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.
Highlights
The interaction of nano-meter structured, metallic, aka. plasmonic, devices with light, especially from lasers, has attracted considerable interest during the last few years
We demonstrate the performance of the method by solving four different problems, namely: (i) The dielectric resonator antenna (DRA) [15, 16]: the problem is solved in the microwave region
There are no cavity walls, and the resonator structures need not be enclosed within perfect electric conductor (PEC) boundary conditions
Summary
The interaction of nano-meter structured, metallic, aka. plasmonic, devices with light, especially from lasers, has attracted considerable interest during the last few years. The concept of the antenna, in particular, transferred from the microwave to the optical region, has attracted enormous interest since the conversion of propagating light into localized, electromagnetic energy, and vice-versa, holds the promise of novel technological applications in many fields, such as in sensing, detection manipulation and communication [5,6,7,8] It is well beyond the scope of this study to give a comprehensive overview. We note that such detailed wealth of prediction comes at a price in the form of significantly increased computational effort and substantial pre- and post-processing work In between these methods is the class of semi-analytical methods that are usually more flexible with respect to geometry, but on the other hand still provide analytical insight. Both bright and dark modes [27] are investigated
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