Abstract
A novel finite difference time domain (FDTD) method based on space transformations is developed that overcomes the inherent obstacles of the conventional FDTD algorithm in a spatially complex domain. Our method leads to an adaptive mesh for the investigated structure based on its geometrical shape without adding additional numerical problems such as late-time instability. In this method, mesh boundaries can follow arbitrary geometrical shapes precisely meaning that discretization errors are minimized. Such errors can be considerable when dealing with large material differences or boundary conditions within the simulation domain. Different meshing and transformation techniques for a variety of different scenarios are presented. We show how boundaries discontinuity can be handled using our method without resulting artificial singularities or zeros. Unlike previous works no dispersive medium has been used so the simulation speed is similar to the standard FDTD method. The usability and superiority of this method in terms of simulation run time and accuracy are shown through a couple of scattering and plasmonic problems. Also, the result of any simulations are validated using finite element method.
Highlights
Plasmonic surfaces have found applications in many areas of science such as effective energy harvesting devices [1]–[2], biomedical applications [3], [4] and even second or third harmonic generation [5], [6]
We show that this approach is more efficient and accurate when using the standard finite difference time domain (FDTD) method
We have only discussed 2D simulations in this work, similar improved scalings should hold in 3D where we would expect a much greater time saving since the time goes as the cube of the MPU
Summary
Plasmonic surfaces have found applications in many areas of science such as effective energy harvesting devices [1]–[2], biomedical applications [3], [4] and even second or third harmonic generation [5], [6]. Surface-enhanced Raman scattering (SERS) [7] benefits from plasmonic effects thanks to the huge nonlinear enhancement of the electric field. In order to fully exploit the SERS effect, we need to use computational electromagnetics to design, optimize and investigate possible plasmonic structures. As sharp edges and nanometer size separations between nanoparticles are required for huge electric field enhancement [9], sophisticated adaptive meshing technique requiring large computational resources are typically needed to accurately model such devices.
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