本論文中，我們發現成長奈米複合材料也是藉由人為方式操縱介質折射率的新途徑，這種由兩種材料組成、尺寸遠小於光波長的奈米結構可被視為是一個等效折射介質，其介於兩種材料之間的光學特性更具有高度的發展潛力，本文關注的課題就是希望藉由低等效折射率之氮化鎵奈米柱陣列的研究，將此光學結構與雙折射率之間的關聯做進ㄧ步的釐清與了解，期許未來能藉由人為操縱的方式，例如改變此兩種材料所組成的體積比（filling factor/volume fraction）來操控光學材料的介質特性，達到操縱介質的折射率即控制光學特性的效果。

　　本文分別架設垂直入射與變角度入射的光路，量測氮化鎵奈米薄膜與氮化鎵奈米柱陣列薄膜這兩個不同的光學結構系統，企圖了解結構的差異性將對TE Mode與TM Mode所表現的雙折射現象(birefingence)有何影響，而本文確實由反射光譜的量測發現氮化鎵奈米柱陣列薄膜有雙折射現象，我們更進ㄧ步從變角度入射的實驗中，將影響折射率的角度變化因素歸納為「空間相位」、「變角度」以及「布魯斯特角」等三方面進行歸納與比較。

　　此外，本文並對「反射光譜量測原理」以及「折射率ｎ値線性擬合方法」做一個完整的說明，我們將介紹如何使用線性擬合公式來求得樣品的等效ｎ值，並說明此式因應光路系統而必須調整相位參數的詳細原因，以正確得到樣品的折射率。此外，本文並對線性擬合公式提出進一步的改進，以計算出更精細TM Mode的折射率數值，擺脫因角度過於接近而無法有效鑑別折射率變化的限制。

1.P. B. Clapham and M. C. Hutley, “Reduction of lens reflexion by the ‘moth eye’ principle,” Nature 244,281−282 (1973).

2.S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29,993−1009 (1982).

3.M. Srinivasarao, “Nano-optics in the biological world: Beetles, butterflies,birds, and moths,” Chem. Rev. 99,1935−1961 (1999).

4.M. E. Motamedi, W. H. Southwell, and W. J. Gunning, “Antireflection surfaces in silicon using binary optics technique,” Appl. Opt. 31, 4371−4376 (1992).

5.P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8, 53−56 (1997).

6.Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142−143 (2001)

7.方治國教授，宜大校訊第16期【科普園地】

8.Hung-Ying Chen, Hon-Way Lin, Chen-Ying Wu, Wei-Chun Chen, Jyh-Shin Chen,and Shangjr Gwo, “Gallium nitride nanorod arrays as low-efractiveindex transparent media in the entire visible spectral region,” 26 May 2008 / Vol. 16, No. 11 / OPTICS EXPRESS 8106

9.T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84, 855−857(2004).

10. T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466−468 (2004).

11. J. Y. Kim, T. Gessmann, E. F. Schubert, J.-Q. Xi, H. Luo, J. Cho, C. Sone, and Y. Park, “GaInN lightemitting diode with conductive omnidirectional reflector having
a low-refractive-index indium-tin oxide layer,” Appl. Phys. Lett. 88, 013501 (2006).

12.H.-M. Kim, T. W. Kang, and K. S. Chung, “Nanoscale ultraviolet-light-emitting diodes using wide-bandgap gallium nitride nanorods,” Adv. Mater. 15, 567−569
(2003).

13. H.-M. Kim, Y.-H. Cho, H. Lee, S. I. Kim, S. R. Ryu, D. Y. Kim, T. W. Kang, and K. S. Chung, “Highbrightness light emitting diodes using dislocation-free indium gallium nitride/gallium nitride multiquantumwell nanorod arrays,” Nano Lett. 4, 1059−1062 (2004).

14. A. Kikuchi, M. Kawai, M. Tada, and K. Kishino,“InGaN/GaN multiple quantum disk nanocolumn lightemitting diodes grown on (111) Si substrate,” Jpn. J. Appl. Phys. 43, L1524−L1526 (2004).

15. A. Kikuchi, M. Tada, K. Miwa, and K. Kishino, “Growth and characterization of InGaN/GaN nanocolumn LED,” Proc. SPIE 6129, 612905 (2006).

16.K. Kishino, A. Kikuchi, H. Sekiguchi, and S. Ishizawa, “InGaN/GaN nanocolumn LEDs emitting from blue to red,” Proc. SPIE 6473, 64730T (2007).

17.T. Palacios, F. Calle, M. Varela, C. Ballesteros, E. Monroy, F. B. Naranjo,M. A. Sanchez-Garacia, E. Calleja, and E. Munoz, Semicond. Sci. Technol.15, 996(2000).

18.Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu (unpublished).

19.K. H. Kim, J. Li, S. X. Jin, J. Y. Lin, and H. X. Jiang, Appl. Phys. Lett. 83,566 (2003).

20.J.-Q. Xi, J. K. Kim, and E. F. Schubert, Nano Lett. 5, 1385 (2005).

21.K. Robbie, L. J. Friedrich, S. K. Dew, T. Smy, and M. J. Brett, J. Vac.Sci.Technol. A 13, 1032 (1995).

