Computational modeling of nano-plasmonic structures is essential to understand their electrodynamic responses before experimental efforts in measurement setups. Similar to the other ranges of the electromagnetic spectrum, there are alternative methods for the numerical analysis of nano-plasmonic problems, while the optics literature is dominated by differential equations that require discretizations of the host media with artificial truncations. These approaches often need serious assumptions, such as periodicity, infinity, or self-similarity, in order to reduce the computational load. On the other hand, surface integral equations based on integro-differential operators can bring important advantages for accurate and efficient modeling of nano-plasmonic problems with arbitrary geometries. Electrical properties of materials, which may be obtained either experimentally or via physical modeling, can easily be inserted into integral-equation formulations, leading to accurate predictions of electromagnetic responses of complex structures. This chapter presents the implementation of such accurate, efficient, and reliable solvers based on appropriate combinations of surface integral equations, discretizations, numerical integrations, fast algorithms, and iterative techniques. As a case study, nanowire transmission lines are investigated in wide-frequency ranges, demonstrating the capabilities of the developed implementations.
Part of the book: Dynamical Systems
In this chapter, we present a comparative study of nanowire arrays for the purpose of transmitting electromagnetic energy to long distances with minimum loss. Silver nanowires at an infrared frequency are considered as a case study, using an accurate simulation environment based on the surface-integral equations and the multilevel fast multipole algorithm (MLFMA). Reliable numerical results are obtained by considering arrays as three-dimensional structures with finite sizes in all dimensions. Nanowires with different cross sections are compared in alternative array configurations to assess and compare their transmission properties. While there are no significantly varying performances for the arrays of few elements, large discrepancies occur as the number of nanowires increases. We show that arrays involving nanowires with hexagonal cross sections in hexagonal arrangements can provide significantly better power transmissions in comparison to others. We also present the superiority of a particular case, where the nanowires and gaps between them, both with hexagonal cross sections, are equally distributed, leading to a honeycomb structure. This type of structures demonstrates high-quality transmissions that can be useful in diverse application areas, such as optical coupling, subwavelength imaging, and energy harvesting.
Part of the book: Nanowires