Electromagnetic Fields Scattered by Sub-Wavelength Sized Object of Drude Type Material in the Optical Region, Using a Finite Element Time Domain Method

The concept of antennas has found renewed interest in near-field optics and the optics of nanometer-structured systems where dimensions are significantly smaller than the wavelength . Optical antennas usually consist of a combination of dielectric and metallic materials. Similar concepts are increasingly studied for nanometer-structured field-emission cathodes and field emitter arrays (FEA). They are used for time-resolved electron interferometry, imaging and for sources in particle accelerators where both single-tip emitters and FEA are currently studied. In this study we implement a finite element time domain (FETD) algorithm for the calculation of the electric field involving metals in the visible range of the electromagnetic spectrum, using a dispersive Drude dielectric model. We compute the distribution of the electric field for an optical antenna setup, consisting of a sharpened dielectric fiber tip and an attached gold nano-particle of sub-wavelength size, excited by an incoming plane wave from the negative z-axis that impinges onto the gold nano-particle. We demonstrate the existence of spots of light of sub-wavelength dimensions, instrumental for circumventing the diffraction limit, i.e., to be able to detect objects smaller than about half the wavelength. We also model the coupling of the incoming plane wave into the dielectric fiber tip via the gold nano-particle. Finally, we demonstrate the importance of the finite element approach. Due to its inherent level of detail (LoD) it allows for the efficient discretization of configurations with a wide span of scales, from nanometer to micrometer, and, equally important, for the conformal and therefore more accurate discretization of curved geometrical features.