An Algebraic Approach to Light-Matter Interactions

A theoretical and computational framework for the study and engineering of light-matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light-matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T-matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach. This is a review of an algebraic approach to light-matter interactions that is theoretically powerful and computationally friendly. Theoretical expressions can be developed and manipulated conveniently thanks to the generality of the basis on which the approach rests, and a compact notation. The tight connections to popular computational tools allow one to readily perform numerical calculations. image