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ility 4 practical resonators toggle practical resonators subsection 4 1 alignment 5 optical delay lines 6 see also 7 references 8 further reading toggle the table of contents optical cavity 19 languages العربية беларуская català deutsch español eesti فارسی français עברית italiano 日本語 한국어 lietuvių bahasa melayu nederlands português русский türkçe 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikimedia commons wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia redirected from laser cavity arrangement of mirrors a glass nanoparticle is suspended in an optical cavity an optical cavity resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that confines light waves similarly to how a cavity resonator confines microwaves optical cavities are a major component of lasers surrounding the gain medium and providing feedback of the laser light they are also used in optical parametric oscillators and some interferometers light confined in the cavity reflects multiple times producing modes with certain resonance frequencies modes can be decomposed into longitudinal modes that differ only in frequency and transverse modes that have different intensity patterns across the cross section of the beam many types of optical cavities produce standing wave modes different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them flat mirrors are not often used because of the difficulty of aligning them to the needed precision the geometry resonator type must be chosen so that the beam remains stable i e the size of the beam does not continually grow with multiple reflections resonator types are also designed to meet other criteria such as a minimum beam waist or having no focal point and therefore no intense light at a single point inside the cavity optical cavities are designed to have a large q factor meaning a beam undergoes many oscillation cycles with little attenuation 1 in the regime of high q values this is equivalent to the frequency line width being small compared to the resonant frequency of the cavity resonator modes edit types of two mirror optical cavities with mirrors of various curvatures showing the radiation pattern inside each cavity light confined in a resonator will reflect multiple times from the mirrors and due to the effects of interference only certain patterns and frequencies of radiation will be sustained by the resonator with the others being suppressed by destructive interference in general radiation patterns which are reproduced on every round trip of the light through the resonator are the most stable these are known as the modes of the resonator 2 resonator modes can be divided into two types longitudinal modes which differ in frequency from each other and transverse modes which may differ in both frequency and the intensity pattern of the light the basic or fundamental transverse mode of a resonator is a gaussian beam resonator types edit the most common types of optical cavities consist of two facing plane flat or spherical mirrors the simplest of these is the plane parallel or fabry pérot cavity consisting of two opposing flat mirrors 3 4 5 6 7 8 9 while simple this arrangement is rarely used in large scale lasers due to the difficulty of alignment the mirrors must be aligned parallel within a few seconds of arc or walkoff of the intracavity beam will result in it spilling out of the sides of the cavity however this problem is much reduced for very short cavities with a small mirror separation distance l 1 cm plane parallel resonators are therefore commonly used in microchip and microcavity lasers and semiconductor lasers in these cases rather than using separate mirrors a reflective optical coating may be directly applied to the laser medium itself the plane parallel resonator is also the basis of the fabry pérot interferometer for a resonator with two mirrors with radii of curvature r 1 and r 2 there are a number of common cavity configurations if the two radii are equal to half the cavity length r 1 r 2 l 2 a concentric or spherical resonator results this type of cavity produces a diffraction limited beam waist in the centre of the cavity with large beam diameters at the mirrors filling the whole mirror aperture similar to this is the hemispherical cavity with one plane mirror and one mirror of radius equal to the cavity length a common and important design is the confocal resonator with mirrors of equal radii to the cavity length r 1 r 2 l 10 11 12 13 14 15 this design produces the smallest possible beam diameter at the cavity mirrors for a given cavity length and is often used in lasers where the purity of the transverse mode pattern is important a concave convex cavity has one convex mirror with a negative radius of curvature this design produces no intracavity focus of the beam and is thus useful in very high power lasers where the intensity of the light might be damaging to the intracavity medium if brought to a focus less common resonator types include optical ring resonators and whispering gallery mode resonators in which a resonance is formed by waves moving in a closed loop rather than reflecting between two mirrors stability edit stability diagram for a two mirror cavity blue shaded areas correspond to stable configurations only certain ranges of values for r 1 r 2 and l produce stable resonators in which periodic refocussing of the intracavity beam is produced if the cavity is unstable the beam size will grow without limit eventually growing larger than the size of the cavity mirrors and being lost by using methods such as ray transfer matrix analysis it is possible to calculate a stability criterion 16 0 1 l r 1 1 l r 2 1 displaystyle 0 leqslant left 1 frac l r_ 1 right left 1 frac l r_ 2 right leqslant 1 values which satisfy the inequality correspond to stable resonators the stability can be shown graphically by defining a stability parameter g for each mirror g 1 1 l r 1 g 2 1 l r 2 displaystyle g_ 1 1 frac l r_ 1 qquad g_ 2 1 frac l r_ 2 and plotting g 1 against g 2 as shown areas bounded by the line g 1 g 2 1 and the axes are stable cavities at points exactly on the line are marginally stable small