三維結構的微波跨越波導，可經由簡化成二維問題以利我們數值計算，二維結構的跨越波導因為具有良好的對稱結構，故分析時我們把波導分成四個小部分結構，且只需模擬其中四分之一部分，利用邊界條件為電牆或磁牆的組合，計算出四種情況的反射係數，最後再利用波導結構的對稱性加以線性組合可算出全區反射、水平穿透和垂直透射係數。本論文提出一個混合直角座標區域和圓柱座標區域中的模態匹配方法來解決二維微波跨越波導的反射問題，在兩座標重疊的區域裡取一曲線做模態匹配，利用這條曲線上解析連續條件－切線場連續、垂直微分場連續來求得反射係數。計算出來的反射、水平穿透和跨越透射能量可精確至第3位小數，計算的結果滿足能量守恆並且可與本實驗室的積分方程法模擬結果互相比較驗證。

We show that a 3-D microwave crossing waveguide can be solved by a 2-D scalar Helmholtz equation with combining boundary conditions for TE and TM modes. Furthermore the crossing waveguide possesses a symmetry along two diagonal axes passing through the origin. Computation of the EM wave fields is decomposed into four smaller tasks of computing reflection coefficient vector of a parallel plate waveguide terminated with a corner made of two perfectly electric or magnetic conducting walls (PECW/PMCW).

In this thesis, we propose a mixed Cartesian and polar coordinate mode-matching method to solve this 2-D corner cube microwave reflection problem. The solution is obtained by applying the continuity condition of both the tangential field and its normal derivative along a given curve inside the overlapped region of the two coordinate systems. We are able to compute up to the third decimal place of the reflection, through and cross transmission coefficients. All results pass the energy conservation test and are verified and compared with those computed by Integral equation method simulation.

目 錄
誌謝 I
中文摘要 II
Abstract III
目錄 IV
第一章 導論 1
1-1 簡介 1
1-2 研究動機 2
1-3 馬克斯威爾方程式 4
1-4 平面電磁波 6
第二章 理論模型 8
2-1 解析連續法 8
2-2 時變電磁場(赫姆霍茲方程式)的邊界值問題 12
2-3 三維問題簡化為二維問題之推導 16
2-4 微波跨越波導的模態 19
第三章 微波跨越波導分析理論 23
3-1 介於直角和圓柱座標中的模態匹配 23
3-2 直角座標中的模態匹配 30
3-3 圓柱座標中的模態匹配 34
第四章 數值計算模擬結果 38
4-1 微波跨越波導的模擬 38
4-2 跨越波導的模擬結果 40
第五章 結論與未來工作 61
參考文獻 63
附錄 65

1. Menzel, Wolfgang and Ingo Wolff, “A method for calculating the frequency-dependent properties of microstrip discontinuities”, IEEE Trans. Microwave Theory Tech. Vol. MTT-25, pp. 107 – 112, 1977.
2. Hammer, M., “Hybrid analytical/numerical coupled-mode modeling of guided-wave devices,” Journal of Lightwave Technology, Vol. 25, pp. 2287 – 2298, 2007.

3. Li, J., D. A. Fattal and R. G. Beausoleil, “Crosstalk-free design for the intersection of two dielectric waveguides,” Optics Express, Vol. 17, pp. 7717–7724, 2009.

4. H.-W. Chang and W.-C. Cheng “Analysis of dielectric waveguide termination with tilted facets by analytic continuity method,” J. of Electromagn. Waves and Appl., Vol. 21, No. 12, 1653-1662, 2007.

5. Ishimaru, A., Electromagnetic Propagation, Radiation, and Scattering, Prentice Hall, Englewood Clifffs, N. J., 1991.

6. Keqian Zhang, Dejie Li, “Electromagnetic Theory for Microwaves and Optoelectronics”, Second Edition.

7. J.-C. Wu, “Analysis of dielectric waveguide termination with a slighty tilted facet,” Master Thesis, Institute Electro-Optical Engineering, National Sun Yet-sen University, Taiwan, 2004.

8. David K. Cheng, “Field and Wave Electromagnetics”, Second Edition.

9. H.-W. Chang, Y.-H. Wu and W.-C. Cheng, “Hybrid FD-FD Analysis of Crossing Waveguides by Exploiting Both the Plus and the Cross Structural Symmetry,” Progress In Electromagnetics Research, PIER 103, pp. 217–240, 2010.


10. W.-C. Cheng, “FD-FD analysis of a dielectric waveguide crossing,” PhD Thesis, Institute Electro-Optical Engineering, National Sun Yat-sen University, Taiwan, 2009.

11. Chang, H.-W., and M.-H. Sheng, “Field analysis of dielectric waveguide devices based on coupled transverse-mode integral equation—mathematical and numerical formulations,” Progress In Electromagnetics Research, PIER 78, pp. 329–347, 2008.