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Blackbody Theory for Hyperbolic Materials

Abstract : The blackbody theory is revisited in the case of thermal electromagnetic fields inside uniaxial anisotropic media in thermal equilibrium with a heat bath. When these media are hyperbolic, we show that the spectral energy density of these fields radically differs from that predicted by Planck's blackbody theory and that the maximum of the spectral energy density determined by Wien's law is redshifted. Finally, we derive the Stefan-Boltzmann law for hyperbolic media which becomes a quadratic function of the heat bath temperature. In 1901, Planck [1] derived the famous law describing the spectral distribution of energy of a blackbody (BB) by introducing the concept of quantum of light, so laying the foundation of quantum physics. In his description of the problem, the electromagnetic field inside a cavity made with opaque walls, which is set at a constant temperature, is studied. In this formulation [2], the cavity is at thermal equilibrium and acts as a heat bath. The walls of the cavity emit and absorb electromagnetic waves so that the field itself becomes equilibrated. The internal energy density of the electromagnetic field in the cavity with volume V for both principal polarization states (abbreviated by s and p) is then given by U
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Svend-Age Biehs, Slawa Lang, Alexander Petrov, Manfred Eich, Philippe Ben-Abdallah. Blackbody Theory for Hyperbolic Materials. Physical Review Letters, American Physical Society, 2015, 115 (17), pp.174301. ⟨10.1103/PhysRevLett.115.174301⟩. ⟨hal-01335142⟩

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