Resonator Cavity

1/16/13Article on optical resonators, cavities - Encyclopedia of Laser Physics and Technology ENCYCLOPEDIA OF OF HOME C A TEGORIES A N B O C P SEA RCH LINKS D Q E R SPOTLIGHT QUIZ F S G T part of the V irtual L ibrary L ASER P HYSICS ASER HYSICS ADVERTISING AND AND T ECHNOLOGY ECHNOLOGY ENCYCLOPEDIA F EEDBA CK H U I V J W K X L Y M Z RP PHOTONICS BUYER'S OFGLOSSA RY L ASERPAPHITS HYSICSRP PHOTONICS BUYER'S AND T ECHNOLOGY GE GUIDE GUIDE The ideal place for finding UYER'S RP PHOTONICS B suppliers! GUIDE This resource is provided by RP Photonics Consulting GmbH. Optical Resonators Definition: arrangements of optical components which allow a beam of light to circulate <<< | >>> | Feedback You can get technical consulting from the author, Dr. Rüdiger Paschotta. RP Fiber Power 4.0 BUYER'S GUIDE BUYER'S GUIDE 2 suppliers for optical resonators are listed. BUYER'S GUIDE Get your entry! Your are not yet listed? 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. This software is a powerful tool for designing fiber amplifiers and fiber lasers. New: ultrashort pulse propagation! See the comprehensive description and nice demos videos! The Encyclopedia in Book Form The two-volume print version of the encyclopedia would deserve a place in your institute or group library! Click on the image to get to Wiley-VCH. 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 (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 www.rp-photonics.com/optical_resonators.html 1/5 rp-photonics. For example. A linear bulk resonator can have two stability zones (see below). and twice per round trip in a linear resonator (except for the end mirrors). light Figure 1: A simple linear experiences various physical effects optical resonator with a which change its spatial curved folding mirror (top) and a four-mirror bow-tie distribution: diffraction. there can be more stability zones.1/16/13 Article on optical resonators. www. ring resonators are sometimes preferred for resonant frequency doubling with a laser source which is sensitive against optical feedback.g. there are rays which exhibit an unlimited increase in transverse offset. When light is injected into a linear resonator via a partially transparent mirror.) The non-normal incidence of light on every resonator mirror of a ring resonator causes astigmatism if a resonator mirror has a curved surface. and thus may not require any dielectric mirror. A linear resonator with the output coupler at an end does not exhibit this phenomenon. focusing or ring resonator (bottom). An optical component within a resonator is hit by the light once per round trip in the case of a ring laser. A ring resonator has only one stability zone. in special cases also gain guiding.Encyclopedia of Laser Physics and Technology different directions (see also: ring lasers). a resonator may contain additional optical elements which are passed in each round trip. reflected light can propagate back to the light source. For unstable resonators. defocusing effects of optical elements (sometimes involving optical nonlinearities). Monolithic ring resonators with high Q factor can exploit total internal reflection at all surfaces. so that they will leave the optical system. (If the internal lens is passed more than once per round trip in the ring resonator. During a resonator round trip. A ring resonator has no end mirrors. or of a resonator arm length. If there is an output coupler mirror. this leads to two different output beams. a laser resonator contains a gain medium which can compensate the resonator losses in each round trip of the light. cavities . etc. A bow-tie ring resonator geometry is often used to minimize astigmatism by keeping the incidence angles small. In either case. saturable absorption. or more than twice in the linear resonator. for variation of the dioptric power of an internal lens. Some important differences between linear resonators and ring resonators are: In a ring resonator. This is not the case for a ring resonator.com/optical_resonators. Therefore. light can circulate in two different directions. e. 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.html 2/5 . and differ very much between stable and unstable resonators (see above). Another possibility is to use a partially transmissive output coupler mirror with a transverse variation of reflectivity (Gaussian reflectivity mirrors). The mode properties can be calculated using an ABCD matrix algorithm. For stable resonators. particularly those with very high output power and high laser gain.1/16/13 Article on optical resonators. the resonator may go through one (for ring resonators) or two (for standing-wave resonators) stability zones [1]. the transverse mode size varies along the resonator axis. where a better beam quality may be achieved. Generally. electric field distributions which are selfreproducing (apart from a possible loss of power) in each resonator round trip. if the waveguide properties are constant. if single-mode fibers are used. e. When a parameter such as an arm length or the dioptric power of focusing element in the resonator is varied. For each of the transverse mode patterns. These are called the mode frequencies or resonance frequencies and are approximately equidistant (but not exactly equidistant due to chromatic dispersion). At the edges of such stability zones.e. This means that the FSR becomes smaller as the resonator length is increased. more complicated shapes correspond to higher-order modes. the mode properties depend on the overall optical setup.com/optical_resonators. Most solid-state bulk lasers are based on stable resonators. which can be calculated only with numerical means. and is constant everywhere in the resonator. is the inverse round-trip time. The lowest-order mode (axial mode. The frequency spacing of the resonator modes. The ratio of the frequency spacing to the width of the resonances (resonator bandwidth) is called the www. The properties of resonator modes depend very much on various details: In waveguide resonators. Only a single transverse mode shape may exist. fundamental mode) has the simplest profile. there are only certain optical frequencies for which the optical phase is selfconsistently reproduced after each round trip (i. The modes of unstable resonators have rather complicated properties. Unstable resonators exhibit a much more complicated mode structure. other focusing effects. the transverse mode structure is determined by the waveguide properties only. and the alignment sensitivity may also diverge.rp-photonics. 