Optical Resonators

Resonators with Bulk Components Versus Waveguide Resonators

An optical resonator can be made from bulk optical components, as shown in Figure 1, or as a waveguide resonator, where the light is guided rather than sent through free space.
Bulk-optical resonators are used e.g. for solid-state bulk lasers. The transverse mode properties depend on the overall setup (including the length of air spaces), and mode sizes can vary significantly along the resonator. In some cases, the mode properties are also significantly influenced by effects such as thermal lensing.
Waveguide resonators are often made with optical fibers (e.g. for fiber lasers) or in the form of integrated optics. The transverse mode properties (see below) are determined by the local properties of the waveguide.
There are also mixed types of resonators, containing both waveguides and parts with free-space optical propagation. Such resonators are used e.g. in some fiber lasers, where bulk-optical components need to be inserted into the laser resonator.

Linear Resonators Versus Ring Resonators

Figure 1: A simple linear optical resonator with a curved folding mirror (top) and a four-mirror bow-tie ring resonator (bottom).

Linear (or standing-wave) resonators (Figure 1, top) are made such that the light bounces back and forth between two end mirrors. For continuously circulating light, there are always counterpropagating waves, which interfere with each other to form a standing-wave pattern.
In ring resonators (Figure 1, bottom), light can circulate in two different directions (see also: ring lasers). A ring resonator has no end mirrors.
In either case, a resonator may contain additional optical elements which are passed in each round trip. For example, a laser resonator contains a gain medium which can compensate the resonator losses in each round trip of the light.
During a resonator round trip, light experiences various physical effects which change its spatial distribution: diffraction, focusing or defocusing effects of optical elements (sometimes involving optical nonlinearities), in special cases also gain guiding, saturable absorption, etc.
Some important differences between linear resonators and ring resonators are:

• In a ring resonator, light can circulate in two different directions. If there is an output coupler mirror, this leads to two different output beams. A linear resonator with the output coupler at an end does not exhibit this phenomenon.
• An optical component within a resonator is hit by the light once per round trip in the case of a ring laser, and twice per round trip in a linear resonator (except for the end mirrors).
• When light is injected into a linear resonator via a partially transparent mirror, reflected light can propagate back to the light source. This is not the case for a ring resonator. Therefore, ring resonators are sometimes preferred for resonant frequency doubling with a laser source which is sensitive against optical feedback.
• A linear bulk resonator can have two stability zones (see below), e.g. for variation of the dioptric power of an internal lens, or of a resonator arm length. A ring resonator has only one stability zone.
• The non-normal incidence of light on every resonator mirror of a ring resonator causes astigmatism if a resonator mirror has a curved surface. A bow-tie ring resonator geometry is often used to minimize astigmatism by keeping the incidence angles small.
• Monolithic ring resonators with high Q factor can exploit total internal reflection at all surfaces, and thus may not require any dielectric mirror.

Stable Versus Unstable Bulk-optical Resonators

Stability of a bulk-optical resonator essentially means that any ray injected into the system with some initial transverse offset position and angle will stay within the system during many round trips. For unstable resonators, there are rays which exhibit an unlimited increase in transverse offset, so that they will leave the optical system.
The stability of a resonator depends on the properties and arrangement of the optical components, basically the curvature of reflecting surfaces, other focusing effects, and the distances between the components. When a parameter such as an arm length or the dioptric power of focusing element in the resonator is varied, the resonator may go through one (for ring resonators) or two (for standing-wave resonators) stability zones [1]. At the edges of such stability zones, the beam sizes at the resonator ends can diverge or go toward zero, and the alignment sensitivity may also diverge.
Most solid-state bulk lasers are based on stable resonators, but unstable resonators have advantages in certain lasers, particularly those with very high output power and high laser gain, where a better beam quality may be achieved. The modes of unstable resonators have very complicated properties. Output coupling is often done with a highly reflecting mirror where part of the circulating light is lost around the edges (or possibly only on one side). Another possibility is to use a partially transmissive output coupler mirror with a transverse variation of reflectivity (Gaussian reflectivity mirrors).


Ricardo Monroy       C.I. 17646658

---