Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law

Kirchhoff’s law of thermal radiation, relating emissivity and absorptance is commonly formulated for opaque bodies in thermodynamic equilibrium with the environment. However, in many systems of practical importance, both assumptions are often not satisfied. We revisit the century-old law and examine the limits of its applicability in an example of Er:YAG and Er:YLF dielectric crystals–potential radiation converters for thermophotovoltaic applications. The (80 at.%) Er:YAG crystal is opaque between 1.45 μm and 1.64 μm. In this spectral range, its absorptance α(λ) is spectrally flat and differentiates from unity only by a small amount of reflection. The shape of the emissivity spectrum ɛ(λ) closely matches that of absorptance α(λ), implying that the Kirchhoff’s law can adequately describe thermal radiation of opaque bodies, even if thermodynamic equilibrium is not satisfied. The (20 at.%) Er:YLF crystal had smaller size, lower concentration of Er ions, and it was not opaque. Nevertheless, its spectrum of emissivity had almost the same shape (between 1.45 μm and 1.62 μm) as the absorptance derived from the transmission measurements. Our results are consistent with the conclusion that the Kirchhoff’s law of thermal radiation can be extended (with caution) to not-opaque bodies away from the thermodynamic equilibrium.