Plasmonic nano antennas are highly attractive at optical frequencies due to their strong resonances -even when their size is smaller than the wavelength -and because of their potential of extreme field enhancement. Such antennas may be applied for sensing of biological nano particles as well as for single molecule detection. Because of considerable material losses and strong dispersion of metals at optical frequencies, the numerical analysis of plasmonic antennas is very demanding. An additional difficulty is caused when very narrow gaps between nano particles are utilized for increasing the field enhancement. In this paper we discuss the main difficulties of time domain solvers, namely FDTD and FVTD and we compare various frequency domain solvers, namely the commercial FEM packages JCMsuite, Comsol, HFSS, and Microwave Studio with the semi-analytic MMP code that may be used as a reference due to its fast convergence and high accuracy.

Abstract. We present a numerical model for time domain reflectometry (TDR) signal propagation in dispersive dielectric materials. The numerical probe model is terminated with a parallel circuit, consisting of an ohmic resistor and an ideal capacitance. We derive analytical approximations for the capacitance, the inductance and the conductance of three-wire probes. We couple the time domain model with global optimization in order to reconstruct water content profiles from TDR traces. For efficiently solving the inverse problem we use genetic algorithms combined with a hierarchical parameterization. We investigate the performance of the method by reconstructing synthetically generated profiles. The algorithm is then applied to retrieve dielectric profiles from TDR traces measured in the field. We succeed in reconstructing dielectric and ohmic profiles where conventional methods, based on travel time extraction, fail.

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 nanoparticle. 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.

Considerable effort has been invested into numerical models of scanning near-field optical microscopy during the last years. The finite difference time domain method, using an orthogonal discretization scheme, has often been used for full-wave three-dimensional studies. Because optical near-field configurations are often characterized by curvilinear shapes, locally refined, tetrahedral grids are better suited to describe the geometry. Where fine geometrical details must be resolved or the field solution is expected to vary rapidly, the elements are made smaller while in the other regions a coarser mesh can be used, thereby reducing the size of the problem and promoting computational efficiency. In this study, we use a finite element approach that solves the electric field vector wave (curl-curl) equation in the time domain (FETD) to investigate a novel, scanning near-field optical probe concept with asymmetric cladding. A specific advantage of the finite element method is its inherent capability to discretize the curl-curl equation in a non-uniform way. The finite element method is therefore particularly suited to approximate the geometry of an optical near-field configuration. We model a simplified setup, introduce specific approximations and discuss the method's capabilities and its potential for modeling more complex configurations.

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