Einstein Relations Connecting Broadband Emission and Absorption Spectra

作者: D. E. McCumber

DOI: 10.1103/PHYSREV.136.A954

关键词: Spontaneous emissionAbsorption spectroscopyAbsorption (logic)Stimulated emissionAtomic physicsEnergy (signal processing)Spectral lineSolid angleOmegaPhysics

摘要: Relations described by Einstein connecting the rates of spontaneous emission, stimulated and absorption radiation an atomic system in free space are generalized to apply broadband spectra quantized systems dilutely distributed a dielectric medium. Although gross features emission can be qualitatively different (especially at low temperatures), various connected any specific frequency simple expressions. For two-level imbedded medium temperature $T$, typical equations stimulated-emission cross sections $\ensuremath{\sigma}(\ensuremath{\omega})$ rate $f(\ensuremath{\omega})$ photons per unit solid angle interval are: ${\ensuremath{\sigma}}_{e}(\ensuremath{\omega})={\ensuremath{\sigma}}_{a}(\ensuremath{\omega})\mathrm{exp}[\frac{\ensuremath{\hbar}(\ensuremath{\mu}\ensuremath{-}\ensuremath{\omega})}{\mathrm{kT}}]=f(\ensuremath{\omega}){(\frac{2\ensuremath{\pi}c}{\ensuremath{\omega}n})}^{2}$, where $\ensuremath{\hbar}\ensuremath{\mu}$ is temperature-dependent excitation potential $n$ index refraction host material.

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