Feature comparisons of 3-D vector fields using earth mover's distance
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Visualization for the Physical Sciences
Computer Graphics Forum
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We recently discovered that C-shaped sub-wavelength (nano) metallic apertures when irradiated at specific resonance frequencies have extraordinary power transmission five to six orders of magnitude beyond what is observed for conventional round or square apertures. These apertures produce optical spot sizes as small as 25-50 nm using visible light in the near-field of the aperture with a brightness 10-100 times higher than that of the illuminating beam. A proper understanding into this remarkable phenomenon can aid in the development and understanding of a multitude of applications of these apertures including dense data storage, particle manipulation, and nano-scale photonic devices. Current scalar visualization approaches typically are insufficient to significantly aid in the understanding of these complex near-field optical problems. For example, two common approaches involving either visualization of scalar electromagnetic wave amplitudes in 2-D or rudimentary arrow plots of the vector fields produced in Finite-Difference-Time- Domain simulations are clearly inadequate. Both techniques provide only partial insight into the problem, as only specific planes can be visualized and therefore the global structure of the fields cannot be readily inferred. Understanding of the three-dimensional electromagnetic vector fields and energy flows related to the illumination of nano-sized apertures is critically important in near-field applications, as simple scalar analysis is not suitable at these small dimensions [8]. 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 non-resonant 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.