Optical Cavity - Stability

Stability

Only certain ranges of values for R₁, R₂, and L produce stable resonators in which periodic refocussing of the intracavity beam is produced. If the cavity is unstable, the beam size will grow without limit, eventually growing larger than the size of the cavity mirrors and being lost. By using methods such as ray transfer matrix analysis, it is possible to calculate a stability criterion:

Values which satisfy the inequality correspond to stable resonators.

The stability can be shown graphically by defining a stability parameter, g for each mirror:

,

and plotting g₁ against g₂ as shown. Areas bounded by the line g₁ g₂ = 1 and the axes are stable. Cavities at points exactly on the line are marginally stable; small variations in cavity length can cause the resonator to become unstable, and so lasers using these cavities are in practice often operated just inside the stability line.

A simple geometric statement describes the regions of stability: A cavity is stable if the line segments between the mirrors and their centers of curvature overlap, but one does not lie entirely within the other.

In the confocal cavity a ray, which is deviated from its original direction in the middle between the of the cavity, is maximally (compared to other cavities) displaced on the return to the middle. This prevents amplified spontaneous emission and is important for a good beam quality and high power amplifiers. In wave optics this is expressed by the eigenvalue degeneration of the modes. On every turn to the left, the 0,0 mode and the 1,0 mode are 90° out of phase, but on the turn back, they are 180° out of phase. Interference of the modes then leads to a displacement.