Are Compact Resonators More Stable?

A simple example demonstrates that point convincingly, without using complicated calculations or software. Imagine that we need a simple linear resonator, consisting of a plane mirror and a concave (focusing) mirror. The latter must have a suitable radius of curvature such that the fundamental mode has a certain beam radius in the resonator. (For a laser resonator, the right mode size is often very important for obtaining good beam quality, a high slope efficiency, etc.) The shorter the resonator, the weaker will be the required curvature of the focusing mirror.

Now imagine a small angular misalignment of the curved mirror, while the plane mirror remains fixed. This misalignment simply makes the resonator mode shift transversely to a new position, where it is again perpendicular to the surface of the curved mirror. (Obviously, the mode always has to be perpendicular to both mirror surfaces.) It becomes clear now that a weak curvature – as needed for a short resonator – implies a larger transverse shift of the mode for a given misalignment angle. And this is bad. Consider, for example, such a shift in the resonator of an end-pumped laser: it will decrease the overlap between the laser beam and the pumped region.

One may believe that the discussed example is only an unusual pathological case, but it isn't: any type of resonator will exhibit this problem if you try to make it shorter and shorter while maintaining the mode size. Fundamentally, you are then pushing the resonator into a regime where the effect of diffraction becomes weak (simply because there is little propagation distance), mirror curvatures have to become correspondingly weaker, and the alignment becomes very sensitive. It is not good to have a resonator length far below the Rayleigh length of the intracavity beam.

A common case is that of a Q-switched laser, which we like to be compact partly because this gives us the shortest pulse duration. The mode size, however, cannot be reduced arbitrarily, because we often need to extract energy from the whole pumped volume in the laser crystal without employing higher-order modes (which would spoil the beam quality), and possibly because a too small mode leads to optical damage of resonator components. We then run exactly into that problem: the resonator will be compact and mechanically stable, but its alignment sensitivity may nevertheless be high.

Well, you might think, this simply means that we need a very good mechanical setup, and initially align that very carefully. However, misalignment is not only caused by mechanical tilts, but also by thermal effects such as thermal lensing in the laser crystal. Even exceptional mechanical stability can therefore not fully solve this problem.

Even though the problem is fundamental and cannot be eliminated with a simple design trick, it is essential to precisely understand such issues when designing laser resonators. First of all, one needs to be aware of the problem, and know that compactness is not necessarily the key to stability. Furthermore, one can at least select the best possible laser resonator design. What “best possible” means, depends on the concrete requirements. Therefore, finding the best solution is only possible after carefully analyzing these requirements, including the relative importance of various design goals. Having done this, one can decide for a type of design and finally employ advanced laser resonator design software to optimize the design.

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