Lecture Notes in Physics

10 H. Schwoerer
The second contribution to the temporal shape of the laser pulse in the focus
is noncompensated angular and temporal dispersion. The shorter the laser
pulses are, the broader is their spectral width and therefore the exact compensation
of all dispersion in space and time picked up by the pulse within the
laser system becomes more and more difficult. The uncompensated dispersion
of a sub 100 fs pulse typically reaches out to about 500 fs to 1 ps and reaches
a level of 10 −4 to 10 −3 of the maximum intensity. That is more than enough
to ionize any matter. But, because of the short duration until the main laser
pulse arrives, this plasma cannot evolve much and does not expand far into
the vacuum. Therefore, the interaction with the main pulse is only slightly
altered by the uncompensated dispersion.
However, the third contribution is of high importance for the fundamental
interaction mechanisms: Because of amplified spontaneous emission (ASE) in
the laser amplifiers, a long background surrounds the main laser pulse. It
starts several nanoseconds in advance of the main pulse and reaches relative
levels of 10 −6 to 10 −9 of the main pulse intensity, depending on the quality
of the pulse-cleaning technology implemented in the laser system. Since the
ionization threshold lies in the vicinity of 10 12 W/cm 2 , the prepulse due to
ASE is sufficient to produce a preplasma in front of the target prior to the
arrival of the main pulse. The preplasma expands with a typical thermal
velocity of about 1000 m/s into the vacuum. Therefore, the underdense plasma
can reach out tens or even hundreds of micrometers when the main laser pulse
impinges on it.
This extended preplasma has two effects on the interaction. The first is
that it affects the propagation of the light due to its density-dependent index
of refraction npl (see, e.g., [3]),
npl =
1 −
nee2 γm0ɛ0ω2 L
, (2.1)
where ne is the local free electron density, e the elementary charge, γ the
Lorentz factor, m0 the electron’s rest mass, ɛ0 the dielectric constant, and
ωL the laser frequency. From (2.1) follows that light can propagate only in a
plasma with a density ne smaller than the critical density ncr:
ne ncr, the light cannot propagate. For a laser wavelength
of 800 nm, which is the center wavelength of all tabletop high-intensity
lasers, the critical plasma density is ncr(800 nm) = 1.7 · 10 21 cm −3 ,whichis
about three orders below solid state density. Consequently, laser light penetrating
into the preplasma is absorbed and reflected if its density reaches the
critical density. Furthermore, we will see below that the laser pulse, as it propagates
through the underdense plasma, can modify the spatial distribution of
the plasma density in such a way that the pulse is focussed or defocused by
the plasma that has previously been generated by its leading wing.