The Uniqueness Theorem for Nonlocal Hydrodynamic Media

We investigate a fundamental electromagnetic theorem, namely the uniqueness theorem, in the context of nonlocal electromagnetics, as simulated by a popular semiclassical model, the hydrodynamic Drude model (HDM), and extensions thereof such as the generalized nonlocal optical response (GNOR). The derivations and proofs presented here give a theoretical foundation to the use of the additional boundary conditions (ABCs), whose necessity is recognized and underlined in virtually all implementations and applications of HDM. Our proofs follow a mathematically relaxed style, borrowing from the literature of established electromagnetics textbooks that study the matter from an engineering perspective. Through this simpler route, we deduce clear and intuitive material-response requirements for uniqueness to hold, while using a familiar parlance in a topic that is mostly studied through a physics perspective. Two numerical examples that examine the problem from either a semianalytical or a purely numerical viewpoint support our findings.