Publication # 450

450. David A. B. Miller, Linxiao Zhu, and Shanhui Fan, "Universal modal radiation laws for all thermal emitters," PNAS 114, no. 17, 4336-4341 (2017) doi:10.1073/pnas.1701606114


Radiation laws must relate the fraction of incident radiation absorbed by an object and the amount of radiation emitted when it is hot so that objects can come to the same temperature just by exchanging electromagnetic radiation. Such laws are fundamentally important and set limits to practical applications such as in the conversion of light to electricity and in heat and thermal management generally. Kirchhoff’s classic results work well in many situations, but fail in others (specifically for “nonreciprocal” materials), and were derived using simplified models that do not apply to modern nanotechnology and light beams. We derive revised versions of laws that avoid these problems and discover additional and unexpected radiation laws that substantially expand the fundamental relations between optical absorption and emission.


We derive four laws relating the absorptivity and emissivity of thermal emitters. Unlike the original Kirchhoff radiation law derivations, these derivations include diffraction, and so are valid also for small objects, and can also cover nonreciprocal objects. The proofs exploit two recent approaches. First, we express all fields in terms of the mode-converter basis sets of beams; these sets, which can be uniquely established for any linear optical object, give orthogonal input beams that are coupled one-by-one to orthogonal output beams. Second, we consider thought experiments using universal linear optical machines, which allow us to couple appropriate beams and black bodies. Two of these laws can be regarded as rigorous extensions of previously known laws: One gives a modal version of a radiation law for reciprocal objects—the absorptivity of any input beam equals the emissivity into the “backward” (i.e., phase-conjugated) version of that beam; another gives the overall equality of the sums of the emissivities and the absorptivities for any object, including nonreciprocal ones. The other two laws, valid for reciprocal and nonreciprocal objects, are quite different from previous relations. One shows universal equivalence of the absorptivity of each mode-converter input beam and the emissivity into its corresponding scattered output beam. The other gives unexpected equivalences of absorptivity and emissivity for broad classes of beams. Additionally, we prove these orthogonal mode-converter sets of input and output beams are the ones that maximize absorptivities and emissivities, respectively, giving these beams surprising additional physical meaning.

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