Editing Optical cavity (section)

==Practical resonators==
If the optical cavity is not empty (e.g., a laser cavity which contains the gain medium), the value of ''L'' needs to be adjusted to account for the index of refraction of the medium. Optical elements such as lenses placed in the cavity alter the stability and mode size. In addition, for most gain media, thermal and other inhomogeneities create a variable lensing effect in the medium, which must be considered in the design of the laser resonator.

Practical laser resonators may contain more than two mirrors; three- and four-mirror arrangements are common, producing a "folded cavity". Commonly, a pair of curved mirrors form one or more confocal sections, with the rest of the cavity being quasi-[[collimated]] and using plane mirrors. The shape of the laser beam depends on the type of resonator: The beam produced by stable, paraxial resonators can be well modeled by a [[Gaussian beam]].  In special cases the beam can be described as a single transverse mode and the spatial properties can be well described by the Gaussian beam, itself.  More generally, this beam may be described as a superposition of transverse modes.  Accurate description of such a beam involves expansion over some complete, orthogonal set of functions (over two-dimensions) such as [[Hermite polynomials]] or the [[Ince polynomials]].  Unstable laser resonators on the other hand, have been shown to produce fractal shaped beams.<ref>{{cite journal |first=G. P. |last=Karman |display-authors=etal |title=Laser optics: Fractal modes in unstable resonators |journal=Nature |volume=402 |issue=6758 |page=138 |year=1999|doi=10.1038/45960 |bibcode=1999Natur.402..138K |s2cid=205046813 |doi-access=free }}</ref>

Some intracavity elements are usually placed at a beam waist between folded sections. Examples include [[acousto-optic modulator]]s for [[cavity dumping]] and [[vacuum]] [[spatial filter]]s for [[transverse mode]] control. For some low power lasers, the laser gain medium itself may be positioned at a beam waist. Other elements, such as [[filter (optics)|filter]]s, [[prism (optics)|prisms]] and [[diffraction grating]]s often need large quasi-collimated beams.

These designs allow compensation of the cavity beam's [[Aberration in optical systems|astigmatism]], which is produced by [[Brewster's angle|Brewster-cut]] elements in the cavity. A Z-shaped arrangement of the cavity also compensates for [[coma (optics)|coma]] while the 'delta' or X-shaped cavity does not.

Out of plane resonators lead to rotation of the beam profile and more stability. The heat generated in the gain medium leads to frequency drift of the cavity, therefore the frequency can be actively stabilized by locking it to unpowered cavity. Similarly the pointing stability of a laser may still be improved by spatial filtering by an [[optical fibre]].

=== Alignment ===
[[File:Metrology-system-paper-4.jpg|thumb|Alignment of a folded cavity using an autocollimator<ref>{{cite web |last=Aharon |url=http://www.plxinc.com/white-papers/metrology-system-for-inter-alignment-of-lasers-telescopes-and-mechanical-datum |title=Metrology System for Inter-Alignment of Lasers, Telescopes, and Mechanical Datum}}</ref>]]
Precise alignment is important when assembling an optical cavity. For best output power and beam quality, optical elements must be aligned such that the path followed by the beam is centered through each element.

Simple cavities are often aligned with an alignment laser—a well-collimated visible laser that can be directed along the axis of the cavity. Observation of the path of the beam and its reflections from various optical elements allows the elements' positions and tilts to be adjusted.

More complex cavities may be aligned using devices such as electronic [[autocollimator]]s and [[laser beam profiler]]s.