Effective Cross-sections
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Effective Cross-sections
The McCumber relation (or McCumber theory) is a relationship between the effective cross-sections of absorption and emission of light in the physics of solid-state lasers.D.E.McCumber. Einstein relations connecting broadband emission and absorption spectra. PRB 136 (4A), 954–957 (1964)P.C.Becker, N.A.Olson, J.R.Simpson. ''Erbium-doped fiber amplifiers: fundamentals and theory'' (Academic, 1999). It is named after Dean McCumber, who proposed the relationship in 1964. Definition Let \sigma_(\omega) be the effective absorption cross-section \sigma_(\omega) be effective emission cross-sections at frequency \omega, and let ~T~ be the effective temperature of the medium. The McCumber relation is :(1) \frac\exp\!\left( \frac\right) =\left(\frac\right)_T =\exp\!\left( \frac\right) where \left(\frac\right)_T is thermal steady-state ratio of populations; frequency \omega_ is called "zero-line" frequency; \hbar is the Planck constant and k_ is the Boltzmann constant. Note that th ...
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Solid-state Laser
A solid-state laser is a laser that uses a gain medium that is a solid, rather than a liquid as in dye lasers or a gas as in gas lasers. Semiconductor-based lasers are also in the solid state, but are generally considered as a separate class from solid-state lasers, called laser diodes. Solid-state media Generally, the active medium of a solid-state laser consists of a glass or crystalline "host" material, to which is added a "dopant" such as neodymium, chromium, erbium, thulium or ytterbium.Z. Su, J. D. Bradley, N. Li, E. S. Magden, Purnawirman, D. Coleman, N. Fahrenkopf, C. Baiocco, T. Adam, G. Leake, D. Coolbaugh, D. Vermeulen, and M. R. Watts (2016"Ultra-Compact CMOS-Compatible Ytterbium Microlaser" ''Integrated Photonics Research, Silicon and Nanophotonics 2016'', IW1A.3. Many of the common dopants are rare-earth elements, because the excited states of such ions are not strongly coupled with the thermal vibrations of their crystal lattices (phonons), and their operati ...
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Heisenberg Uncertainty Principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, ''x'', and momentum, ''p'', can be predicted from initial conditions. Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Introduced first in 1927 by the German physicist Werner ...
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