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

102 2.1.6 Mode-locking techniques [Ref. p. 134
shifts of those GTI oscillations so that a special selection of mirrors makes it ultimately possible
to obtain the right dispersion compensation. Some tuning of the oscillation peaks can be obtained
by the angle of incidence [00Sut]. A specially designed pair of DCMs has been used to cancel the
spurious GTI oscillation [01Kae] where an additional quarter-wave layer between the AR-coating
and the DCM structure was added in one of the DCMs. Also this design has its drawbacks and
limitations because it requires an extremely high precision in fabrication and restricts the range of
angles of incidence.
After this overview it becomes clear that there is no perfect solution to the challenge of ultrabroadband
dispersion compensation. At this point ultrabroadband chirped mirrors are the only
way to compress pulses in the one- to two-optical-cycle regime and normally a larger selection of
chirped mirrors are required to “match and reduce” the residual unwanted GDD oscillations from
all mirrors inside the laser cavity.
2.1.6 Mode-locking techniques
2.1.6.1 Overview
Passive mode-locking mechanisms are well-explained by three fundamental models: slow saturable
absorber mode-locking with dynamic gain saturation [72New, 74New] (Fig. 2.1.5a), fast
saturable absorber mode-locking [75Hau1, 92Hau] (Fig. 2.1.5b) and slow saturable absorber modelocking
without dynamic gain saturation which in the femtosecond regime is described by soliton
mode-locking [95Kae1, 95Jun2, 96Kae] and in the picosecond regime by Paschotta et al. [01Pas1]
(Fig. 2.1.5c). The physics of most of these techniques can be well explained with Haus’s master
equation formalism as long as at steady state the changes in the pulse envelope during the propagation
inside the cavity are small. At steady state the pulse envelope has to be unchanged after
one round trip through the cavity.
Passive mode-locking, however, can only be analytically modeled in the weak saturation regime,
which is typically not the case in SESAM mode-locked solid-state lasers. However, this formalism
still provides a useful approach to describe mode-locking techniques in an unified fashion. Recent
numerical simulations show that analytical results with fast saturable absorbers only slightly underestimate
numerical solutions and correctly describe the dependence on saturated gain, gain
bandwidth and absorber modulation taking into account more strongly saturated absorbers and
somewhat longer saturation recovery times in SESAM mode-locked solid-state lasers [01Pas1].
A short introduction to Haus’s formalism is given in Sect. 2.1.6.2 and Table 2.1.10. Afterwards
we will describe all mode-locking techniques using this formalism and summarize the theoretical
prediction for pulse shape and pulse duration (Table 2.1.11). For solid-state lasers self-Q-switching
instabilities in passive mode-locking are a serious challenge. Simple guidelines to prevent those
instabilities and obtain stable cw mode-locking are presented in Sect. 2.1.6.8.
2.1.6.2 Haus’s master equations
Haus’s master equation formalism [95Hau2] is based on linearized differential operators that describe
the temporal evolution of a pulse envelope inside the laser cavity. At steady state we then
obtain the differential equation:
Landolt-Börnstein
New Series VIII/1B1