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

Abstract 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 an...

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Autores principales:	Ekembu K. Tanyi, Brandi T. Burton, Evgenii E. Narimanov, M. A. Noginov
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/381814156a004de287f9bbac1e25569d
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spelling	oai:doaj.org-article:381814156a004de287f9bbac1e25569d2021-12-02T16:08:00ZThermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law10.1038/s41598-017-01544-32045-2322https://doaj.org/article/381814156a004de287f9bbac1e25569d2017-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-01544-3https://doaj.org/toc/2045-2322Abstract 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.Ekembu K. TanyiBrandi T. BurtonEvgenii E. NarimanovM. A. NoginovNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-11 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Ekembu K. Tanyi Brandi T. Burton Evgenii E. Narimanov M. A. Noginov Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law
description	Abstract 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.
format	article
author	Ekembu K. Tanyi Brandi T. Burton Evgenii E. Narimanov M. A. Noginov
author_facet	Ekembu K. Tanyi Brandi T. Burton Evgenii E. Narimanov M. A. Noginov
author_sort	Ekembu K. Tanyi
title	Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law
title_short	Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law
title_full	Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law
title_fullStr	Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law
title_full_unstemmed	Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law
title_sort	thermal radiation of er doped dielectric crystals: probing the range of applicability of the kirchhoff’s law
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/381814156a004de287f9bbac1e25569d
work_keys_str_mv	AT ekembuktanyi thermalradiationoferdopeddielectriccrystalsprobingtherangeofapplicabilityofthekirchhoffslaw AT branditburton thermalradiationoferdopeddielectriccrystalsprobingtherangeofapplicabilityofthekirchhoffslaw AT evgeniienarimanov thermalradiationoferdopeddielectriccrystalsprobingtherangeofapplicabilityofthekirchhoffslaw AT manoginov thermalradiationoferdopeddielectriccrystalsprobingtherangeofapplicabilityofthekirchhoffslaw
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Thermal radiation of Er doped dielectric crystals: Probing the range of applicability of the Kirchhoff’s law

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