Stability of Resonators – an Ambiguous Term

Posted on 2009-04-05. Permanent link: http://www.rp-photonics.com/spotlight_2009_04_05.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: encyclopedia articles on optical resonators, laser resonators, stability zones, alignment sensitivity; Spotlight article of 2006-11-28

In the context of optical resonators, stability is a property with very different meanings:

• Generally, stability of some device is usually understood to be something like a low sensitivity to uncontrolled external influences. For example, an industrial laser should have a laser resonator which is not easily misaligned by vibrations or temperature changes.
• For optical resonators, however, there is also an entirely different meaning of the word stability. Originally, this came from considering a ray circulating in the resonator: the resonator is called stable essentially when any ray injected with some initial transverse offset position and angle will stay within the resonator during many round trips. When some resonator property (e.g. an arm length of the focusing power of some lens) is continuously varied, there are certain zones in which the resonator is stable in that sense (→ stability zones). A resonator has modes both in stable and unstable regions, but their properties are much more complicated in unstable regions.

The trouble is that these kinds of stability are extremely different:

• A laser resonator may exhibit a diverging alignment sensitivity at the edge of a stability zone. Even a bit within that zone, the laser can be highly sensitivity to the slightest misalignment, and in fact also to other effects such as aberrations of a thermal lens. Therefore, even uttermost mechanical stability may not be sufficient to get a robust laser.
• There are lasers with unstable resonators which are very stable in the common sense and can thus serve as industrial lasers.

In some cases, the requirements for stability in both senses can even be conflicting. In particular, Q-switched solid-state lasers are mechanically most stable when built with a very compact (possibly even monolithic) resonator setup. This, however, together with the requirement of having a sufficiently large effective mode area on all optical components (the laser crystal, the Q-switch, dielectric mirrors) may force one to operate the laser near such an sensitive stability edge. That can be a severe problem, making it very hard to obtain a robust setup, despite the good mechanical stability.

Obviously, it is essential in such situations to understand very well the involved trade-offs in order to find the overall best technical solution.