Advanced Integral Equation and Hybrid Methods for the Efficient Analysis of General Waveguide and Antenna Structures

Three new numerical methods for the calculation of passive waveguide and antenna structures are presented in this work. They are designed to be used within a comprehensive hybrid CAD tool for the efficient analysis of those building blocks for which the fast mode-matching/2-D finite element technique cannot be applied. The advanced algorithms introduced here are doubly higher order, that is higher order basis functions are considered for current/field modeling whereas geometry discretization is performed with triangular/tetrahedral elements of higher polynomial degree

Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell's equations

The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices we have become used to in everyday life. The numerical solution of these equations is hampered by two fundamental problems: first, in the high frequency regime, very fine meshes need to be used in order to avoid the pollution effect well known for the Helmholtz equation, and second the large scale systems obtained from the vector valued equations in three spatial dimensions need to be solved by iterative methods, since direct factorizations are not feasible any more at that scale. As for the Helmholtz equation, classical iterative methods applied to discretized Maxwell equations have severe convergence problems.We explain in this paper a family of domain decomposition methods based on well chosen transmission conditions. We show that all transmission conditions proposed so far in the literature, both for the first and second order formulation of Maxwell's equations, can be written and optimized in the common framework of optimized Schwarz methods, independently of the first or second order formulation one uses, and the performance of the corresponding algorithms is identical. We use a decomposition into transverse electric and transverse magnetic fields to describe these algorithms, which greatly simplifies the convergence analysis of the methods. We illustrate the performance of our algorithms with large scale numerical simulations

Recent advances in surface enhanced Raman spectroscopy (SERS): finite difference time domain (FDTD) method for SERS and sensing applications

There have been significant advancements in the field of surface-enhanced Raman spectroscopy (SERS). Despite being an ultra-sensitive analytical technique, challenges, such as how to get a proper match between the SERS substrate and light for better signal enhancement to obtain a stable, sensitive SERS substrate, prevent its widespread applications. Finite-difference time-domain (FDTD) method, a numerical tool for modeling computational electrodynamics, has recently been used to investigate SERS for understanding the underlying physics, and optimally design and fabricate SERS substrates for molecular analysis. In this review, we summarize the trend of using FDTD method in SERS studies by providing an introduction of fundamental principles, the studies of optical responses, electromagnetic (EM) field distribution, enhancement factor (EF) of SERS, the application in design and fabrication of SERS substrates, and SERS for biosensing and environmental analysis. Finally, the critical issues of using inherently approximate FDTD method and future improvement for solving EM problems and SERS applications are discussed