variations in cavity length can cause the resonator to become unstable and so lasers using these cavities are in practice often operated just inside the stability line a simple geometric statement describes the regions of stability a cavity is stable if the line segments between the mirrors and their centers of curvature overlap but one does not lie entirely within the other in the confocal cavity if a ray is deviated from its original direction in the middle of the cavity its displacement after reflecting from one of the mirrors is larger than in any other cavity design this prevents amplified spontaneous emission and is important for designing high power amplifiers with good beam quality practical resonators edit 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 17 some intracavity elements are usually placed at a beam waist between folded sections examples include acousto optic modulators for cavity dumping and vacuum spatial filters 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 filters prisms and diffraction gratings often need large quasi collimated beams these designs allow compensation of the cavity beam s astigmatism which is produced by brewster cut elements in the cavity a z shaped arrangement of the cavity also compensates for 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 edit alignment of a folded cavity using an autocollimator 18 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 autocollimators and laser beam profilers optical delay lines edit optical cavities can also be used as multipass optical delay lines folding a light beam so that a long path length may be achieved in a small space a plane parallel cavity with flat mirrors produces a flat zigzag light path but as discussed above these designs are very sensitive to mechanical disturbances and walk off when curved mirrors are used in a nearly confocal configuration the beam travels on a circular zigzag path the latter is called a herriott type delay line a fixed insertion mirror is placed off axis near one of the curved mirrors and a mobile pickup mirror is similarly placed near the other curved mirror a flat linear stage with one pickup mirror is used in case of flat mirrors and a rotational stage with two mirrors is used for the herriott type delay line the rotation of the beam inside the cavity alters the polarization state of the beam to compensate for this a single pass delay line is also needed made of either a three or two mirrors in a 3d respective 2d retro reflection configuration on top of a linear stage to adjust for beam divergence a second car on the linear stage with two lenses can be used the two lenses act as a telescope producing a flat phase front of a gaussian beam on a virtual end mirror see also edit optical feedback multiple prism grating laser oscillator or multiple prism grating laser cavity coupled mode theory vertical cavity surface emitting laser references edit paschotta rüdiger q factor encyclopedia of laser physics and technology rp photonics lotsch h k v 1967 the scalar theory for optical resonators and beam waveguides optik 26 112 130 fox a g li t 1961 resonant modes in a maser interferometer bell syst tech j 40 2 453 488 doi 10 1002 j 1538 7305 1961 tb01625 x ismail n kores c c geskus d pollnau m 2016 fabry pérot resonator spectral line shapes generic and related airy distributions linewidths finesses and performance at low or frequency dependent reflectivity optics express 24 15 16366 16389 bibcode 2016oexpr 2416366i doi 10 1364 oe 24 016366 pmid 27464090 lotsch h k v 1968 the fabry perot resonator part i optik 28 65 75 lotsch h k v 1969 the fabry perot resonator part ii optik 28 328 345 lotsch h k v 1969 the fabry perot resonator part iii optik 28 555 574 lotsch h k v 1969 the fabry perot resonator part iv optik 29 130 145 lotsch h k v 1969 the fabry perot resonator part v optik 29 622 623 boyd g d gordon j p 1961 confocal multimode resonator for millimeter through optical wavelength masers bell syst tech j 40 2 489 508 doi 10 1002 j 1538 7305 1961 tb01626 x boyd g d kogelnik h 1962 generalized confocal resonator theory bell syst tech j 41 4 1347 1369 doi 10 1002 j 1538 7305 1962 tb03281 x lotsch h k v 1969 the confocal resonator system i optik 30 1 14 lotsch h k v 1969 the confocal resonator system ii optik 30 181 201 lotsch h k v 1970 the confocal resonator system iii optik 30 217 233 lotsch h k v 1970 the confocal resonator system iv optik 30 6 563 576 yariv amnon 1989 quantum electronics 3rd ed wiley p 142 isbn 0 4716 0997 8 karman g p et al 1999 laser optics fractal modes in unstable resonators nature 402 6758 138 bibcode 1999natur 402 138k doi 10 1038 45960 s2cid 205046813 aharon metrology system for inter alignment of lasers telescopes and mechanical datum further reading edit koechner william solid state laser engineering 2nd ed springer verlag 1988 an excellent two part review of the history of optical cavities siegman anthony e 2000 laser beams and resonators the 1960s pdf ieee journal of selected topics in quantum electronics 6 6 1380 1388 bibcode 2000ijstq 6 1380s citeseerx 10 1 1 205 5688 doi 10 1109 2944 902192 s2cid 15892498 archived from the original pdf on 2007 01 07 retrieved 2006 08 01 cite journal cite uses deprecated parameter citeseerx help siegman anthony e 2000 laser beams and resonators beyond the 1960s pdf ieee journal of selected topics in quantum electronics 6 6 1389 1399 bibcode 2000ijstq 6 1389s citeseerx 10 1 1 205 5995 doi 10 1109 2944 902193 s2cid 796212 archived from the original pdf on 2007 01 07 retrieved 2006 08 01 cite journal cite uses deprecated parameter citeseerx help authority control databases international gnd national united states france bnf data czech republic israel other idref yale lux v t e lasers types chemical dye bubble liquid crystal gas carbon dioxide excimer helium neon ion nitrogen free electron diode solid state er yag nd yag raman ruby ti sapphire x ray science active medium amplified spontaneous emission continuous wave laser ablation laser linewidth lasing threshold population inversion ultrashort pulse optics beam expander beam homogenizer chirped pulse amplification gain switching gaussian beam injecti...