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308 So l i d - S t at e La s e r s Ultrafast Solid-State Lasers 309

12.3.2 Aberrations
Misalignment of stretcher and compressor optics can have deleteri-
ous effects on ultrafast pulses. The main effects to watch for are
spherical aberration, chromatic aberration (when using lenses), ther-
mal distortion, and spatial chirp. One way to address spherical aber-
rations is to use a ray-tracing software package when designing a
stretcher. Chromatic aberrations can either be eliminated by removing
any lenses in the system or be greatly reduced by using F-numbers
(Focal length/Beam diameter) greater than ~20 for 40 nm of band-
width. Spatial chirp can be greatly reduced by making sure that (1) in
stretchers, the spread-out spectrum does not receive any tilt, and (2) in
compressors, the gratings, as well as their lines, are parallel face to face.
(For thermal distortions, see Sec. 12.4.) More on these and other aberra-
tions can be found in Muller et al. 20

12.3.3 Amplifier Schemes
The main goal of amplification is to bring low-energy pulses in the
nanojoule regime to high-energy pulses in the millijoule to joule regime
for high-intensity experiments. At these levels, with say 20-fs pulses,
intensities greater than 1 × 10 W/cm can be obtained, which is
2
19
extremely useful in high-field physics and materials processing. To
efficiently extract the stored energy from the amplifier, one must reach
the material’s saturation fluence. For a four-level laser, this is given by
hw
F sat = (12.7)
(
2 πσ w)
where h is Plank’s constant, and σ(w) is the stimulated emission cross
section as a function of frequency. In the case of Ti:sapphire, the satu-
ration fluence is ~1 J/cm , and working at 2F will typically give the
2
sat
best extraction efficiency. However, one must be careful, because
Yb:KGW (ytterbium-doped potassium gadolinium tungstate) has a
2
saturation fluence of ~10 J/cm , and 2F will exceed the material’s
sat
damage threshold, making energy extraction very difficult, though
not impossible.
Two types of amplifier schemes are used in amplifying ultrafast
pulses (at least where a storage medium is concerned): regenerative
amplification and multipass amplification. This section illustrates the
advantages and disadvantages of both schemes. Regardless of which
scheme is used, the effect of B integral, gain narrowing, and frequency
pulling prevent ultrafast amplifiers from producing pulses as short as
those that come from the oscillator. Gain narrowing is a result of a
finite gain bandwidth in the amplifying medium:

nt(, w ) n ( , w = 0 e ) σw N (12.8)
()∆
i