此篇論文介紹利用週期性結構的高反射特性，來設計位於W頻帶(75~　110 GHz)的低損耗率的矩形波導管，此週期性結構由高折射率的介電質與低折射率的介電質交互週期排列，其每一層介電質的厚度由破壞性干涉的原理來決定，此結構將可看見周期性的高反射率頻帶，在此頻帶內反射率將趨近於一，利用此特性來設計波導管，可以得到損耗率低於任何金屬波導管。另外我們亦會討論金屬波導管耦合進入Bragg waveguide的效率，以及利用時域分析討論TE01模的穿透。

We investigate the transmission loss of the rectangular waveguide mode (TE01) at W-band with a Bragg structured sidewall. To design and fabricate the Bragg sidewall, we first study the propagation properties of a periodic multilayer structure, each layer consisting of a high refractive index and a low refractive index dielectric material. The thicknesses of dielectric materials are properly designed to form the destructive interference at the operating region. The periodic bandgap is observed with the reflection coefficient close to unity at the stop band. This Bragg sidewall can perfectly confine the energy in the rectangular waveguide with extremely low attenuation much lower than any metallic wave guide.

致謝.............................i
摘要.............................ii
Abstract.........................iii
目錄.............................iv
附圖目錄..........................v
Chapter1 緒論.............1
1.1 兆赫波簡介................1
1.2 兆赫波-應用...............1
1.3 研究動機..................3
Chapter2 Bragg mirror......5
2.1 理論推導..................5
2.2 Matching for destructive interference at different incident angle..................10
2.3 Bloch wave in PSS.......11
2.4 Experiment result.......15
Chapter3 Bragg waveguide..17
3.1 Bragg parallel waveguide.17
3.2 Bragg rectangular waveguide.18
3.3 理論結果..................23
3.4 Comparison between Matlab code and HFSS simulation..31
3.5 Cladding mode............33
Chapter4 Modal analysis...37
4.1 HFSS simulation..........37
4.2 模式分析理論計算...........37
4.3 模式分析結果..............40
4.4 Time domain analysis.....47
Chapter5 實驗設計與數據.....52
5.1 實驗設計..................52
5.2 實驗數據分析..............54
Chapter6 結論..............56
References........................57

