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Optical Resonators

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Definition: arrangements of optical components which allow a beam of light to circulate

German: optische Resonatoren

How to cite the article; suggest additional literature

An optical resonator (or resonant optical cavity) is an arrangement of optical components which allows a beam of light to circulate in a closed path. Such resonators can be made in very different forms.

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 for solid-state bulk lasers, for example. Their 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

linear resonator and ring resonator

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:

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 [2]. 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 rather 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).

Resonator Modes

Resonator modes are essentially self-consistent field distributions of light – more precisely, electric field distributions which are self-reproducing (apart from a possible loss of power) in each resonator round trip.

The properties of resonator modes depend very much on various details:

For each of the transverse mode patterns, there are only certain optical frequencies for which the optical phase is self-consistently reproduced after each round trip (i.e. the round-trip phase shift is an integer multiple of 2π). These are called the mode frequencies or resonance frequencies and are approximately equidistant (but not exactly equidistant due to chromatic dispersion). The frequency spacing of the resonator modes, also called free spectral range (FSR), is the inverse round-trip time, or more precisely the inverse round-trip group delay. This means that the FSR becomes smaller as the resonator length is increased. The ratio of the frequency spacing to the width of the resonances (resonator bandwidth) is called the finesse and is determined by the power losses per resonator round trip. A related measure is the Q factor, which is the ratio of resonance frequency and bandwidth.

The article on resonator modes gives more details.

Resonant Enhancement

If e.g. an end mirror is partially transparent, light can be fed into the resonator from outside. The highest internal optical power (and the maximum transmission through a resonator) can be achieved when the (monochromatic) input light has a frequency matching that of one of the modes, and the spatial shapes are also matched (→ mode matching). Particularly for low-loss resonators, the circulating intracavity power can then greatly exceed the input power by means of resonant enhancement (→ enhancement cavities).

Resonant enhancement is also possible for a regular train of light pulses, when the frequencies of the pulse train match the optical resonances. In the time domain, this means that the pulse period matches the resonator's round-trip time, or an integer fraction of it.

Subtle Properties of Bulk-optical Resonators

The physics of bulk-optical resonators is surprisingly rich in nature. Some interesting aspects are:

Application of Optical Resonators

Optical resonators are used for, e.g., the following purposes:

Bibliography

[1]L. W. Casperson, “Mode stability of lasers and periodic optical systems”, IEEE J. Quantum Electron. 10 (9), 629 (1974)
[2]V. Magni, “Multielement stable resonators containing a variable lens”, J. Opt. Soc. Am. A 4 (10), 1962 (1987)
[3]P. Lalanne et al., “Photon confinement in photonic crystal nanocavities”, Laser & Photon. Rev. 2 (6), 514 (2008)
[4]A. E. Siegman, Lasers, University Science Books, Mill Valley, CA (1986)
[5]N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, 2nd edn., Springer, Berlin (2005)

(Suggest additional literature!)

See also: cavities, enhancement cavities, laser resonators, resonator design, resonator modes, stability zones, unstable resonators, free spectral range, finesse, bandwidth, Q factor, mode matching, etalons, mode cleaner cavities, reference cavities, Fabry–Pérot interferometers, Spotlight article 2006-11-21, Spotlight article 2006-11-28, Spotlight article 2009-04-05, Spotlight article 2016-07-05

In the RP Photonics Buyer's Guide, 4 suppliers for optical resonators are listed.

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