臺灣博碩士論文加值系統

利用光子晶體結構所設計的光學元件在近年來的應用變得非常廣泛，本論文也研究了可利用一般IC之CMOS製程的實際參數，來設計二維光子晶體的光調制元件，並成功設計出可以以半導體製程技術做成的光波偏振器的晶片，此研究將積體電路製程用於光子晶體製造，使元件大小由公分等級縮小為微米等級，並可利用IC半導體製程進行光子晶體量產。
另外在生物眼睛的光學特性研究上，此研究是首次將螢火蟲小眼中的錐晶體分成兩種折射率週期性的替換，以形成190層拋物面的結構，在光軸上可看成是由一維的週期性光子晶體結構組成。經由幾何光學原理模擬了整個小眼屈光部分，並根據模擬的光追跡來觀察探討其小眼的輸出行為，再利用轉移矩陣觀察其穿透率。結果發現在小眼光軸上的穿透率有濾波存在，而小眼四周圍的視細胞則無濾波效果存在但可接收其他可見光。故推測小眼中各視細胞可接收不同的光波段。另外討論螢火蟲複眼的聚光效率，計算結果以輸入光為平行光來看的，一顆複眼的重疊影像聚光效率會比並列影像多了大約900倍。並且也發現我們這樣的結構也有徑向梯度折射率存在。

In recent years, it is very popular for applying photonic crystal (PC) structure to design optical components. In this thesis, we designed a two-dimensional photonic crystal optical modulator by using the general complementary metal-oxide semiconductor (CMOS) integrated circuit (IC) processing parameters. Chips of optical polarizer have been successfully designed by adopting the technologies of semiconductor fabrication. This study extends the fabrication of ICs to that of PCs and makes the shrinkage of device dimension from the order of centimeter to that of micrometer possible. Moreover, it is achievable to use the IC processes for the PC production.
As to the research for the optical properties of biological eyes, this is the first study to investigate the firefly’s eyes by replacing its crystalline cone with the periodic indices of refraction and constructing a configuration of 190 parabolic layers. It was treated as a one-dimensional periodic photonic crystal on the optical axis. By using the principles of geometric optics, we simulated its dioptric portion and realized its behavior of the visual output according to the optical ray-tracing. We further applied the transfer matrix to observe its transmission and found that there exists the filtering capability on its optical axis. On the contrary, there is no such filtering effect but with the capability of receiving other visible light for the retinal cell nuclei around the axis. It might be deduced that all the retinal cell nuclei of the firefly’s eyes can receive the different range of light wave. Besides, we also discussed the focusing efficiency of the firefly’s eyes. Based on the input of collimating light, the efficiency of an overlapped image focused by a compound eye is higher than that of a parallel image by nine hundred times. Furthermore, there is radial gradient index existing by using such a configuration proposed in this thesis.

Contents

中文摘要…………………………………………………………. iii
Abstract…………………………………………………………… iv
誌謝………………………………………………………………. vi
Contents…………………………………………………………. vii
List of Figures…………………………………………………. ix
List of Tables………………………………………………….. x
Chapter 1 A polarizer chip based on CMOS Cu-interconnect for optical telecommunications1
1.1Introduction……………………… 1
1.2 Design and simulation………………………………… 2
1.2.1 Fabrication parameters………………………………… 2
1.2.2 PML boundary condition……………………………… 7
1.2.3 Simulation geometry and convergence analysis………. 9
1.3 Results…………………………………………………. 12
1.3.1 Performance of a 3N-SL polarizer chip……………….. 12
1.3.2 Slab waveguide propagation efficiency……………….. 16
1.3.3 Double-cascade mode…………………………………. 17
1.3.4 Optical properties vs. wavelength……………………... 19
1.4 Discussions……………………………………………. 23
1.4.1 Stability………………………………………………... 23
1.4.2 Advantages of IC Cu-interconnect technology………... 23
1.5 Conclusions……………………………………………. 24
Chapter 2 Study of the optical characteristics of firefly’s eyes…. 26
2.1 Introuction to compound eyes…………………………. 36
2.2 Apposition eyes….……………..……………………... 39
2.3 Superposition eyes…………………………….………. 42
2.3.1 Refractive superposition eyes………………………… 42
2.4 Transfer matrix of one dimensional non-periodical multiple layered films………………………………….
44
Chapter 3 Experiment ..………………………………………. 54
3.1 Overview………………………………………………. 54
3.2 Anatomy on the eye of firefly………………….……… 57
Chapter 4 The optics design and simulation of Ommatidium of firefly…………………………………………………...
64
4.1 Overwiew……………………………………………… 64
4.2 Optics design and simulation………………………….. 64
4.3 Result and analysis on the ray-tracing simulation…….. 69
Chapter 5 Transmission analysis and discussion on the compound eye of firefly……………………………………………
76
5.1 Overwiew……………………………………………… 76
5.2 Transmission efficiency analysis of apposition eyes….. 76
5.3 Transmission efficiency analysis on superposition Eyes…………………………………………………….
85
5.4 Analysis on transmission efficiency through transfer
matrix method and discussions……………………….
93
Chapter 6 Analysis and discussion on the gradient refractive index of the Ommatidium of firefly…………………… 115
6.1 Introduction……………………………………………. 115
6.2 Analusis and discussion on gradient refractive index…. 115
Chapter 7 Conclusion and future perspective……………………. 130
Reference …………………………………………………………. 136
Appendix I…………………………………………………………. 140

