Investigation into nanowire coupling efficiency through the simulation of Maxwell’s equation
Date Issued
2016
Date
2016
Author(s)
Kao, Chien-Yu
Abstract
An explicit finite-difference scheme for solving the three-dimensional Maxwell’s equations in staggered grids is presented in time domain. The aim of this thesis is to solve the Faraday’s and Amp`ere’s equations in time domain within the discrete zero-divergence context for the electric and magnetic fields (or Gauss’s law). The local conservation laws in Maxwell’s equations are also numerically preserved all the time using proposed the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme. Following the method of lines, the spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then properly discretized to get a phase very accurate solution. To achieve the goal of getting the best dispersive characteristics, this centered scheme minimizes the difference between the exact and numerical phase velocities. The significant dispersion and anisotropy errors manifested normally in finite difference time domain methods are therefore much reduced. The dual-preserving (symplecticity and dispersion relation equation) solver is numerically demonstrated to be efficient for use to get in particular a long-term accurate Maxwell’s solution. By applying the developed FDTD scheme, we aim to study the wave propagation issue on nanowires. The efficency of evanescent coupling between two air-clad silica nanowires with diameter D = 350nm in HE11 single-mode operation is addressed. In the overlapping region, we can see that the electric, magnetic and poynting fields vary between two nanowires by cutting 2D-planes and 1D-Y-axis with different a streamwise positions. From the property of conservation of energy of Poynting theory, we confirm the validity of the propoesd finite difference method. Based on the computed 3D result of solving the Maxwell’s equations, we can clearly predict not only the streamlines of eletric and magnetic fields of HE11 mode in two nanowires but can also reveal the streaklines of them in the overlapping region.
Subjects
staggered grids
Evanescent wave
silica nanowires
coupling efficiency
numerical phase velocities
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-105-R03525003-1.pdf
Size
23.54 KB
Format
Adobe PDF
Checksum
(MD5):212cf3c1a0f067c29eec246521ecd457