The presentation consists of two parts. In the first part, we present our recent work on fast electromagnetic integral equation solvers for complex structures. In particular, we address representations for the computation of Green’s functions for complex environments including layered and periodic environments. Then we discuss how these representations can be used to rapidly evaluate spatial convolutions between the Green’s functions and extended source distributions by using hierarchical decomposition methods and interpolations. We demonstrate how these methods can be implemented on conventional Central Processing Unit (CPUs) and new Graphics Processing Unit (GPU) based computing systems. Coupled with iterative integral equation solvers these codes can allow for the rapid analysis and design of complex and large-scale microwave and optical devices.
Using the developed analytical and computational methods, in the second part of the talk, we discuss phenomena of optical wave guidance and radiation occurring on chains, viz. linear arrays, of metallic (plasmonic) nanoparticles of several types. In particular, we demonstrate that nanoparticle chains coupled with surfaces support a variety of optical phenomena, including traveling and leaky waves of different types. We show these waves can remain bound to the chain, radiate into surface wave beams, or radiate into space and surface wave beams. Radiation into surface waves may be exploited to create a leaky surface-wave antenna with potential applications to surface wave microscopy. Next we study optical waves on twisted nanoparticle chains, in which the chain elements are anisotropic and their axis in the transverse direction is twisted with a certain angle between consecutive chain elements. We show that such elements support traveling waves that can be either bound to the chain or radiate out of the chain. The properties of these twisted chains are unique in that due to the twist and periodicity they share properties of chiral (helical) waveguides and general periodic gratings. Such twisted chains and related phenomena can be used to construct waveguides and optical antennas for optical polarization control.
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