2.1 Ultrafast solid-state lasers - ETH - the Keller Group

96 2.1.5 Pulse propagation in dispersive media [Ref. p. 134
For optimum soliton formation of a sub-10-fs pulse inside the laser, only a very small amount of
a constant negative total intracavity dispersion is necessary to form a stable soliton pulse (2.1.74).
For example, we estimated the necessary dispersion to be only −10 fs 2 for a Ti:sapphire laser
producing 6.5-fs pulses [97Jun3, 98Sut]. Here we assumed an estimated self-phase modulation
coefficient of about 0.07/MW, an average output power of 200 mW using a 3 % output coupler
and a pulse repetition rate of 86 MHz. This results in an intracavity pulse energy of 77.5 nJ. With
(2.1.74) then follows an estimated negative group delay dispersion of −10 fs 2 in a cavity round
trip.
There are different methods for dispersion compensation, such as the Gires–Tournois Interferometer
(GTI), grating pairs, prism pairs and chirped mirrors. The dispersion compensation is
summarized in Table 2.1.9 with the symbols defined in Fig. 2.1.16.
2.1.5.2.1 Gires–Tournois interferometer (GTI)
A Gires–Tournois Interferometer (GTI) [64Gir, 92Kaf] is a very compact dispersion-compensation
element, which basically replaces one flat laser cavity mirror. The negative dispersion is obtained
due to the Fabry–Perot interferometer, operated in reflection (Fig. 2.1.16a). Normally, in a GTI
the rear mirror is highly reflective over the whole wavelength range (i.e. ideally 100 %) whereas
the front mirror has a relatively low reflectivity, typically a few percent. The spacer layer in the
Fabry–Perot should contain a non-absorbing material and is very often air, such that the thickness
can be easily changed. The phase shift varies nonlinearly by 2 π for each free spectral range,
calculated as Δ ν = c/2nd, wheren and d are the refractive index and the thickness of the spacer
material, respectively. Within each free spectral range, the GDD oscillates between two extremes
the magnitude of which is proportional to d 2 and also depends on the front-mirror reflectivity.
Ideally, the GTI is operated near a minimum of the GDD, and the usable bandwidth is some
fraction (e.g. one tenth) of the free spectral range, which is proportional to d −1 :
d 2 φ
dω 2 ∝ d2 ,
{
Bandwidth of
d 2 }
φ
dω 2 ∝ 1 d . (2.1.22)
In Table 2.1.9 the material dispersion in the GTI spacer layer was neglected. The bandwidth
compared to the other techniques is limited, thus a GTI is typically used for pulse durations above
100 fs. There is a trade-off: A broader bandwidth is obtained with a smaller Fabry–Perot thickness
but then the amount of negative dispersion is strongly reduced. For example, an air-spaced GTI
with 80 μm thickness and a top reflectivity of 4 % produces a negative dispersion of about −0.13 ps 2
at a wavelength of 799 nm. In comparison a 2.25 μm thick air space results in about −100 fs 2 at
a wavelength of 870 nm.
Tunable GDD can be achieved if the spacer material is a variable air gap, which however
must be carefully stabilized to avoid unwanted drifts. More stable but not tunable GDD can be
generated with monolithic designs, based e.g. on thin films of dielectric media like TiO 2 and SiO 2 ,
particularly for the use in femtosecond lasers. The main drawbacks of GTI are the fundamentally
limited bandwidth (for a given amount of GDD) and the limited amount of control of higher-order
dispersion.
2.1.5.2.2 Grating pairs
Grating pairs [69Tre] produce negative dispersion due to the wavelength-dependent diffraction
(Fig. 2.1.16b). To obtain a spatially coherent beam two paths through the grating pair are required.
Compared to prism pairs (Sect. 2.1.5.2.3), pairs of diffraction gratings can generate higher
dispersion in a compact setup. However, because of the limited diffraction efficiency of gratings,
the losses of a grating pair are typically higher than acceptable for use in a laser cavity, except in
Landolt-Börnstein
New Series VIII/1B1