Topology visualization of the optical power flow through a novel C-shaped nano-aperture

An ideal visualization tool that has not been used before in studying the optical behavior of near-field apertures is three-dimensional vector field topology. The global view of the vector field structure is deduced by locating singularities (critical points) within the field and augmenting these points with nearby streamlines. We have used for the first time, to the best of our knowledge, three-dimensional topology to analyze the topological differences between a resonant C-shaped nano-aperture and various nonresonant conventional apertures. The topological differences between these apertures are related to the superiority in power throughput of the C-aperture versus conventional round and square sub-wavelength apertures. We demonstrate how topological visualization techniques provide significant insight into the energy enhancement mechanism of the C aperture, and also shed light on critical issues related to the interaction between multiple apertures located in close proximity to each other, which gives rise to cross-talk, for example as a function of distance. Topological techniques allow us to develop design rules for the geometry of these apertures and their desired spot sizes and brightness. The performance of various sub-wavelength apertures can also be compared quantitatively based on their topology. Since topological methods are generically applicable to tensor and vector fields, our approach can be readily extended to provide insight into the broader category of finite-difference-time-domain nano-photonics and nano-science problems.