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

110 2.1.6 Mode-locking techniques [Ref. p. 134
This analytical result can explain the much shorter 7–12 ps pulses in actively mode-locked
diode-pumped Nd:YAG [89Mak1] and Nd:YLF [89Mak2, 90Kel1, 90Wei, 90Juh] lasers because the
laser mode area in those diode-pumped lasers is very small which results in significant SPM pulse
shortening (2.1.54). For example, our experiments with an actively mode-locked diode-pumped
Nd:YLF laser [95Bra2] are very well explained with (2.1.54). In this case the lasing wavelength is
1.047 μm, the gain bandwidth is Δλ g =1.3 nm, the pulse repetition rate is 250 MHz, the output
coupler is 2.5 %, the average output power is 620 mW, the mode radius inside the 5 mm long
Nd:YLF crystal is 127 μm × 87 μm and the loss modulation of the acousto-optic mode-locker is
about 20 %. We then obtain a FWHM pulse duration of 17.8 ps (2.1.54) which agrees well with the
experimentally observed pulse duration of 17 ps. Without SPM we would predict a pulse duration
of 33 ps (2.1.49).
Equation (2.1.54) would predict that more SPM continues to reduce the pulse duration. However,
too much SPM will ultimately drive the laser unstable. This has been shown by the numerical
simulations of Haus and Silberberg [86Hau] which predict that pulse shortening in an actively modelocked
system is limited by roughly a factor of 2 in the case of SPM only. They also showed that
the addition of negative GVD can undo the chirp introduced by SPM, and therefore both effects
together may lead to stable pulse shortening by a factor of 2.5.
However, experimental results with fiber lasers and solid-state lasers indicate that soliton shaping
in the negative GVD regime can lead to pulse stabilization and considerable more pulse shortening.
We have extended the analysis of Haus and Silberberg by investigating the possible reduction
in pulse width of an actively mode-locked laser as a result of soliton-like pulse formation, i.e.,
the presence of SPM and an excessive amount of negative GVD [95Kae2]. We show, by means of
soliton perturbation theory, that beyond a critical amount of negative GVD a soliton-like pulse is
formed and kept stable by an active mode-locker. If the bandwidth of the gain is large enough, the
width of this solitary pulse can be much less than the width of a Gaussian pulse generated by the
active mode-locker and gain dispersion alone. We established analytically that the pulse shortening
possible by addition of SPM and GVD does not have a firm limit of 2.5. Numerical simulations
and experiments with a regeneratively actively mode-locked Nd:glass laser [94Kop2] confirm these
analytical results. The pulse-width reduction achievable depends on the amount of negative GVD
available. For an actively mode-locked Nd:glass laser a pulse shortening up to a factor of 6 may
result, until instabilities arise.
2.1.6.4 Passive mode-locking with a slow saturable absorber and
dynamic gain saturation
Dynamic gain saturation can strongly support pulse formation in passive mode-locking and has allowed
pulses with duration much shorter than the absorber recovery time. Dynamic gain saturation
means that the gain undergoes a fast pulse-induced saturation that recovers between consecutive
pulses. This technique has been used to produce sub-100-fs pulses with dye lasers and dye saturable
absorbers even though the absorber recovery time was in the nanosecond regime. Dynamic gain
saturation can only help if the following conditions are fulfilled (Fig. 2.1.5a):
1. The loss needs to be larger than the gain before the pulse:
q 0 >g 0 , (2.1.56)
where q 0 is the unsaturated loss coefficient (2.1.6) and g 0 is the small signal gain coefficient in
the laser.
2. The absorber needs to saturate faster than the gain. From (2.1.14) (i.e. slow saturable absorber
and gain) then follows that
Landolt-Börnstein
New Series VIII/1B1