Mirrors of Equal Curvature

With R₁ = R₂ = R we obtain, from (1),

............(1)

......(2)
The beam waist that occurs at the center of the resonator L₁ = L₂ = R/2 is
.......(3)
If we further assume that the mirror radii are large compared to the resonator length R >> L, the above formula simplifies to
..... (4)
As follows from (4) in a resonator comprised of large-radius mirrors, the beam diameter changes very little as a function of distance.
A resonator comprised of mirrors having a radius of curvature on the order of 2 to 10 m, that is, several times longer than the length of the resonator, is one of the most commonly employed configurations. Such a large-radius mirror resonator has a reasonable alignment stability and a good utilization of the active medium.

FIGURE 1. Common resonator configurations (intracavity radiation pattern is shaded).

A special case of a symmetrical configuration is the concentric resonator that consists of two mirrors separated by twice their radius, that is, R = L/2. The corresponding beam consists of a mode whose dimensions are fairly large at each mirror and which focus down to a diffraction-limited point at the center of the resonator. A concentric resonator is rather sensitive to misalignment, and the small spot can lead to optical damage.
Another very important special case of a resonator with mirrors of equal curvature is the confocal resonator. For this resonator the mirror separation equals the curvature of the identical mirrors, that is, R = L. From (2), (3) we obtain the simplified relation
.......(5)

The confocal configuration gives the smallest possible mode dimension for a resonator of given length. For this reason, confocal resonators are not often employed since they do not make efficient use of the active material.