Band Structure Analysis of Three-Dimensional Photonic Crystal by the Finite-Difference Frequency-Domain Method
Date Issued
2007
Date
2007
Author(s)
Lin, Yen-Hung
DOI
en-US
Abstract
An Yee-mesh-based three-dimensional (3-D) finite-difference frequency-domain (FDFD) method is proposed for the band structure analysis of 3-D photonic crystal (PC) devices.
With uniform meshes and periodic boundary conditions in the numerical implementation, it is easy to derive eigenvalue matrix equations from Maxwell's curl equations to obtain the band structures of the 3-D PCs.
For dealing with the dielectric discontinuity in the PC structures, the index-averaging scheme is employed to improve the numerical accuracy and accelerate the numerical convergency.
In this work, two kinds of 3-D simple-cubic PCs are first considered, including spheres structures and scaffold structures. The band structures of these two PCs are obtained by using our 3-D FDFD method.
Comparsion of our results with those from other numerical methods is performed and discussed. The influence of the index-averaging scheme on the 3-D PCs analysis is also investigated.
We also consider 3-D PC slabs with finite thickness. Their band structures can be successfully obtained with non-guided modes referred as light cone in the band diagrams.
To reduce the computing time and memory, the mirror symmetry of 3-D PC slabs is introduced in the numerical simulations. The mode profiles of even and odd modes can be
obtained and coincide with other numerical investigations. We also calculate the band structures of 3-D PC slabs suspended in air, dielectric materials, and periodic backgrounds, respectively.
It is found that the phtonic bandgaps appear for larger index difference between the PC slabs and the background region.
Our 3-D FDFD algorithm is demonstrated to be a useful numerical tool to find out the band diagrams of 3-D PC structures for more practical applications.
Subjects
光子晶體
有限差分頻域法
光子晶體能帶結構
Photonic crystal
Finite-difference frequency-domain method
Photonic band structure
Type
thesis
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