[1] J. J. G. M. van der Tol, J. W. Pedersen, E. G. Metaal, Y. S. Oei, H. van Brog and I. Moerman, “Mode evolution type polarization splitter on InGaAsP/InP,” IEEE Photonics Technol. Lett. Vol. 5 ,1412-1414, 1993.
[2] J. J. G. M. van der Tol, J. W. Pedersen, E. G. Metaal, J. J.-W. van Gaalen, Y. S.Oei and F. H. Groen, “A short polarization splitter without metal overlays on InGaAsP-InP,” IEEE Photonics Technol. Lett. Vol. 9, 209-211, 1997.
[3] T. Hayakawa, S. Asakawa and Y. Kokubun, “Arrow-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process,” J. Lightwave Technol. Vol. 15, 1165-1170, 1997.
[4] L. Zhang and C. Yang, “A novel polarization splitter based on the photonic crystal fiber with nonidentical dual cores,” IEEE Photonics Technol. Lett. Vol. 16, 1670-1672, 2004.
[5] L. Zhang and C. Yang, “Polarization splitter based on photonic crystal fibers,” Opt. Express Vol. 11, 1015-1020, 2003.
[6] S. H. Voldman, “The impact of technology scaling on ESD robustness of aluminum and copper interconnects in advanced semiconductor technologies,” IEEE Trans. CPMT Part C. Vol. 21, 265-277, 1998.
[7] T. Saito, H. Ashihara, K. Ishikawa, M. Miyauchi, Y.Yamada and H. Nakano, “A reliability study of barrier-metal-clad copper interconnects with self-aligned metallic caps,” IEEE Trans. Electron Devices. Vol. 51, 2129-2134, 2004.
[8] J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. Vol. 114, 185–200, 1994.
[9] Exner S, Die Physiologie der facettirten Augen von Krebsen undInsekten. Leipzig, Vienna, Deuticke Verlag, 1891.
[10] Horridge G. A, Optical mechanisms of clear zone eyes, Clarendon Press, Oxford, 1975.
[11] Horridge G. A, “The Eye of the Firefly Photuris,”Proceedings of the Royal Society of London B, Vol. 171, 445-463, 1969.
[12] Horridge G. A, Giddings C, & Stange G, “The superposition eye of skipper butterflies,” Proceedings of the Royal Society of London B, Vol. 182, 457–495, 1972.
[13] Nilsson D.-E, “Three unexpected cases of refracting superposition eyes in crustaceans ,” Journal of Comparative Physiology A, Vol. 167, 71–78, 1990.
[14] Caveney S, “The phylogenetic significance of ommatidium structure in the compound eyes of polyphagan beetles,” Canadian Journal of Zoology, Vol. 64, 1787–1819,1986.
[15] Horridge G. A, and Miriam McLean, “The Dorsal Eye of the Mayfly Atalophlebia (Ephemeroptera) ,” Proceedings of the Royal Society of London B, Vol. 200, 137-150, 1978.
[16] Yagi, N., and Koyama, N., “ The Compound Eye of Lepidoptera: Approach from Organic Evolution,”Maruzen Co., Tokyo, 1963.
[17] Wu M-Y, Tian L-J, and Peng L-H, “ The optical imaging of compound eye of Beijing firefly Phrococelia pekinensis,” Acta entomologica sinica, Vol. 36(2), 159–161, 1993.
[18] Wu W-G, Wang G-Y, Feng C-H and Shi S-Z, “Structure and optical properties of the compound eye of Beijing firefly Pyrococelia pekinensis,” Acta entomologica sinica,Vol. 25(3), 260–263, 1982.
[19] W.H. Biggley, J.E. Lloyd, and H.H. SeligeR, “ The spectral distribution of firefly ligh. II,” The Journal of General Physiology, Vol.50, 1681–1692, 1967
[20] A. B. Lall, H. H. Seliger, W.H. Biggley, and J. E., “ Ecology of colors of firefly bioluminescence,” Llooyd, Science, new Series, Vol. 210, 560–562, 1980.
[21] D. Booth, A. J. A. Stewart, and D. Osorio, “Colour vision in the glow-worm Lampyris noctiluca (L.) (Coleoptera:Lampyridae): evidence for a green-blue chromatic mechanism,” Journal of Experimental Biology Vol. 207, 2373–2378, 2004.
[22] Wu Meiying, “Desing of a model ommatidium of rfiiing firefly compound eye and studied by ray tracing,” ACTA BIOPHYSICA SINICA, Vol. 10,269–273, 1994.
[23] Land M.F. and Nilsson D.-E., Animal Eyes, Oxford University Press , Oxford, 2002.
[24] Amazon.com: Introduction to Optics (2nd Edition): Books: Frank J. Pedrotti,Leno S. Pedrotti by Frank J. Pedrotti,Leno S. Pedrotti
[25] Focus software, zemax optical design program Users Guide, Version 10.0, 2001.
[26] Chung Ping Liu, Kuei Jen Lee, Cheng-Hao Ko and Bi-Zen Dong, Optical and Laser Technology, Vol. 39, 415–420, 2007.
[27] Cheng-Hao Ko and Kuei Jen Lee, Japanese Journal of Applied Physics, Vol. 45,5039–5045, 2006.
[28] Cheng-Hao Ko and Kuei Jen Lee, Optics Express, Vol. 14, 5250–5259, 2006.
[29] Hsi-Fu Shih, Chi-Lone Chang, Kuei Jen Lee and Chi-Shen Chang, IEEE Transactions on Magnetics, Vol. 41, 1058–1060, 2005.