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). also called free spectral range (FSR). but unstable resonators have advantages in certain lasers.g. and the distances between the components.g. In bulk-optical resonators. cavities . with Hermite–Gaussian functions. or more precisely the inverse round-trip group delay. basically the curvature of reflecting surfaces. the beam sizes at the resonator ends can diverge or go toward zero. Resonator Modes Resonator modes are essentially self-consistent field distributions of light – more precisely.Encyclopedia of Laser Physics and Technology The stability of a resonator depends on the properties and arrangement of the optical components.html 3/5 . the round-trip phase shift is an integer multiple of 2π). the transverse mode patterns can be described e. g. Some interesting aspects are: The modes of a resonator with a transverse variation of optical gain or loss in general do not form an orthogonal set of functions. cavities . the elements of the ABCD matrix and the Gaussian beam radius can be complex numbers. and so-called twisted beams.g. there are interesting effects such as image rotation. the circulating intracavity power can then greatly exceed the input power by means of resonant enhancement (→ enhancement cavities).rp-photonics. The article on resonator modes gives more details. Application of Optical Resonators Optical resonators are used for. light can be fed into the resonator from outside. and the spatial shapes are also matched (→ mode matching). the total power in a superposition of such modes is not simply the sum of the power in the different modes. Resonant Enhancement If e. There are technically interesting methods (often of numerical nature) for designing a resonator with given properties. this means that the pulse period matches the resonator's round-trip time. Subtle Properties of Bulk-optical Resonators The physics of bulk-optical resonators is surprisingly rich in nature. the following purposes: as laser resonators. when the frequencies of the pulse train match the optical resonances.1/16/13 Article on optical resonators. 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. the frequency of a laser is locked to a resonance frequency of a www. or an integer fraction of it.g. A related measure is the Q factor. e. Under some conditions. For example.g. Particularly for low-loss resonators. Resonant enhancement is also possible for a regular train of light pulses. The design of a laser resonator has important influences on various aspects of laser operation.g. on the alignment sensitivity and the beam quality..Encyclopedia of Laser Physics and Technology finesse and is determined by the power losses per resonator round trip. where e. In situations with general astigmatism (such as in some nonplanar ring laser resonators). which is the ratio of resonance frequency and bandwidth.com/optical_resonators. where the resonator losses are compensated by a gain medium to maintain or build up optical power as etalons for filtering the frequency content of optical radiation for filtering the transverse (→ mode cleaner cavities) shape of optical radiation as short-term optical frequency standards (when e. These non-normal modes have some peculiar properties.html 4/5 . an end mirror is partially transparent. In the time domain. e. polarization rotation. resonators with nonnormal modes can be treated with complex Gaussian beam analysis. resonator modes. finesse.Encyclopedia of Laser Physics and Technology stable reference cavity) for precise length measurements. Mill Valley. C A (1986) [4] N. stability zones. Q factor.1/16/13 Article on optical resonators. Lalanne et al. Laser Resonators and Beam Propagation. Berlin (2005) See also: cavities. RP Photonics Consulting GmbH All rights reserved worldwide Last update: 2012-10-03 www. in order to achieve efficient frequency doubling of light from a low-power singlefrequency laser for precisely measuring low-level losses by recording the decay of the power of intracavity radiation (cavity ring-down spectroscopy) for generating chromatic dispersion effects. Opt. Spotlight article 2009-04-05 How do you rate this article? Your general impression: Technical quality: Usefulness: Readability: C omments: don't know poor satisfactory good excellent don't know don't know don't know poor poor poor satisfactory satisfactory satisfactory good good good excellent excellent excellent If you want a response.g. Am. E. 2 (6). free spectral range. Rüdiger Paschotta.html 5/5 . enhancement cavities. A 4 (10). mode matching. resonator design. you may leave your e-mail address in the comments field. Weber. Hodgson and H. e. 2nd edn. e. mode cleaner cavities.. Fabry–Pérot interferometers. 514 (2008) [3] A. Submit © Dr. unstable resonators. reference cavities. “Photon confinement in photonic crystal nanocavities”. Soc. Laser & Photon. cavities . e. Siegman.g. bandwidth. Spotlight article 2006-11-21. Springer. Lasers. with a Gires–Tournois interferometer Bibliography [1] V. 1962 (1987) [2] P.. modes. laser resonators.com/optical_resonators. University Science Books. Magni. Spotlight article 200611-28. “Multielement stable resonators containing a variable lens”. etalons.g. Rev. J.rp-photonics. exploiting the periodically occurring resonances when the resonator length is changed for exploiting the resonant enhancement of intracavity power (→ enhancement cavities). or directly send an e-mail.