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Roundtrip gainRoundtrip gain refers to the laser physics, and laser cavitys (or laser resonators). It is gain, integrated along a ray, which makes a roundtrip in the cavity. Additional recommended knowledge
Roundtrip gain in geometric opticsGenerally, the Roundtrip gain may depend on the frequency, on the position and tilt of the ray, and even on the polarization of light. Usually, we may assume that at some moment of time, at reasonable frequency of operation, the gain is function of the Cartesian coordinates , , and . Then, assuming that the geometrical optics is applyable the roundtrip gain can be expressed as follows: , where is path along the ray, parametrized with functions , , ; the integration is performed along the whole ray, which is supposed to form the closed loop. In simple models, the flattop distribution of pump and gain is assumed to be constant. In the case of simlest cavity, the roundtrip gain , where is length of the cavity; the laser light is supposed to go forward and back, this leads to the coefficient 2 in the estimate. In the steadystate continuous wave operation of a laser, the roundtrip gain is determined by the reflectivity of the mirrors (in the case of stable cavity) and the magnification coefficient in the case of unstable resonator (unstable cavity). Coupling parameterThe coupling parameter of a laser resonator determines, what part of the energy of the laser field in the cavity goes out at each roundtrip. This output can be deermined by the transmitivity of the output coupler, or the magnification coefficient in the case of unstable cavity ^{[1]}. Roundtrip lossThe roundtrip loss determines, what part of the energy of the laser field becomes unusable at each roundtrip; it can be absorbed or scattered. At the selfpulsation, the gain lates to respond the variation of number of photons in the cavity. Within the simple model, the roundtrip loss and the output coupling determine the damping parameters of the equivalent oscillator Toda ^{[2]} ^{[3]}. At the steadystate operation, the roundtrip gain exactly compensate both, the output coupling and losses: . Assuming, that the gain is small (), this relation can be written as follows: Such as relation is used in analytic estimates of the performance of lasers ^{[4]}. In particular, the roundtrip loss may be one of important parameters which limit the output power of a disk laser; at the power scaling, the gain should be decreased (in order to avoid the exponential growth of the amplified spontaneous emission), and the roundtrip gain should remain larger than the background loss ; this requires to increase of the thickness of the slab of the gain medium; at certain thickness, the overheating prevents the efficient operation ^{[5]}. For the analysis of processes in active medium, the sum can be also called "loss" ^{[1]}; however, such a notation leads to a confusion as soon as we are interested, which part of the energy is absorbed and scattered, and which part of such a "loss" is actually useful output of the laser. References


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Roundtrip_gain". A list of authors is available in Wikipedia. 