THERMODYNAMIC CONSTRAINTS ON REFLECTANCE RECIPROCITY AND KIRCHHOFFS LAW

Contrary to common belief, neither reciprocity of the bidirectional re flectance distribution function (BRDF) nor the directional form of Kir chhoff's electromagnetic radiation law can be demonstrated on the basi s of energy conservation. The BRDF is generally considered reciprocal as an extension of Helmholtz reciprocity, but Helmholtz reciprocity do es not always hold. We describe the flaw in a thermodynamic demonstrat ion of reciprocity that uses an enclosure calculation. Some conclusion s can be drawn from the enclosure calculation, but reciprocity require s more restrictive conditions. We conclude that, although they can be violated, reciprocity and the directional form of Kirchhoff's law gene rally hold because of the quantum-mechanical principle of time-reversa l invariance, which applies to most materials. (C) 1998 Optical Societ y of America.