2. Kerr-lens mode-locking principle

Figure 1. Summary of diverse femtosecond thin-disk oscillators adopted from [26]. More details including the references

Figure 2. (a) Four key elements: thin-disk technology, dispersive mirrors, Kerr-lens mode-locking and geometrical energy scaling concept form femtosecond thin-disk oscillator technology described and (b) graphical representation of the rapid

can be found in [26].

94 High Power Laser Systems

thin-disk KLM oscillator development in our group.

The refractive index n of a material depends on the incident electric field intensity. A Gaussian intensity distribution causes an increase of the refractive index in the central part of the beam relative to its outer regions therefore forming a nonlinear lens. The higher the light intensity, the stronger the action of such a lens. The lens becomes stronger for smaller beam radii ω and media with higher nonlinear refractive index n2. Self-focusing occurs for a highintensity, pulsed laser-beam (red, Figure 3) and reduces losses due to the hard aperture blocking the continuous wave (CW) beam of lower intensity. In a resonator-cavity, this mechanism initiates mode-locking and acts as an artificial saturable absorber. Catastrophic run away damage can happen when a critical power is reached and the length of the medium exceeds the self-focusing length. The first oscillator working on the KLM principle was discovered by Spence et al. [18] and referred to as self-mode-locking or magic modelocking. Piche [39] explained the mode-locking mechanism on the basis of self-focusing and only a few authors recognized the potential of the self-focusing effect for mode-locking before the invention of KLM [40, 41]. Since that time, KLM established itself as the method of choice for ultrashort-pulse generation and numerous studies were done on resonator design, theoretical numerical and analytical description of KLM and experiments on ultrashort pulse generation. Mostly, experiments were performed with the Ti:Sa gain medium, which has several outstanding features: an extremely broad gain bandwidth, short upper-state lifetime as well as high thermal conductivity [19]. Understanding that shortest possible pulses can only be obtained when nonlinearities and dispersion are balanced to form so-called soliton pulses [42, 43] preceded the invention of KLM. However, this technique constituted the decisive building-block to enable robust, usable solid-state femtosecond oscillators. With Kerr-lens mode-locked solitonic Ti:Sa oscillators up to several 100 mW average power and up to MW-level peak-power were realized with pulse durations approaching few optical cycles, all in a compact, reliable setup that was superior to the old dye-based technology. This ensured its worldwide adoption in many optical laboratories and nearly immediate commercialization.

Figure 3. Basic principle of KLM. Self-focusing occurs for a high-intensity beam (red) and reduces the losses due to a hard aperture (two black knifes) blocking the low-intensity (CW) beam. This mechanism initiates mode-locking and acts as an artificial saturable absorber.
