An Improved FDTD Method to Calculate Nonlocal Response in Plasmonics

The study of nonlocal effects has become a hot topic in nano-optics. There are many models to describe nonlocal effects. One of the more widely used is the Maxwell hydrodynamics Drude model, which provides a quantum pressure correction term that can be combined with quantum first-principles calculations. However, it is usually solved by the FDTD method via the auxiliary difference equation technique where the quantum pressure correction term is converted into current density or polarization intensity. This method is severely limited, especially when the quantum pressure correction term includes electron–electron exchange energy, correlation energy, and others beyond Thomas–Fermi (TF) energy. Instead, here we propose to directly couple Maxwell's equations with a hydrodynamic model without the need for term conversion. It is confirmed as a general FDTD numerical method and can be taken as a more convenient tool for the study of nonlocal response.