364 Ultrashort Sources II: Examples
Because the pump power is limited an increase in pulse energy can only be at
the expense of repetition rate. Several different techniques have been developed.
A cavity dumper can be inserted in the Kerr lens mode-locked Ti:sapphire
laser resonator [83,84]. This allows the fs pulse to build up in a high Q cavity
with essentially no outcoupling losses. When a certain energy is reached the
outcoupler (typically based on an acousto-optic modulator) is turned on, and the
pulse is coupled out of the cavity. Repetition rates typically range from a few
100 kHz to a few MHz. Pulse energies of up to the 100-nJ level are possible.
Another method tries to capitalize on the inherent trend in solid-state lasers to
show relaxation oscillations and self Q switching. In such regimes the envelope
of the mode-locked pulse train is modulated. The Q-switched and mode-locked
output can be stabilized by (weakly) amplitude modulating the pump at a fre-
quency of several hundred kHz that is derived from the Q-switched envelope in
a feedback loop [85].
A third technique is based on long laser cavities (up to tens of meters) resulting
in low repetition rates of a few MHz. Careful cavity and dispersion design are
necessary to avoid the multiple pulse lasing and the instabilities that are usually
associated with long cavities [86]. For example, 200 nJ, 30-fs pulses at a repe-
tition rate of 11 MHz were obtained with a chirped mirror cavity and external
pulse compression with prisms [87].
6.7.3. Cr:LiSAF, Cr:LiGAF, Cr:LiSGAF,
and Alexandrite
The chromium ion has maintained its historical importance as a lasing medium.
Ruby is produced by doping a sapphire host with Cr
2
O
3
. The ruby laser being a
three-level system, requires high pump intensities to reach population inversion.
It is a high gain, narrow bandwidth, laser, hence not suited for ultrashort pulse
applications.
A broadband lasing medium is alexandrite, consisting of chromium doped
chrysoberyl (BeAl
2
O
4
:Cr
3+
). The alexandrite laser is generally flashlamp
pumped (absorption bands from 380 to 630 nm), with a gain bandwidth rang-
ing from 700 to 820 nm, and is therefore sometimes used as an amplifier
(mostly regenerative amplifier) for pulses from Ti:sapphire lasers. It is one of
rare laser media in which the gain cross section increases with temperature, from
7 · 10
−21
cm
2
at 300
◦
Kto2· 10
−20
cm
2
at 475
◦
K [72].
Of importance for femtosecond pulse generation are the Cr
3+
:LiSrAlF
6
or
Cr:LiSAF, Cr
3+
:LiSrGaF
6
or Cr:LiSGAF and Cr
3+
:LiCaAlF
6
or Cr:LiCAF
lasers. These crystals have similar properties as shown in Table 6.3. The gain cross
section is relatively low compared with other diode pumped laser crystals (30×
less than that of Nd:YAG for example). The thermal conductivity is 10 × smaller
Solid-State Lasers 365
Table 6.3
Room temperature physical properties of Cr:LiSAF, Cr:LiSGAF, and
Cr:LiGAF. The second-order dispersion of LiSAF is indicated for two
different Cr doping concentrations. A, B, C, and D are the parameters of
the Sellmeir formula n
2
i
= A
i
+ B
i
/(λ
2
− C
i
) − D
i
λ
2
. with i = o (ordinary)
or e (extraordinary), and λ
expressed in µm.
Property Cr:LiSAF Cr:LiSGAF Cr:LiCAF Units Ref.
Sellmeir coeff.
A
o
1.95823 1.95733 1.91850
A
e
1.95784 1.95503 1.91408
B
o
0.00253 0.00205 0.00113 µm
2
B
e
0.00378 0.00252 0.00155 µm
2
C
o
0.02671 0.03836 0.04553 µm
2
C
e
0.01825 0.03413 0.04132 µm
2
D
o
0.05155 0.04765 0.02525 µm
−2
D
e
0.02768 0.03822 0.01566 µm
−2
n
o
(850 nm) 1.38730 1.38776 1.37910
Nonlinear index 3.3 10
−16
3.3 10
−16
3.7 10
−16
cm
2
/W [73]
Dispersion k
(850 nm, 0.8%) 210 280 fs
2
/cm [91,92]
Dispersion k
(850 nm, 2%) 250 fs
2
/cm [91]
Third-order
dispersion k
1850 1540 fs
3
/cm [91,92]
Peak absorption 670 630 nm
Peak gain at 850 835 763 nm
cross section σ
π
4.8 10
−20
3.3 10
−20
1.3 10
−20
cm
2
[93]
Fluorescence
τ
F
(300
◦
K) 67 88 170 µs [93]
T
1/2
69 75 255
◦
C [88]
Expansion coeff.
along c-axis −10 0 3.6 10
−6
/K [93]
along a-axis 25 12 22 10
−6
/K [93]
c-axis thermal
conductivity 3.3 3.6 5.14 W/mK [94]
Thermal index
dependence dn/dT −4.0 −4.6 10
−6
/K [94]
than for Ti:sapphire. Therefore, thin crystals are generally used for better cool-
ing, which makes the mounting particularly delicate. The gain drops rapidly with
temperature, because of increasing nonradiative decay. Stalder et al. [88] define
a temperature T
1/2
at which the lifetime drops to half of the radiative decay time
measured at low temperature. As shown in Table 6.3, this critical temperature
is particularly low for Cr:LiSAF and Cr:LiSCAF (70
◦
C) which, combined with
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