Improved Finite-Difference Frequency-Domain Method for Modal Analysis of Optical Waveguides and Photonic Crystal Devices
Date Issued
2004
Date
2004
Author(s)
Yu, Chin-Ping
DOI
en-US
Abstract
An improved finite-difference frequency-domain (FDFD) method is
proposed for the modal analysis of optical waveguides and photonic
crystal (PC) devices. For dealing with the dielectric discontinuity
in the waveguide structures, the electromagnetic fields at both
sides of the dielectric interface are approximated by interpolation
and extrapolation and the continuity boundary conditions (BCs) are
fulfilled. To obtain the lossy properties of optical waveguides, the
perfectly matched layers (PMLs) are employed as the BCs of the
computing window in this FDFD model.
The calculated results of 1-D slab waveguides and 2-D optical fibers
demonstrate that this improved FDFD formula can efficiently increase
the numerical accuracy and reduce the numerical errors caused by the
oblique and curved dielectric interfaces. Utilizing this FDFD model,
the leaky properties of 1-D ARROWs structures can be successfully
obtained. For channel and rib waveguides with dielectric corners in
the structures, it can also provide sufficiently accurate numerical
results. This FDFD model is also demonstrated possessing the ability
in reducing the demand of the size of the computing window. Besides,
the FDFD model is successfully applied to analyze the
characteristics of PC related devices, including planar PC
waveguides, photonic crystal fibers, and PC resonant cavities. The
properties of the guided and leaky modes of the PC devices are
obtained and a good agreement with other numerical simulations is
achieved.
As for the analysis of band structures of 2-D PCs, a compact FDFD
eigenvalue algorithm with rapid numerical convergence is proposed.
The band diagrams, photonic band gaps (PBGs), and the finger plots
of 2-D PCs are obtained. The proposed method can perform better than
other popularly used numerical methods.
Subjects
有限差分法
光子晶體
有限差分頻域法
光波導
optical waveguide
photonic crystal
finite difference method
Finite difference frequency domain method
Type
thesis
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