oscillate at the driving
laser frequency. However, harmonic radiation is only observed under
conditions in which substantial atomic ionization also occurs. We are
therefore trying to understand how to "engineer" the radiation field
to optimize harmonic generation. One parameter available for this purpose
is the polarization of the radiation.
The figure show the harmonic spectrum of a model atom driven by
elliptically polarized radiation. The polarization of the driving
field is indicated in the upper right-hand corner; the polarization
ellipses of the harmonics are indicated, and the harmonic intensities
are given by the positions of the centers of the ellipses (on a
logarithmic scale). The complex dependence of polarization upon
harmonic order is similar to what is observed in recent experiments,
and in more extensive calculations we are currnetly performing on
the three-dimensional hydrogen atom.