[1] Chang, T.H. “Lecture Note of Course Electrodynamics.”
[2] Mendis, R., Nag, A., Chen, F. & Mittleman, D. M. A tunable universal
terahertz filter using artificial dielectrics based on parallel-plate waveguides.
Appl. Phys. Lett. 97, 131106, 10.1063/1.3495994 (2010).
[3] L. Ye, R. Xu, Z. Wang, and W. Lin, “A novel broadband coaxial probe to
parallel plate dielectric waveguide transition at THz frequency,” Optics
Express, vol. 18, no. 21, pp. 21725-21731, 2010/10/11, 2010.
[4] Y. Zhao, and D. R. Grischkowsky, “2-D Terahertz Metallic Photonic Crystals
in Parallel-Plate Waveguides,” IEEE Transactions on Microwave Theory and
Techniques, vol. 55, no. 4, pp. 656-663, 2007.
[5] S. Harsha, N. Laman, D. Grischkowsky, "High-Q terahertz Bragg resonances
within a metal parallel plate waveguide", Appl. Phys. Lett., vol. 94, 2009.
[6] H. Zhan, R. Mendis, and D. M. Mittleman, “Superfocusing terahertz waves
below λ/250 using plasmonic parallel-plate waveguides,” Optics Express, vol.
18, no. 9, pp. 9643-9650, 2010/04/26, 2010.
[7] E. S. Lee, J.-K. So, G.-S. Park, D. Kim, C.-S. Kee, and T.-I. Jeon, “Terahertz
band gaps induced by metal grooves inside parallel-plate waveguides,” Optics
Express, vol. 20, no. 6, pp. 6116-6123, 2012/03/12, 2012.
[8] Z. Abbas, R. D. Pollard, and R. W. Kelsall, “A rectangular dielectric
waveguide technique for determination of permittivity of materials at W-
band,” IEEE Transactions on Microwave Theory and Techniques, vol. 46, no.
12, pp. 2011-2015, 1998.
[9] Fischer, BM, M Walther and P Uhd Jepsen. “Far-Infrared Vibrational Modes of DNA Components Studied by Terahertz Time-Domain Spectroscopy.”
Physics in medicine and biology 47, no. 21 (2002):3807.
[10] Federici, John F, Brian Schulkin, Feng Huang, Dale Gary, Robert Barat, Filipe
Oliveria and David Zimdars. “Thz Imaging and Sensing for Security
Applications-Explosives, Weapons and Drugs.” Semiconductor Science and
Technology 20, no. 7 (2005): S266
[11] J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless
communications,” J. Appl. Phys. 107(11), 111101 (2010).
[12] P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans.
Microw. Theory Tech. 52(10), 2438–2447 (2004).
[13] C. Kulesa, “Terahertz spectroscopy for astronomy: from comets to
cosmology,” IEEE Trans. THz Sci. Tech. (Paris) 1, 232–240 (2011).
[14] S. Atakaramians, S. Afshar V, T. M. Monro, and D. Abbott, “Terahertz
dielectric waveguides,” Advances in Optics and Photonics, vol. 5, no. 2, pp.
169-215, 2013/06/30, 2013.
[15] B.-S. Sun, X.-L. Tang, X. Zeng, and Y.-W. Shi, “Characterization of
cylindrical terahertz metallic hollow waveguide with multiple dielectric
layers,” Applied Optics, vol. 51, no. 30, pp. 7276-7285, 2012/10/20, 2012.
[16] Y. Matsuura, and E. Takeda, “Hollow optical fibers loaded with an inner
dielectric film for terahertz broadband spectroscopy,” Journal of the Optical
Society of America B, vol. 25, no. 12, pp. 1949-1954, 2008/12/01, 2008.
[17] X.-L. Tang, Y.-W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission
characteristics of terahertz hollow fiber with an absorptive dielectric inner-
coating film,” Optics Letters, vol. 34, no. 14, pp. 2231-2233, 2009/07/15,2009.
[18] X.-L. Tang, Y.-W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission
characteristics of terahertz hollow fiber with an absorptive dielectric inner-
coating film,” Optics Letters, vol. 34, no. 14, pp. 2231-2233, 2009/07/15,
2009.
[19] Jackson, John David. Classical Electrodynamics: Wiley . 1999.
[20] T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, “Terahertz
time-domain spectroscopy studies of the optical constants of the nematic
liquid crystal 5CB,” Applied Optics, vol. 42, no. 13, pp. 2372-2376,
2003/05/01, 2003.
[21] R. Mendis, and D. M. Mittleman, “An investigation of the lowest-order
transverse-electric (TE1) mode of the parallel-plate waveguide for THz pulse
propagation,” Journal of the Optical Society of America B, vol. 26, no. 9, pp.
A6-A13, 2009/09/01, 2009.
[22] R. Mendis, and D. M. Mittleman, “Comparison of the lowest-order
transverse-electric (TE1) and transverse-magnetic (TEM) modes of the
parallel-plate waveguide for terahertz pulse applications,” Optics Express, vol.
17, no. 17, pp. 14839-14850, 2009/08/17, 2009.
[23] R. Mendis, and D. Grischkowsky, “Undistorted guided-wave propagation of
subpicosecond terahertz pulses,” Optics Letters, vol. 26, no. 11, pp. 846-848,
2001/06/01, 2001.
[24] Pozar, David M. Microwave Engineering: John Wiley & Sons, 2009.
[25] M. van Exter and D. Grischkowsky, “Carrier dynamics of electrons and holes
in moderately doped silicon,” Phys. Rev. B, vol. 41, pp. 12140–12149, 1990.