Unitary control of optical absorption and emission

Thermal radiation is a pervasive phenomenon, with significant implications in renewable energy, imaging, and sensing technologies. Unitary control changes the absorption and emission of an object by transforming the external light modes that the photonic structures interact with. It is widely used in applications and underlies coherent perfect absorption. However, two basic questions remain unanswered: (i) Given a specific object, what are the achievable absorptivity, emissivity, and nonreciprocal contrast for each mode under unitary control? (ii) How can the desired absorptivity, emissivity, or nonreciprocal contrast for each mode be obtained through unitary control? The first question seeks to understand the capabilities and limitations of unitary control, while the second question focuses on practical implementation. Here, we provide a complete solution to both questions using the mathematical theory of majorization. We demonstrate that unitary control can achieve perfect violation or preservation of Kirchhoff's law in nonreciprocal objects, as well as uniform absorption or emission for any object.