Nonlocal and Quantum Tunneling Contributions to Harmonic Generation in Nanostructures: Electron Cloud Screening Effects

Our theoretical examination of second and third harmonic generation from metal-based nanostructures predicts that nonlocal and quantum tunneling phenomena can significantly exceed expectations based solely on local, classical electromagnetism. Mindful that the diameter of typical transition metal atoms is approximately 3{\AA}, we adopt a theoretical model that treats nanometer-size features and/or sub-nanometer size gaps or spacers by taking into account: (i) the limits imposed by atomic size to fulfill the requirements of continuum electrodynamics; (ii) spillage of the nearly-free electron cloud into the surrounding vacuum; and (iii) the increased probability of quantum tunneling as objects are placed in close proximity. Our approach also includes the treatment of bound charges, which add crucial, dynamical components to the dielectric constant that are neglected in the conventional hydrodynamic model, especially in the visible and UV ranges, where interband transitions are important. The model attempts to inject into the classical electrodynamic picture a simple, perhaps more realistic description of the metal surface by incorporating a thin patina of free-electrons that screens an internal, polarizable medium.