Boundary methods for optical nano structures

Abstract

In this paper, boundary methods for solving Maxwell equations are outlined with a focus on the Multiple Multipole Program (MMP) that is very advanced and well suited when high reliability and accuracy of the results is required. After the presentation of the Generalized Point Matching (GPM) technique, that is currently the best method when matrices with high condition numbers shall be handled, different field expansions are given and applied to relatively simple structures for demonstrating the concept. Simple 2D and 3D simulations are shown as illustrations. After this, a method for the efficient handling of axi-symmetric structures by means of ring multipoles is presented. Finally, the method is applied to a few illustrative structures that exhibit attractive features, namely plasmon resonances and optical nano jets. General remarksCurrently, nanotechnology provides the possibility to fabricate structures below 1 micron size that are resonant at optical wavelengths. Resonating structures and even more systems of coupled resonators lead to many pronounced physical effects that are fascinating, promising for new applications, and difficult to understand at the same time. Typical examples are dielectric photonic crystals [1,2], metallic photonic crystals [3], and more general metamaterials [4] that allow one to obtain materials with electromagnetic or optical properties that are not available in natural materials, for example, very high, very low, or even negative index of refraction [5].Because of the difficulties, limitations, and costs of nano fabrication, it is of high importance that optical nano structures are carefully designed and analyzed by means of numerical simulations. Since the most interesting effects are based on resonances, the corresponding software must be based on Maxwell theory. It is well-known, that the standard Maxwell equations do not describe the atomistic light matter interaction that is usually accounted for by means of macroscopic material models. In order to simplify the procedure, the macroscopic material models are kept as easy as possible. For example, one often assumes that an optical material is at least piecewise homogeneous, isotropic, linear, loss-free, non-magnetic, and free of dispersion; that it does not change its properties in time; and so on. These simplifications are not only helpful but they also cause inaccuracies of the simulations and sometimes prevent one from finding attractive effects that might be exploited in the future. A very important restriction of the macroscopic description is its validity for the analysis of particles that are so small that they only consist of a few layers of atoms or molecules. Measurements of gold nano spheres [6] demonstrated that the macroscopic, complex permittivity seems to have a slightly larger imaginary part for spheres with 10 nm diameter then for

Discontinuous Galerkin methods in nanophotonics

“…Among the wide range of available methods we find a large number of techniques for specific applications. For example, the multiple multipole technique (MMP) is ideally suited to simulate spheroidal particles [14]. The Wannier function expansion can accurately describe large-scale photonic crystals with a comparatively small number of degrees of freedom [15,16].…”

Plasmonic oligomers in cylindrical vector light beams

“…3 as well presents the simulated extinction spectra for different structures. The spectra have been calculated by using the MMP method [17]. It is apparent that the experimental results show a good qualitative agreement with the numerical predictions.…”

Optical Sensing with Simultaneous Electrochemical Control in Metal Nanowire Arrays

“…A simulation of the field decay length and the extinction spectrum was performed by the multiple multipole program (MMP) using the MaX-1 software package [38]. Various geometries (e.g., width, height, rounding of the corners) have been simulated and compared to experimental data.…”