The most widely used laser resonators or cavities have either plane or spherical mirrors ofrectangular or circular shape, separated by some distance L.

**Resonator Configuration**

The most
widely used laser resonators or cavities have either plane or spherical mirrors
ofrectangular or circular shape, separated by some distance L. There have
appeared Plane Parallel Resonators, Concentric (Spherical) Resonators, Confocal
Resonators,Generalized Spherical Resonators and Ring Resonators.

Plane Parallel Resonator consists of two plane mirrors set parallel to each other, as Shown in the figure below. The one round trip of wave in the cavity should be an integral number times 2ı , the resonant frequencies is ı = kc/(2L), k is an integral number, c is the speed of light in the medium, L is the cavity length. The frequency difference between two consecutive modes (possible standing wave in the cavity) is c/(2L). This difference is referred to as the frequency difference between two consecutive longitudinal modes; the word longitudinal is used because the number k indicates the number of half wavelengths of the mode along the laser resonator, i.e., in the longitudinal direction.

Concentric
resonator consists of two spherical mirrors with the same radius R separated by
a distance L=2R, so that the centers are coincident. The resonant frequencies
use the same equation as above. Confocal resonator consists of two spherical
mirrors of the same radius of curvature R separated by a distance of L such
that their foci F1 and F2 coincident. In this case, the center of curvature of
one mirror lies on the surface of another mirror, L=R. The resonant frequency
cannot be readily obtained from geometrical optics consideration.

Resonators
formed by two spherical mirrors of the same radius of curvature R and separated
by a distance L such that R<L<2R, i.e., in between confocal and
concentric, are called Generalized Spherical Resonators, which is also often
used.

Ring
Resonator is a particularly important class of laser resonators. The path of
the optical rays is arranged in a ring configuration or more complicated
configurations like folded configurations. We can compute the resonant
frequencies by imposing the constraints that the total phase shift along the
ring path or the closed loop path must be equal to the integral numbers of 2ı .
Then the resonant frequencies are ı = kc/Lp, where k is an integral number, Lp
is the loop path length.

Cavities
can be identified as stable or unstable according to whether they make the
oscillating beam converge into the cavity or spread out of the cavity. The
output mirror of the laser resonator is finely coated to reach the required
reflection into the cavity, if the beam is too intense, the mirror May suffer
breakage. Breakage is serious because it causes shut down of the production. So
for powers up to 2kW, lasers mainly use stable cavity designslaser output is
from the center of optical axis. Stable cavity design allows the beam to
oscillate many times inside the cavity to get high gain, the focal property and
directionality are improved. For higher powered lasers, unstable cavities are often
used laser output comes from the edge of the output mirror, which is often a
totally reflecting metal mirror. The ring shaped beam reduces the intensity of
the beam, thus reduces the risk of breakage. In the same time ring shaped beam
is poor for focusing. Unstable cavities are suitable for high gain per round
trip laser systems, which don’t require large numbers of oscillation between
the mirrors.

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