Cavity Stability of the HeNe Laser:

In the case of a cavity having mirrors 1 and 2 which have radii of curvature
R_{1} and R_{2 }respectively,
that are separated by a distance L there are requirements that govern cavity
stability. If a ray is traced as it is reflected back and forth between
the mirrors in the cavity, it becomes apparent that not all combinations
of radii and cavity lengths result in stable cavities. If a ray is initially
directed parallel to the cavity axis, it may diverge from its original
trajectory after repeated reflections. If divergence occurs, the cavity
sustains very high diffraction loss and is said to be unstable. The condition
which must be satisfied for the cavity to be considered stable is shown
below:

^{8}

where R_{1} and R_{2 }are
the radii of curvature for the two mirrors and L is again the separation
between them. Outside of this condition, the laser cavity is not stable
because the reflected rays diverge from a path parallel to the cavity axis.