On the band structures and defect states of planar photonic crystals
Date Issued
2007
Date
2007
Author(s)
Lin, Jhih-Chang
DOI
en-US
Abstract
Photonic bandgap materials are becoming more and more important in optoelectronic applications. Recently, the study of the defect states of photonic crystals with microcavity has received the attention on the applications of lasers, filters, and modulators. Band structures and defect modes are two main characteristics of the photonic crystals. According to the analysis of band structures, traditional methods are usually used to determine the band structures by the cosine of Bloch phase. However, it may have the numerical instability problem about solving band structures of some photonic crystals. As a result, a novel model to express the relationships among the tangential fields at any layer interface of multi-layer waveguides is presented in this study. The bandedge equations instead of the traditional dispersion equations are derived in order to determine band structures accurately and more easily.
Based on the analysis of defect states, it may cause the numerical instability by using traditional methods. In addition, it will result spurious solutions from solving defect states of photonic crystals and eliminate the spurious solutions by checking the exponential function of the Bloch phase. Therefore, this study presents a new method to analyze the defect states of photonic crystals. Adopting this method, the problem of numerical instability and spurious solutions can be avoided in this analysis.
Subjects
光子晶體
缺陷態
帶隙結構
平面波導
週期結構
photonic crystal
band structure
defect state
planar waveguide
periodic structure
Type
thesis
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