Editing Optical cavity (section)

==Stability==
[[Image:Laser resonator stability.svg|thumb|right|300px|Stability diagram for a two-mirror cavity. Blue-shaded areas correspond to stable configurations.]]

Only certain ranges of values for ''R''<sub>1</sub>, ''R''<sub>2</sub>, 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:<ref>{{cite book |first=Amnon |last=Yariv |year=1989 |title=Quantum Electronics |edition=3rd |publisher=Wiley |isbn=0-4716-0997-8 |page=142}}</ref>

:<math>  0 \leqslant \left( 1 - \frac{L}{R_1} \right) \left( 1 - \frac{L}{R_2} \right) \leqslant 1.</math>
Values which satisfy the inequality correspond to stable resonators.

The stability can be shown graphically by defining a stability parameter, ''g'' for each mirror:
:<math> g_1 = 1 - \frac{L}{R_1} ,\qquad g_2 = 1 - \frac{L}{R_2}</math>,
and plotting ''g''<sub>1</sub> against ''g''<sub>2</sub> as shown. Areas bounded by the line ''g''<sub>1</sub> ''g''<sub>2</sub> = 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, if a ray is deviated from its original direction in the middle of the cavity, its displacement after reflecting from one of the mirrors is larger than in any other cavity design. This prevents [[amplified spontaneous emission]] and is important for designing high power amplifiers with good beam quality.