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Standing-wave Resonators

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Optical resonators can be made with two or more mirrors and possibly other optical components. Some of them are standing-wave resonators, also called linear resonators, where the light is reflected with normal incidence on two end mirrors. A consequence of that is that a standing wave (see Figure 2), formed by two counter-propagating optical waves, is formed within the resonator (at least in a simple situation with light in only one resonator mode). This is in contrast to the situation in a ring resonator, where standing waves may occur only in the immediate vicinity of mirrors: there, the radiation is reflected with non-normal incidence, leading to a spatial overlap between incoming and reflected wave only in a limited volume.

The resonator modes of a linear resonator are always exactly perpendicular to the end mirrors; if such a resonator is somewhat misaligned, the modes adjust their position such as to still maintain that condition.

If a linear resonator is made from two mirrors only, it can also be called a Fabry–Pérot resonator (→ Fabry–Pérot interferometers).

Standing-wave resonators can be realized not only with bulk components, but also with optical fibers.

In cases where the occurrence of standing waves is not relevant, the term linear resonator is more common. Linear resonators are often preferred over ring resonators because they are usually simpler to build and align.

Stability Zones

An optical resonator made with free-space optics (i.e., not with waveguides) can have stability zones, outside which it is an unstable resonator. While ring resonators can have only one stability zone, linear resonators generally have two of those.

Calculation of Mode Properties

The software RP Resonator is a particularly flexible tool for calculating all kinds of mode properties, even including misalignment effects, and allowing sophisticated design optimizations. Both standing-wave and ring resonators are supported. You can take into account alignment sensitivity and thermal lensing, and even design a resonator for operation in a specific stability zone.

The Standing-wave Pattern

The standing-wave pattern of the optical intensity can be largely washed out if the intracavity light is spread over multiple resonator modes, since the spatial pattern is somewhat different for each mode. Also, polarization effects may lead to such results; this is sometimes exploited with the twisted-mode technique.

If light is injected through an end mirror of a linear resonator (with some transmittance), part of that light is reflected back with full spatial overlap with the incident wave. That property of a linear resonator is sometimes disadvantageous, e.g. when a laser is sensitive to backreflected light. Therefore, mode cleaner cavities, for example, are often made as ring resonators, where the reflected beam is easily separated from the incident beam.

In some situations, the standing waves in a linear resonator are relevant for an application. For example, standing-wave effects in linear laser resonators can give rise to spatial hole burning, and this can make it difficult to achieve single-frequency operation for realizing a narrow-linewidth laser. Here, gain saturation in the laser gain medium (e.g. a laser crystal) is determined by the standing-wave pattern, rather than being homogeneously distributed in the medium. As a result, the gain of the lasing mode is saturated more than that of any competing modes, which are thus favored.

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