3-dimensional eigenmodal analysis of plasmonic nanostructures

Abstract

We introduce a 3-dimensional electromagnetic eigenmodal algorithm for the theoretical analysis of resonating nano-optical structures. The method, a variant of the Jacobi-Davidson algorithm, solves the electric field vector wave, or curl-curl, equation for the electromagnetic eigenmodes of resonant optical structures with a finite element method. In particular, the method includes transparent boundary conditions that enable the analysis of resonating structures in unbounded space. We demonstrate the performance of the method. First, we calculate the modes of several dielectric resonator antennas and compare them to theoretically determined results. Second, we calculate the modes of a nano-cuboid and compare them to theoretically determined results. Third, we numerically analyze spherical nanoparticles and compare the result to the theoretical Mie solution. Fourth, we analyze optical dipole antenna configurations in order to assess the method's capability for solving technologically relevant problems.

Mode analysis of second-harmonic generation in plasmonic nanostructures

“…These methods can be separated into two main categories: those developed in the quasi-static [13][14][15][16][17][18][19][20][21] and dipolar [22] approximations and those using a full wave analysis method [23][24][25][26]. Each category includes several formulations, such as volume [27] and surface integral equations methods [23], direct application of the Green's tensor method [22,28], and direct expression of the electrostatic interaction between surface charges [14,[16][17][18][19]. All these methods correspond to the derivation of an eigenvalue problem.…”

An Eigenanalysis Study of Tunable THz and Photonic Unbounded Structures Employing Finite Element Method

“…Therefore, the use of a non-linear eigensolver or the incorporation of linearization technique is demanded for the solution of the eigenproblem (7). In this paper, in order to overcome the non-linearity arising from the frequency dispersive dielectric permittivity, which influences matrix [M] directly, an initial estimation for the eigenvalue k 0 0 of the expected eigenmode is performed, [51]. The main idea is to handle the non-linearity caused by the ABCs employing a linearization technique, just as in our previous work, [9], [53], assuming a given complex dielectric constant for the metallic structures.…”

Insight into the eigenmodes of plasmonic nanoclusters based on the Green’s tensor method

“…Quite a few numerical techniques that compute the eigenmodes of a system are available [34][35][36][37][38][39][40][41][42]. For example, an electrostatic eigenmode solver based on the boundary integral equation was used to show that the near field of the plasmonic structures could be expressed as the linear superposition of the eigenmodes [42].…”

“…Knowledge of the eigenmodes of a plasmonic system can also be exploited for increasing the accuracy and speed of a numerical technique [44]. However, it should be noted that the discretization of the structure necessary for computing the eigenmodes of the plasmonic structure using numerical techniques, even within the electrostatic limit, makes the solvers time consuming and memory intensive [41,42,45,46]. Furthermore, many of these techniques require initial guess values of the modes for accurate computation.…”