A Field-Based Surface Integral Formalism for the Nonlocal Hydrodynamic Response from Nanoparticles

In this paper, a field-based surface integral formalism is proposed for the nonlocal hydrodynamic response of a metallic particle immersed in a homogeneous dielectric background. The key difference from the classical surface integral equation (SIE) lies in an extra integral equation stemming from the governing differential equation behind the hydrodynamic model (HDM), which requires the intro- duction of an additional unknown and, accordingly, an ad- ditional boundary condition (ABC) for the solution. The derivation of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) is significantly modified. Compared to the potential-based formalism, the field-based formalism formalism can improve the computa- tion speed and ensure better convergence of results.