The Hemi-spherical Resonator
This cavity is created by one plan mirror facing a concave spherical mirror with a radius of curvature equal to the length of the resonator cavity (Fig). This resonator is very similar to the spherical resonator in properties, with low sensitivity to mirror misalignments as well as low diffraction losses. This resonator also offers the additional advantage of a lower manufacturing cost due to the utilization of a plan mirror instead of a spherical mirror. He-Ne lasers often utilize this type of resonator set up.
Every laser requires a resonator cavity in which the laser beam can recirculate, passing through the gain medium several times, thus providing feedback and amplification of the laser light. The resonator cavity typically encompasses the gain medium, however, which is often the case in semiconductor lasers, the resonator cavity is part of the gain medium, where a full-mirrored and a half-mirrored optical coating is applied to opposite ends of the gain medium.
The light inside the resonator cavity will reflect via the mirrors multiple times. During this reflection process, constructive interference will select for only certain frequencies or wavelengths, whereas destructive interference will annihilate other wavelengths. The more often a beam is reflected through the optical cavity, the more stable its frequency pattern will be. Furthermore, the probability of stimulated emission to take place is proportional to the time the beam spends inside the gain medium. The partially reflecting mirror through which the laser beam eventually exits (the optical coupler) is usually designed to have only a 1-20% pass-through rate. This way the reflection rate and beam quality can be controlled very precisely. Most resonator cavities consist of two facing mirrors. Depending on whether the mirrors are plane or spherical and the combination in which they are arranged, several types of optical resonators have been identified:
The Plane-Parallel Resonator
This is probably the simplest and most intuitive of all optical resonator types, consisting of two opposing flat mirrors (See figure below). This is also often referred to as the Fabry-Perot cavity, named after Charles Fabry and Alfred Perot, two French physicists who developed the original Fabry-Perot optical interferometer or etalon in 1913. In the plane-parallel resonator, the light beam strikes the opposing mirrors at perfect 90-degree angles. In order for this to work properly, the two mirrors have to be in perfect parallel alignment, or a “drift” of the intra-resonator beam will result. This will cause the optical axis to be off-center and the resulting laser light will be inadequate. Since it is very difficult to arrange two mirrors in such perfect parallel alignment, this type of resonator, although very simple conceptually, is only used in semiconductor lasers, where the resonating cavity is very short and optical coatings are directly applied to the surface of the laser medium itself.
The Confocal Resonator
The confocal resonator is probably the most widely used resonator in laser construction. It has the least amount of diffraction losses. This resonator consists of two concave mirrors facing each other, where the radius (or curvature) of each mirror is identical and is equal to the length of the resonator cavity itself (See Figure below). Since the laws of optics dictate that the focal length of a concave spherical mirror is one-half its radius of curvature, the focal point of both mirrors coincide in the center of the resonator cavity. The confocal laser shows much less sensitivity to misalignments of the mirrors and is thus easy to align with very little diffraction losses.
The Spherical Resonator
This is similar to the confocal resonator in that it has two concave mirrors with identical radii facing each other. The difference however, is that their radius of curvature is equal to one-half the length of the resonator cavity (See Figure below). This type of arrangement causes a very tight focusing of the beam at the exact center of the cavity. The spherical resonator cavity set up has similar advantages to the confocal resonator in that it has a very low sensitivity to misalignment of the mirror and very low diffraction losses. One disadvantage of this system however is that it only offers a very limited use of the volume of the active medium, due to its small beam diameter, which in turn yields a less efficient stimulated emission process.
The Concave-Convex Resonator
This resonator system consists of one concave mirror with a radius of curvature that is longer than the length of the resonator cavity, facing on convex mirror with a negative radius of curvature (See Figure below). This resonator has the advantage that the beam focus is usually outside the optical cavity and therefore it is more protected from damage due to the high temperatures of a focused beam. This is usually the preferred resonator setup for a laser with higher power.
The Resonator Cavity
