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Stability Zones

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Definition: parameter regions of an optical resonator where the resonator is geometrically stable

German: Stabilitätszonen

Category: optical resonators

How to cite the article; suggest additional literature

When a parameter of a laser resonator (optical cavity) such as an arm length or the dioptric power (inverse focal length) of the focusing element in the resonator is varied, the resonator may go through one (for ring resonators) or two (for standing-wave resonators) stability zones.

In a purely geometric analysis, stability means that a ray injected into the optical system will stay at a finite distance from the axis even after many round trips. In this regime, the resonator modes (self-reproducing field configurations, calculated with wave optics) are of much simpler structure than for an unstable resonator. The properties of the resonator modes can vary strongly within a stability zone and also between different zones.

stability zones

Figure 1: Stability zones of a standing-wave laser resonator. The curves show the beam radii at the end mirrors and in the laser crystal as functions of the focusing power (dioptric power) of the thermal lens of the gain medium, which is roughly proportional to the pump power. Here, the left zone is zone II according to Magni, and the right one is zone I.

Properties of Stability Zones for Linear Resonators

The detailed properties of stability zones are very important for the issue of resonator design, in particular as a part of laser design, because the properties of a laser resonator can be essential for laser performance. Resonator stability zones have been explored in a huge volume of literature. A paper by Magni [2] presented a detailed analysis for linear resonators. Some important properties are discussed in the following:

Properties of Stability Zones for Ring Resonators

Similar to Ref. [2] for linear resonators, Ref. [3] presented an analysis for ring resonators. These have somewhat simpler properties, which however are similar to those of linear resonators in many respects:

The differences to linear resonators are related to the fact that in a ring resonator the laser beam passes the thermal lens only once per round trip, instead of twice as in a linear resonator.

Consequences for Resonator Design

Some of the consequences of such properties for the design of laser resonators (particularly for solid-state bulk lasers) are shortly discussed in the following:


[1]S. De Silvestri et al., “Novel stability diagrams for continuous-wave solid-state laser resonators”, Opt. Lett. 11 (8), 513 (1986)
[2]V. Magni, “Multielement stable resonators containing a variable lens”, J. Opt. Soc. Am. A 4 (10), 1962 (1987)
[3]S. De Silvestri et al., “Rod thermal lensing effects in solid-state laser ring resonators”, Opt. Commun. 65 (5), 373 (1988)
[4]V. Magni et al., “Recent developments in laser resonator design”, Opt. Quantum Electron. 23, 1105 (1991)
[5]N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, 2nd edn., Springer, Berlin (2005)

(Suggest additional literature!)

See also: resonator design, laser resonators, alignment sensitivity, lasers, thermal lensing, Spotlight article 2006-10-01
and other articles in the category optical resonators

Dr. R. Paschotta

This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) and software could become very valuable for your business!

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