VUV Spectroscopy of Atoms, Molecules and Surfaces

8 VUV light generation: possibilities and limitations
Figure 1.2: A schematic of the tunneling picture, or two-step model, used to describe the
mechanism of high-harmonic generation for a single atom. From [34].
multi-photon ionization with the absorption of more photons than required
for ionization, giving rise to peaks in the photoelectron kinetic-energy spectrum
separated by one photon energy [35]. In the two-step model the electric
light field is assumed to vary sufficiently slowly that it makes sence to consider
an electron tunneling through the barrier created in the atomic Coulomb potential
by the field. Since the Coulomb potential is most strongly bent at the
field extrema, the ionization probability is strongly peaked in time. The possibility
exists that an electron released this way is pushed back towards the
residual ion, following the sign change of the electric field vector, as shown
in figure 1.2. Upon re-scattering the electron may acquire additional kinetic
energy, recognized as a plateau in the ATI spectrum extending from ∼3Up to
∼10Up [36, 37, 38] where Up is the average quiver energy of the free electron
oscillating in the field. The electron may also recombine with the ion, thereby
releasing a photon with a frequency which is an odd multiple of the laser frequency
(HHG). The maximum instantaneous kinetic energy of a returning
electron turns out to be equal to 3.2Up, and adding the ionization potential
Ip—the energy released upon recombinement to the ground state—yields the
cut-off energy, Ecut=Ip +3.2Up, observed in high-harmonic radiation spectra
[32].
The average quiver energy of a free electron with charge −e and mass m
depends on the frequency ω and peak intensity I of the light field through
the relation Up = e 2 I/4mω 2 =9.33 × 10 −14 I[W/cm 2 ]λ[µm] 2 and is often
called the ponderomotive energy. This originates from the fact that the timeaverage
of the Lorentz force, also called the ponderomotive force, in the case
of a light field with slowly varying electric- and magnetic field amplitudes,