The dielectric waveguide component has become a mature industry in these days in making it and understanding how it works. There are many theoretical and numerical methods to solve these waveguide modes. For example, the rigorous vectorial coupled transverse mode integral equation formulation (VCTMIE), finite-difference frequency-domain method (FDFD), vectorial beam propagation method (VBPM) and modal expansion method with simple bases (MEMSB)¡Ketc. With the exception of the MEMSB method and the alike, all these methods work very hard to handle interface boundaries and many require many terms meet the convergence requirements.
In this thesis, we propose a rigorous modal expansion method based on a set of orthogonal transverse magnetic bases to analyze arbitrarily profiled 2-D cylindrical dielectric waveguides. First, we expand the mode field solution of a general multi-layered waveguide by linear combination of 1D homogeneous solutions. Magnetic and components are chosen for its continuity property across the material interface. The choice of Magnetic field over electric field also reduces the number of terms and minimizes the Gibb¡¦s phenomenon. Our new vector bases eliminate the numerical difficulty of working with the singular term of the cylindrical differential operators. When compared with the results using simple bases, we further reduce one quarter of terms without loosing any accuracy.
Although the process of deriving the formulation of this vector cylindrical basis expansion technique is complex because Bessel functions and their derivatives are involved, the resulting matrix eigenvalue-eigenvector equation is much simpler than that of the simple bases and the new the result is also more accurate. We also extended the analysis to study the 2-D cylindrical dielectric waveguide problem.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0706105-172702 |
| Date | 06 July 2005 |
| Creators | Liu, Han-qiang |
| Contributors | Mei-Ying Chang, Tzong-Lin Wu, Hung-Wen Chang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0706105-172702 |
| Rights | campus_withheld, Copyright information available at source archive |
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