Unitary control of optical absorption and emission: theory and algorithm

Unitary control changes the optical absorption and emission of an object by transforming the external modes. We answer two basic questions: Given an object, what absorptivity, emissivity, and their difference are attainable via unitary control? How to obtain given absorptivity, emissivity, and their difference? We show that both questions can be answered using the mathematics of majorization. We further provide explicit algorithms for the practical implementation of unitary control.