臺灣博碩士論文加值系統

在本論文中我們研究具有光子能隙的二維六角結構管狀光子晶體，此種光子晶體也包含了之前被研究過的二維六角結構柱狀作為它的特例。在比較分析之後，我們可以得知不論在相同材質或不同材質所組成的六角圓柱結構光子晶體，隨著填充率或介電係數的增加，Energy Band有往低頻區段移動的趨勢，而Complete Gap(不論何種偏振方向、行徑方向皆無相對應的能態存在)的寬度則是會有先上升再下降的趨勢。介電係數的改變並不會影響產生Complete Gap的結構，改變介電係數只會影響能隙的寬度以及出現的頻段。而在混合不同材質的六角圓柱結構光子晶體中，產生的能帶也有隨著介電係數上升，能帶往低頻移動的趨勢。此時產生最大Gap的條件，為圓柱半徑相等。而在六角圓管結構光子晶體中，我們也發現了將填充物的形狀從圓柱換成圓管時，會有類似填充率下降時Energy Band往高頻移動的現象，在這種情形之下，有可能使原本不會產生Complete Gap的頻段發生Complete Gap。我們也找出了會發生此種從無 Complete Gap到有Complete Gap的的六角圓管結構光子晶體。

In this paper, the photonic crystal with two-dimensional hexagonal pipes structures is investigated. This photonic crystal includes the special case that with the two-dimensional hexagonal cylinders structure. In this investigation, we know that the energy band of the hexagonal cylinders structure photonic crystal will shift to lower frequency when the filling rate and dielectric coefficient increasing. And the width of complete gap will increase then decreasing. The structure of the Complete Gap is not effected by the alteration of dielectric coefficient. It would effect the width of band gap and frequencies when the dielectric coefficient been changed. In the different materials of hexagonal cylinders structure photonic crystal, the energy band gaps shift to lower frequencies when the dielectric coefficient increasing. When the cylinders radii are equal, the conditions of maximum gap been found. And in the hexagonal pipe structure photonic crystals, when the fitting materials are changed from cylinders to pipes, the energy band shift to higher frequencies just as the filling rate is decreasing. In this condition, it would be Complete Gape that it should not be Complete Gape. The Complete Gap of the hexagonal pipes structure photonic crystals would be found by this way.

誌謝…………………………………………………………………………………ii
摘要………………………………………………………………………………..…iii
ABSTRACT………………………………………………………………………….vi
目錄…………………………………………………………………………………...v
表目錄…………………………………………………………………………….…vii
圖目錄………………………………………………………………………………viii
1. 緒論………………………………………………………………………………1
1.1 前言………………………………………………………………………...1
1.2 文獻探討…………………………………………………………………….2
1.3 研究動機及目的……………………………………………………………8
1.4 論文架構…………………………………………………………………...10
2. 研究理論基礎……………………………………………………………………13
2.1 光子晶體的基礎理論……………………………………………………...13
2.2 平面波展開法……………………………………………………………18
3. 研究方法…………………………………………………………………………22
3.1 研究方法簡介………………………………………………...……………22
4. 分析與討論………………………………………………………………………25
4.1 相同材質組成的氮化硼六角晶格介電圓柱光子晶體…………………...25
4.2 不同材質組成的氮化硼六角晶格介電圓柱光子晶體…………………...39
4.3 不同材質組成的氮化硼六角晶格介電圓管光子晶體…………………...43
5. 結論………………………………………………………………………………48
6. 未來研究方向…………………………………………………………………..49
參考文獻…………………………………………………………………………….50
自傳………………………………………………………………………………….54

