Resonator Design

A resonator commonly employed for KLM is an astigmatically compensated arrangement consisting of two focusing mirrors and two flat mirrors. In order to obtain a high nonlinearity, the Kerr medium is inserted into the tightly focused section of the resonator, as shown in Fig. 1(a). Taking into account the astigmatism of the Brewster cut crystal and the tilted mirrors, the resonator shown in Fig. 1(a) has to be evaluated in the tangential and sagittal plane. The curved mirrors correspond to lenses with focal lengths f , which are different for the two planes, the same is true for the equivalent lengths l of the laser crystal. Figure 1(b) depicts the equivalent resonator. The function of the two prisms is to provide dispersion compensation in the resonator, as will be explained in the next subsection.

FIGURE 1. (a) Resonator for Kerr lens mode locking and (b) equivalent resonator.

The operation of a KLM laser is a tradeoff between output power, stability, and tolerance to the exact position of the components. An analytical treatment of nonlinear resonators has shown that for a given pump power and pump spot size, the most critical parameters are:
(a) the distance z of the two focusing mirrors;
(b) the location x of the Kerr medium with respect to the mirrors, and
(c) the spot size variation s at the aperture.
The Kerr lens sensitivity s is highest near the limit of the stability range of the resonator, therefore loss-modulation efficiency has to be traded off against stable laser performance.

FIGURE 2. Spot sizes as a function of intracavity peak power for two orthogonal directions.

Because of the Brewster angle design, these resonators behave differently in the tangential and sagittal planes. This is illustrated in Fig. 2 which shows the change in beam size in two orthogonal directions at the flat mirror for a resonator configuration as depicted in Fig. 1. Since the spot size changes essentially in only one direction, a slit rather than a round aperture is usually employed for the adjustment of the proper loss modulation.