Abstract

One can predict the thermal emission spectrum of any material from the knowledge of its absorbance and its temperature: this is the Kirchhoff–Planck law. We show that if McCumber’s relation holds and if the spatial distribution of the excited state is uniform, the Kirchhoff–Planck law can be generalized by introducing the chemical potential difference between the metastable and ground manifolds involved in the transition. The proposed formalism makes it possible to determine the emission spectra of an optical structure driven out of equilibrium solely from its transmission and reflection spectra and the level of excitation, considerably simplifying computations compared to a direct approach. An example is shown for a multilayer with embedded luminescent ions. Experimental emission spectra from Yb3+-doped Y2O3 taken at and out of thermal equilibrium are found to be in qualitative agreement with the theory.

© 2011 Optical Society of America

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