本論文主要是以傳輸矩陣法研究三個一維光子晶體結構的光學特性及其相關的應用。第一個主題中我們試著以兩種不同材料的光子晶體構成1/4波長布拉格反射鏡，並在兩反射鏡之間加上具負折射的缺陷層以設計成一個多層膜費比-普洛共振器。我們利用傳輸矩陣法推出穿透率對特定工作波長的解析解，得到兩個在設計上的選擇規則，並探討入射角和吸收對透射譜的影響。鑑於目前負折射材料均為人工介質，光在此類介質傳播具色散的特性，因此我們也探討了色散的影響。在第二個主題裡我們探討一維光子晶體的異質結構的特性。從模擬中我們發現當構成異質結構的兩光子晶體的帶隙有重疊時，異質結構的全方向反射頻譜較形成它的原先兩光子晶體之全方向反射頻譜都要來得大。我們也討論了缺陷對異質結構反射譜的影響。最後一個主題我們針對一個摻雜質的光量子井結構，分別計算當其缺陷分別為正折射、負折射以及單負介質的透射譜，當缺陷層為不同材料時，此結構可以用來作多通道的濾波器或是多通道的光學開關，而藉由改變缺陷的個數或是其介電常數，我們可以調整通道的個數及濾波的頻率。

In this thesis, we study the optical and electromagnetic properties of three one-dimensional multilayer structures by using the “ transfer matrix method” (TMM).
In the first topic, we design a multilayer Fabry-Perot resonator (FPR) with two different quarter-wave stacks-dielectric mirrors by setting a left handed material (LHM) defect between them. From the analytic solution for single designed wavelength by TMM, we found there will be two selection rules when we design it to make resonant peaks exist. The influences of the incidence angle and loss on the reflectivity are also studied. Because LHMs are artificially engineered structures which have dispersive permittivity and permeability, we have a practical design for an artificial metamaterial LHM defect operating at wavelength 600 nm.
In the second topic, we studied the omnidirectional total reflection frequency range of a multilayered dielectric heterostructure which is made of two PCs with the same materials but have different thickness ratios of their two layers. We see that the 100% reflection range of the heterostructure becomes larger as compared to PC1 and PC2. Larger omnidirectional reflection range can be obtained for Na3AlF6/Ge structure by combing the two photonic crystals as considered here. For obtaining this large frequency range, the photonic band gaps of two constituent PCs should overlap with each other. We also discuss the interface defect by setting a layer of Na3AlF6 or Ge in the heterostructure between PC1 and PC2. We found the reflection between the 1st and 2nd gaps would be enhanced when we add a layer of Ge(<0.1 period).
In the finial topic, we studied the optical properties of a structure as an “impurity band based photonic quantum well” (IBBPQW) with different kinds of defects. Defects made of normal material with positive refractive index, single-negative materials and left-handed materials were studied. By examining the transmittance spectra of the structures having different defect numbers and different kinds of defects, we found that multi-channel optical switches or filters can be realized.

[1] Yablonovitch, E., "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987
[2] John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, 2486-2489, 1987
[3] Pendry, J., "Photonic band structure," J. Mod. Opt.,Vol. 41, 209-229, 1994.
[4] Jonopoulos, J. D., P. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature.,Vol. 386, 143-149, 1997.
[5] Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of μ and ε," Sov. Phys. Usp., Vol. 10, 509-514, 1968.
[6] J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, "Extrenely low freguency plasmons in metallic mesostructures," Phys. Rev. Lett ., Vol. 76, No 25, pp.4773-4795, 1996.
[7] J.B. Pendry, A.J. Holden, and D.J. Robbins, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory and Tech., Vol.47, No.11, pp.2075-2096, 1999.
[8]D. R. Smith, and W.J. Padilla, and D.C. Vier "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol.84, No.18, pp.4184-4187, 2000.
[9]Winn, J. N., Y. Fink, J. N. Winn, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal,"
Opt. Lett., Vol. 23, 1573-1575, 1998.
[10]Fink, Y., J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science., Vol. 282, 1679-1682, 1998.
[11]Srivastava,S.K. and S.P. Ojha,”Enhancement of omnidirectional reflection bands in one-dimensional photonic crystal structures with left handed materials,” Progress In Electomagneticsm PIER 68,91-111,2007.
[12]Srovastava,R.,J.P.Pandey,K.B.Thapa,and S.P. Ojha,”structural parameters in the formation of monidirectional high reflectors” Progress In Electromagnetics Research,PIER 70,53-78,2007.35.2008
[13]Xin Wang,Xinhua Hu,Yizhou Liu,and Jian Zi,”Enlargment of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic heterostructures,”Appl. Phys. Lett. Vol 80, No.23 , 2002.
[14]S.K. Srivastava,and S.P. Ojha,”Enhancement of omnidirectional reflection materials,” Progress In Electromagnetic Research , Progress In Electromagnetics Reasearch, PIPER 68, pp.91-111,2007.
[15] R.Srivastava,K.B Thapa, S.PTI,and S.P.Ojha,”Omnidirection reflection in one dimensional photonic crystal,” Progress In Electromagnetics Research B,Vol. 7. pp.133-143,2008.
[16]R. Srivastava,S. Pati,and S.P. Ojha,”Enhancement of omnidirectional reflection in photonic crystal heterostructures,” Progress In Electromagnetic Research B, Vol. 1, pp. 197-208,2008.
[17]C. Zhang,F. Qiao,J. Wan,and J. Zi,”Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures,” Appl. Phys.Lett. 87,3174,2000.
[18]J. Zi, J.Wan,and C.Zhang “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures . Appl. Phys.Lett. 73,2084,1998.
[19] Wang, X., X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, "Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures," Appl. Phys.Lett., Vol. 80, 4291-4293, 2002.
[20] http://www.nanonet.go.jp/english/mailmag/2005/057b.html
[21] Yeh, P., Optical Waves in Crystals , John Wiley & Sons, New York, 1988.
[22] Pochi Yeh, Optical Waves in Layered Media , John Wiley & Sons,Singapore Sons, 1991.
[23] Born, M. and E. Wolf, "Principles of Optics," Cambridge University Press, 1998.
[24]Jiang Hai-Tao, Chen Hong, Liu Nian-Hua, Zhu Shi-Yao “Engineering Photonice Crystal Impurity Bands for Multiple Channelled Optical Switches”. Chin. Phys. Lett. 21(1) 101~103, 2004.
[25]Fang Y T,Zhou J and Pun E Y B “High-Q filters based on one-dimensional photonic crystals using epsilon-negative materials”Appl. Phys. B 86 587,2006.
[26]Xiaoyoug Hu, Zheng Liu and Qihuang Gong ,“A multichannel filter in a photonic crystal heterostructure containing single-negative materials”
J. Opt. A: Pure Appl. Opt. 9 877-883, 2007.
[27]欒丕綱、陳啟昌，光子晶體，五南圖書，一版，台北(2005)。
[28]李正中，薄膜光學與鍍膜技術”，藝軒圖書，四版，台北。
[29] J.B.Pendry,A.J.Holden ,D.J.Robbins,W.J.Stewart, J.Phys. Condens.Matter 10(1998)4785.
[30] J.B.Pendry,A.J.Holden ,D.J.Robbins,W.J.Stewart, IEEE Trans. Microwave Theory Tech.47(1999)2075.
[31]Chien-Jang. Wu , “document of Selection rules for negative index in multilayer Fabry-Perot resonators containing left-handed defect”.