VUV Spectroscopy of Atoms, Molecules and Surfaces

6 VUV light generation: possibilities and limitations
has been reached in LBO [20] as well as LiBO [21], both of which have
absorption edges at ∼160 nm. Moving towards shorter wavelengths means
switching to gases which are isotropic media and by symmetry considerations
can be shown to prohibit the generation of even-order harmonics [11]. The
most popular choises are the rare gases and metal vapours, the latter being
more difficult to handle experimentally but providing broad autoionizing,
i.e. doubly-excited, states appropriate for resonant enhancement [22]. Gases
and wavelengths for four-wave mixing are preferentially chosen such that the
frequency of either the driving- or generated light fields are closest possible
to a resonant (multi-photon) transition in the non-linear medium. In the
vicinity of such a transition the dispersion varies considerably, being negative
(positive) above (below) the atomic level, thus making it easier to fulfil the
phase-matching requirements. As an example, the 5p–5d transition of Xe
at 119.2 nm is often used to enhance the amount of 118 nm light generated
by frequency-tripling of 355 nm, with the phase-matching condition being
tuned by varying the Xe gas pressure (cf. chapter 3). It should be noted that
the phase-matching conditions in general are easier fulfilled by difference- as
opposed to sum-frequency mixing, because the negative dispersion required in
the latter case only can be obtained on the upper side of a resonant transition.
On the other hand, sum-frequency generation is possible down to ∼60 nm
while difference-frequency mixing becomes difficult below ∼110 nm [13, 19].
Typically, 10 9 –10 11 photons/pulse are generated [23] in a ∼10 −6 relative
bandwidth [24, 25] with the higher value obtained in the case of resonant
enhancement.
For wavelength generation effectively down to ∼160 nm and possibly
∼130 nm, the alternative technique of stimulated Stokes and anti-Stokes
Raman shifting may also be applied [26, 27]. Here, light is generated with a
frequency which is equal to that of the driving field shifted up (anti-Stokes)
or down (Stokes) by n times the frequency of a characteristic transition in
the applied medium. Typically, H2 with its relatively large vibrational ν =0
↔ ν = 1 transition frequency is employed. The anti-Stokes process assumes
a population in the ν = 1 level which is provided by the Stokes process.
The generation efficiency decreases rapidly with increasing order, with n =
2 being a typical choise for practical applications [28].
1.3 High-harmonic generation
Proceeding to intensities where the light field can no longer be considered a
perturbation to the Coulomb field exerted on an atomic electron, the perturbative
expansion of the polarization no longer converges [29]. This is usually
considered the strong-field regime and corresponds to intensities in the 10 13 –