Integral-Equation Formulations of Plasmonic Problems in the Visible Spectrum and Beyond

• Published in: InTech eBooks
• Main Author: Çekinmez, Abdulkerim
• Format: Book Chapter
• Language: English
• Published: IntechOpen 01.01.2017
• Subjects: Differential Equations; Mathematics
• ISBN: 9535130153; 9789535130154
• DOI: 10.5772/67216

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.