Modelocking
A-7
ual oscillations of the electric field and results in a “red-shifted” leading
edge. Conversely, the trailing edge of the pulse is “blue-shifted.” SPM will,
thus, broaden the spectrum of the pulse and provide a positive chirp.
In order to achieve near transform-limited output pulses, it is necessary to
compensate for the pulse spreading caused by positive GVD and SPM. In
the Tsunami, this is accomplished with prism pairs in the femtosecond
regime (which provide negative GVD linear over a large bandwidth) and
with a Gires-Tournois interferometer (
GTI) in the picosecond regime
(which provides larger net negative
GVD, but linear over a narrow band-
width).
GVD Compensation
The materials in the Tsunami contribute positive GVD and, in combination
with SPM in the Ti:sapphire rod, induce a positive chirp on the pulse. Con-
sequently, the circulating pulse continues to broaden as it propagates
through the cavity unless negative GVD is present to balance these effects.
As discussed earlier, a material exhibits GVD when the second derivative of
its refraction index, with respect to wavelength (d
2
n/d
λ
2
), is non-zero. This
is a special case that is only valid when all wavelengths follow the same
path through a material. This can be extended to any optical system having
a wavelength dependent path length (P). GVD is then governed by the sec-
ond derivative of the optical path with respect to wavelength (d
2
P/d
λ
2
).
For this reason, a prism pair can be used to produce negative GVD. This is
generally the preferred intracavity compensation technique for ultrashort
pulse lasers because (a) losses can be minimized by using the prisms at
Brewster’s angle, and (b) the negative GVD is nearly linear over a large
bandwidth. Ideally, for stable short-pulse formation, the round trip time in
the cavity must be frequency independent, i.e., Tg(
ω
) =
d
φ
/d
ω
= constant,
where Tg(
ω
) is the group delay time,
φ
is the phase change, and
ω
is the fre-
quency. In reality, dispersion is not purely linear, and higher order disper-
sion terms become significant for shorter output pulse widths (larger
bandwidths).
In the fs Tsunami laser, a four-prism sequence configuration is used to pro-
vide negative
GVD (Figure A-6).
The net intracavity GVD can be changed by translating prisms Pr
2
and Pr
3
perpendicular to their bases. This is achieved using a single micrometer
adjustment. By translating Pr
2
and Pr
3
further into the intracavity beam,
more optical material is inserted into the cavity and the net intracavity
GVD
becomes less negative.
The different spectral components of the pulse are spatially spread between
prisms Pr
2
and Pr
3
. This allows wavelength selection to be conveniently
accomplished by moving a slit between these two prisms in the direction of
the spectral spread. Varying the slit separation selects the output bandwidth
(and hence pulse width). As the output wavelength is tuned, it is necessary
to optimize intracavity dispersion by adjusting Pr
2
and Pr
3
, in order to main-
tain the shortest output pulse width. To a first approximation, the prisms
need to be translated at the same rate as the slit to maintain the minimum
pulse duration.
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