22.D. Vick, J. J. Friedrich, S. K. Dew, M. J. Brett, K. Robbie, M. Seto, and T.Smy, Thin Solid Films 339, 88 (1999).

23.K. Kaminska and K. Robbie, Appl. Opt. 43, 1570 (2004).

24.J. Zhong, H. Chen, G. Saraf, Y. Lu, C. K. Choi, J. J. Song, D. M. Mackie, and H. Shen, “Integrated ZnO nanotips on GaN light emitting diodes for enhanced emission efficiency,” Appl. Phys. Lett. 90, 203515(2007).

25.Jin, S. X.; Li, J.; Lin, J. Y.; Jiang, H. X. Appl. Phys. Lett. 2000, 77,3236-3238.

26.Choi, H. W.; Dawson, M. D.; Edwards, P. R.; Martin, R. W. Appl.Phys. Lett.2003, 83, 4483-4485.

27.D. E. Aspnes, “Optical properties of thin-films,” Thin Solid Films 89, 249−262 (1982).

28.Tito E. Huber, Frank Boccuzzi, and Leo Silber,” Electromagnetic wave propagation through a wire array composite,” Physical Review B Volume 59, Number11,15 March 1999-I

29.Hisao KIKUTA, Hiroshi TOYOTA and Wanji YUl,” Optical Elements With SubWavelength Structured Surfaces,” Optical Review Vol. 10, No. 2 (2003)

30.Yuanping Sun and Yong-Hoon, Hwa-Mok Kimb and Tae Won Kang,” High efficiency and brightness of blue light emission from dislocation-free InGaN/GaN quantum well nanorod arrays.” Phys. Rev. Lett. 87, 093115(2005).

31. Jian Jim Wang,a_ Lei Chen, Xiaoming Liu, Paul Sciortino, Feng Liu,Frank Walters, and Xuegong Deng,” 30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography.” Phys.Rev. Lett. 89, 141105(2006).

32.O. L. Muskens, M. T. Borgström and E. P. A. M. Bakkers, J. Gómez Rivasa ,”
Giant optical birefringence in ensembles of semiconductor nanowires.” Phys.Rev. Lett. 89, 233117(2006).

33.Wang JJ, Deng X, Liu X, Nikolov A, Sciortino P, Liu F, Chen L ,” Ultraviolet wave plates based on monolithic integration of two fully filled and planarized nanograting layers.” Optical Letter 2006 Jun 15;31(12):1893-5

34.D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz,“Composite medium with simultaneously negative permeability and permittivity.”
Phys. Rev. Lett. 84, 4184−4187 (2000).

35.D. R. Smith, J. B Pendry, and M. C. K. Wiltshire,“Metamaterials and negative refractive index,” Science305, 788−792 (2004).

36.J.-Q. Xi, J. K. Kim, and E. F. Schubert, “Silica nanorod-array films with very low refractive indices,” Nano Lett. 5, 1385−1387 (2005).

37.J.-Q. Xi, J. K. Kim, E. F. Schubert, D. Ye, T.-M. Lu, and S.-Y. Lin, “Very low-refractive-index optical thin films consisting of an array of SiO2 nanorods,”Opt. Lett. 31, 601−603 (2006).

38.J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu,and J. A. Smart, “Optical thin-film materials with low refractive index for
broadband elimination of Fresnel reflection,” Nat. Photonics1, 176−179 (2007).

39.C.-H. Hsu, H.-C. Lo, C.-F. Chen, C. T. Wu, J.-S. Hwang, D. Das, J. Tsai, L.-C. Chen, and K.-H. Chen,“Generally applicable self-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4,471−475 (2004).

40.Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H.Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen,“Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770−774 (2007).

41.H.-Y. Chen, H.-W. Lin, C.-H. Shen, and S. Gwo, “Structure and photoluminescence properties of epitaxially oriented GaN nanorods grown on Si (111) by plasma-assisted molecular-beam epitaxy,” Appl. Phys. Lett. 89,243105 (2006), and references therein.

42.氮化銦磊晶薄膜及量子點材料之研究,林弘偉著,清華大學碩士論文

43.3E. Calleja, M. A. Sánchez-García, F. J. Sánchez, F. Calle, F. B. Naranjo, E.Muñoz, S. I. Molina, A. M. Sánchez, F. J. Pacheco, and R. García, J.Cryst. Growth 201/202, 296 (1999).

44.L. W. Tu , C.L.Hsiao, T.W.Chi, I.Lo, and K.Y.Hsieh, Appl. Phys.Lett.82, 1601 (2003)

45.5K. A. Bertness, A. Roshko, N. A. Sanford, J. M. Barker, and A. V.Davydov, J. Cryst. Growth 287, 522 (2006)

46.C.-H. Shen, H.-Y. Chen, H.-W. Lin, S. Gwo, A. A. Klochikhin, and V. Yu.Davydov, Appl. Phys. Lett. 88, 253104 (2006).

47.G. Yu, G. Wang, H. Ishikawa, and M. Umeno, T. Soga, T. Egawa, J. Watanabe,and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,”Appl. Phys. Lett. 70 (24), 16 June 1997