Sum rules and scaling in nonlinear optics

Nonlinear optics is a mature field characterized by a wealth of phenomena that are well understood. The microscopic origins of these phenomena are known to be in the quantum process of light-matter interactions; yet, no general prescription is available for optimizing the nonlinear response. It is even more difficult to understand the important features of a complex system that lead to the best response. This paper reviews work on how scaling, with the use of sum rules, can be applied to identify universal properties associated with a large nonlinear-optical response. An analysis using sum rules and scaling unifies our understanding of the nonlinear-optical response of a broad class of quantum systems through the scale-invariant intrinsic nonlinearities.