Statistics and thermodynamics of luminescent radiation

We have investigated luminescent radiation produced by semiconductor lasers. By using the grand canonical ensemble for the radiation field produced by the recombination of electron-hole pairs, the power spectrum and thermodynamic functions (i.e., total energy, entropy, and radiation pressure) are derived in the context of quantum statistics. The correlation function of the luminescent radiation field is also calculated and compared with blackbody radiation. Numerical calculations are performed to study the effect of the band gap and chemical potential of the luminescent material on the correlation function and various thermodynamic functions; for example, we consider the deviation of the total-energy density from the predictions of the Stefan-Boltzman law. The stimulated emission case is discussed with the introduction of negative temperature. Finally, the probability distribution and fluctuations of the photon numbers in the radiation field are discussed.