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Extra info for 44.Photonics Technology
Until the early twentieth century, wave experiments were essentially limited to the visible part of the electromagnetic spectrum, although sound waves, which can exhibit coherence, were also studied. Coherent radiation sources now cover the electromagnetic spectrum from ultra-low frequency (ULF) waves used for underwater communications, through millimeter-waves, and the far infrared (FIR) and infrared (IR) regions of the spectrum, to the vacuum ultraviolet (VUV). Freeelectron devices, including microwave tubes and free-electron lasers (FELs), cover most of this range, while atomic lasers are predominant in the IR-UV range.
Finally, this result must be independent of the equilibrium temperature, thus yielding the following relations for the coefficients: B12 = B21 } 3 ω12 B π 2 c3 21 (51) = A21 (52) This result shows that for an idealized, two-level atomic system, the transition rates can be expressed in terms of a single coefficient. Simple considerations also lead to the fact that, in thermal equilibrium, the emission rate stimulated by the blackbody photons is proportional to the spontaneous emission rate and the average photon number in the radiation modes at the transition frequency Ͷ12: A21 = exp B21Wt (ω12 ) }ω12 kB T −1 (53) For example, at room temperature, the wavelength scale of thermal radiation is of the order of 50 Ȑm, and thermally 549 stimulated emission will dominate at longer wavelengths.
In the context of quantum mechanics, atomic levels can be viewed as the stable interference of electron wavefunctions in the Coulomb field of the nucleus. The experiments of Clinton Joseph Davisson and Lester Halbert Germer (1) first demonstrated the diffraction of electron waves by a nickel crystal. Recently, remarkable experiments using Bose-Einstein condensates to generate coherent atomic beams have been performed at MIT (2), where the coherence of the condensate wavefunction was verified by measuring its interference with a second atomic beam.