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Thermodynamic of photoluminescence far from the radiative limit

The radiance of thermal emission, as described by Plancks law, depends only on the emissivity and temperature of a body, and increases monotonically with temperature rise at any emitted wavelength. Nonthermal radiation, such as photoluminescence (PL), is a fundamental light matter interaction that conventionally involves the absorption of an energetic photon, thermalization, and the emission of a redshifted photon. Until recently, the role of rate conservation when thermal excitation is significant, has not been studied in any nonthermal radiation. A question: What is the overall emission rate if a high quantum efficiency (QE), PL material, is heated to a temperature where it thermally emits a rate of 50 photons/sec at its bend edge, while in parallel is PL excited at a rate of 100 photons/sec. Recently, we discovered that the answer is an overall rate of 100 blueshifted photons/sec. In contrast to thermal emission, the PL rate is conserved with temperature increase, while each photon is blueshifted. Further rise in temperature leads to an abrupt transition to thermal emission where the photon rate increases sharply. These findings show that PL is an ideal optical heat pump. Here we study, for the first time, the emission rate of PL radiation at moderate QE where nonradiative processes dominate the dynamics. Though conservation of photon rate does not apply, we predict that the emission rate at 100% QE is an upper limit for the overall emission rate regardless of the QE. Also, the transition temperature to thermal emission is QE independent.