Kramers-Kronig Relations for Nonlinear Optical Materials and Metamaterials: New Sum Rules for Harmonic Generation

In this talk, we discuss the application of Kramers-Kronig-like relations for harmonic generation. From these integral relations, rooted in causality, and quantum-mechanical basis functions, we derive new sum rules for the second harmonic generation process. We also discuss an alternative quantum mechanical derivation, their application to two- and three-level systems, and their connection to the empirical Miller’s rule.