A previous paper analyzed in detail the difficulties associated with the application of numerical methods to Hallén's integral equation with the approximate kernel for the case of a lossless surrounding medium. The present paper extends to the case where the medium is conducting and points out similarities and differences between the two cases. Our main device is an analytical/asymptotic study of the antenna of infinite length.
A novel computational scheme that models the scattering of light at interfaces in a deep-nanometric (deep-nm) plasmonic system is presented. The nonclassical effects associated with the collective motion of free electrons in metals of the system are investigated by a nonlocal hydrodynamic (HD) model. Due to the HD model, three types of interfaces, that is, the dielectric-dielectric interface, the dielectric-metal interface, and the metal-metal interface, are distinguished. The scattering of light at these interfaces is described by Boundary Integral Equations (BIEs), which are constructed by using the surface equivalence principle, the concept of the Green' function and the interface conditions. The BIEs are numerically solved by the boundary element method (BEM) for 3D nanoparticles of arbitrary shapes. To validate, the computed results are first quantitatively contrasted with analytical solutions from the Mie theory for spherical core-shell structures, with good agreements being demonstrated in both the near field and the far field. Then, a qualitative study is performed for dimers consisting of spheres with various gap sizes for both the classical local response model and the nonlocal HD model. The observed trends agree well with the results reported in previous works.
We alleviate the unnatural oscillations occurring in the current distribution along a linear cylindrical antenna center-driven by a delta-function generator and embedded in a conducting medium. The intensely fluctuating current arises as a small-z0 asymptotic (or numerical) solution of the classical integral equations of antenna theory, for a cylindrical dipole of infinite (or finite) length, where z0 is the discretization length. To alleviate the oscillations, we employ an appropriate effective current further to the recent remedy of oscillations attained for a perfectly conducting linear cylindrical antenna of finite length for the case where the surrounding medium is free space. We derive asymptotic formulas for the infinite antenna, which are then put to numerical test. Furthermore, we point to the physical significance of the effective current whose function transcends a mere computational device.
A novel boundary element implementation that models multiple scattering of plasmonic nanowires is presented. The modeling is based on potentials and the materials constituting the wires can be local (described by the local response model) or nonlocal (described by the nonlocal hydrodynamic model). The nonlocal hydrodynamic model (HDM) provides an important approximation describing nonclassical effects associated with the collective motion of free electrons in metals. The modeling is challenging as different interface conditions are needed at a boundary which separates 1) a local medium from a local medium; 2) a local (nonlocal) medium from a nonlocal (local) medium; and 3) a nonlocal medium from a nonlocal medium. The algorithm can address constructs of arbitrary geometry and material composition within the HDM; thus, it becomes a complete numerical tool for exploration of nonlocal nanowires. Fictitious sources are imposed at the boundaries, linking the scattered fields to the imposed sources, and matching the interface conditions at the boundaries. This procedure yields a set of Boundary Integral Equations (BIEs). Then, the BIEs are numerically solved utilizing the Boundary Element Method (BEM). The results from the BEM solver are verified quantitatively and qualitatively showing good agreement in both the near-and the far-field regimes.
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