[1] Tokushima, M., Kosaka, H., Tomita, A., Yamada, H., “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide”, Appl. Phys. Lett. 76, 952, 2000.
[2] Knight, J. C., Broeng, J., Birks, T. A. and Russell, P. St. J., “Photonic Band Gap Guidance in Optical Fibers”, Science 282, 1476, 1998.
[3] http://33tt.com/print.php?articleid=139
[4] Yablonovitch, E., “Inhibited Spontaneous Emission in Solid-state Physics and Electronics”, Phys. Rev. Lett. 58, 2059, 1987.
[5] John, S., “Strong Localization of Photons in Certain Disordered Dielectric Superlattice”, Phys. Rev. Lett. 58, 2486, 1987.
[6] 蔡雅芝, “淺談光子晶體”, 物理雙月刊 21, 445, 1998.
[7] Yablonovitch E. and Gmitter, T. J., “Photonic Band Structure：The Face-Centered-Cubic Case”, Phys. Rev. Lett. 63, 1950, 1989.
[8] Ho, K. M., Chart, C. T. and Soukoulis, C. M., “Existence of a photonic Gap in Periodic Dielectric Structure”, Phys. Rev. Lett. 65, 3152, 1990.
[9] http://nano.nchc.org.tw/photonic/ch1.php
[10] Yablonovitch, E., Gmitter T. J. and Lung, K. M., “Photonic Band Structure：The Face-Centered-Cubic Case Employing Nonspherical Atoms”, Phys. Rev. Lett. 67, 2295, 1991.
[11] Plihal M. and Maradudin, A. A., “Photonic Band Structures of Two-Dimensional Systems：The Triangular Lattices”, Phys. Rev. B 44, 8565, 1991.
[12] Villeneuve P. R. and Piché, M., “Photonic Band Gaps in Two-Dimensional Square and Hexagonal Lattices”, Phys. Rev. B 46, 4969, 1992.
[13] Villeneuve P. R. and Piché, M., “Photonic Band Gaps in Two-Dimensional Square Lattices：Square and Circular Rods”, Phys. Rev. B 46, 4973, 1992.
[14] Cassagne, D., Jouanin, C. and Bertho, D., “Photonic Band Gaps in Two-Dimensional Graphite Structure”, Phys. Rev. B 52, R2217, 1995.
[15] Cassagne, D., Jouanin, C. and Bertho, D., “Hexagonal Photonic-Band-Gap Structures”, Phys. Rev. B 53, 7134, 1996.
[16] Parker, Andrew R., McPhedran, Ross C.,McKenzie, David R., Botten, Lindsay C. and Nicorovici. Nicolae-Alexandru P., Photonic engineering: Aphrodite's iridescence. Nature, 409, 36, January 4 2001.
[17] Lin, S., Chow, E., Bur, J., Johnson, S. and Joannopoulos, J.. “Low-loss, wide-angle Y splitter at approximately 1.6-um wavelengths built with a two-dimensional photonic crystal ”, Opt. Lett. 27, 1400, 2002.
[18] Biró, L. P., Bálint, Zs., Kertész, K., Vértesy, Z., Márk, G. I., Horváth, Z. E. Balázs, J., Méhn, D., Kiricsi, I., Lousse, V. and Vigneron, J.-P., “Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair”, Phys. Rev. E 67, 21907, 2003.
[19] Lodahl, Peter, Floris A., Driel, Van, Nikolaev, Ivan S., Irman, Arie, Overgaag, Karin, Vanmaekelbergh Daniël and Vos, Willem L., “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals”, Nature 430, 654, 2004.
[20] Chern, R. L., Chang, C. Chung, Chang, Chien C., and Hwang, R. R., “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration”, Phys. Rev. E 68, 026704, 2003.
[21] Chang, Chien C., Chi, J. Y., Chern, R. L., Chang, C. Chung, Lin, C. H. and Chang, C. O., “Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap”, Phys. Rev. B 70, 075108, 2004.
[22] Gaillot, D., Yamashita, T. and Summers, C. J., “Photonic band gaps in highly conformal inverse-opal based photonic crystals”, Phys. Rev. B 72, 205109, 2005.
[23] Labilloy, D., Benisty, H., Weisbuch, C., Krauss, T. F., Rue, R. M. De La, Bardinal, V., Houdré, R., Oesterle, U. Cassagne, D. and Jouanin, C., “Quantitative Measurement of Transmission, Reflection, and Diffraction of Two-Dimensional Photonic Band Gap Structures at Near-Infrared Wavelengths”, Phys. Rev. Lett. 79, 4147 1997.
[24] Reynolds, A., López-Tejeira, F., Cassagne, D., García-Vidal, F. J., Jouanin, C. and Sánchez-Dehesa, J., “Spectral properties of opal-based photonic crystals having a SiO2 matrix”, Phys. Rev. B 60, 11422, 1999.
[25] Albert, J. P., Jouanin, C., Cassagne, D. and Bertho, D., “Generalized Wannier function method for photonic crystals”, Phys. Rev. B 61, 4381, 2000.
[26] Romanov, S. G., Maka, T., Torres, C. M. Sotomayor, Müller, M., Zentel, R., Cassagne, D., Manzanares-Martinez, J. and Jouanin, C., “Diffraction of light from thin-film polymethylmethacrylate opaline photonic crystals”, Phys. Rev. E 63, 056603, 2001.
[27] Kaliteevski, M. A., Martinez, J. M., Cassagne, D. and Albert, J. P., “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal”, Phys. Rev. B 66, 113101, 2002.
[28] Torres, J., Coquillat, D., Legros, R., Lascaray, J. P., Teppe, F., Scalbert, D., Peyrade, D., Chen, Y., Briot, O., d’Yerville, M. Le Vassor, Centeno, E., Cassagne, D. and Albert, J. P., “Giant second-harmonic generation in a one-dimensional GaN photonic crystal”, Phys. Rev. B 69, 085105, 2004.
[29] http://ab-initio.mit.edu/photons/
[30] John D. Joannopoulus：Photonic Crystal, Princeton University Press, 1995
[31] 欒丕綱, 陳啟昌：光子晶體-從蝴蝶翅膀到奈米光子學, 五南圖書出版股份有限公司, 2005