本研究探討次微米光柵之設計、製造與應用。在光柵設計中，基於嚴格耦合波理論，我們探討光由從光密介質經次波長光柵到光疏介質的一級穿透與反射效率及光柵週期和結構幾何形狀之間的關係，由模擬可知次微米光柵之繞射效率取決於光柵幾何形狀而繞射角度在於光柵週期之精確性。 此外，為了提高次微米光柵光學膜片的生產速度、大面積化與量產性，本研究採用超精密加工刻劃製作模仁並利用滾壓技術成形光柵。 在超精密加工中，我們將光柵之形貌設計、光柵週期和切削速度等參數來觀測其加工結果，並以光學檢測方式探討光柵繞射效率與繞射角度之關係影響。
在光柵應用中，液晶顯示器背光模組和折射率量測將應用於次微米光柵膜片上。 液晶顯示器背光模組所面臨到的問題是需要改善光使用率、光輝度值和整體均勻性，藉由導光棒上之優化結構可控制出光角度、消除暗帶和熱點現象。 目的為使入射紅、綠、藍三原色光源經次微米光柵後可在出光面產生均勻且垂直出射的高輝度的白光。 另一應用為設計一組分色背光模組以取代彩色濾光片，模組包含導光棒、次微米光柵、V形槽導光板與柱狀透鏡。 當準直LED入射光源耦合至導光棒後，經過特定入射角度將次微米光柵分光後，其繞射光線以適當的角度導入柱狀透鏡，以便將色彩對映到適切的像素並在顯示器液晶層中。 最後之應用為設計出一成本低廉、精度高，折射率值量測範圍廣，又可快速量測的折射率量測儀器，以符合市場需求。 此系統利用次微米光柵的繞射現象，並結合司乃耳定律來進行量測。 研究內容包含光學系統的模擬與設計和光學量測驗證，並探討折射率量測精度、誤差分析、可量測折射率範圍。

The sub-micron gratings have been designed, fabricated, and tested. In the grating design, based on the rigorous coupling wave analysis (RCWA), we analyze the relationship between the first order transmission/reflection efficiency and the period of the grating for various shapes as rays pass through the sub-micron gratings. The results show that the diffraction efficiency and diffraction angle strongly depends on the value of the period and its profile. In the grating fabrication, the diamond turning of high-precision imprinting molds and roll-to-roll UV embossing process have the properties of continuous production, high productivity, less manufacturing time, versatility of substrates, and higher imprinting speeds. The diamond turning experiments are conducted to examine the effects of shape design, grating period and cutting speed on machinability of the mold, and the gratings patterned on the light bar are then discussed about the diffraction efficiency and diffraction angle by the optical measurement.
In the grating application, the sub-micron gratings are applied for the Liquid Crystal Display (LCD) backlight and the refractive index measuring approach. One problem facing current LCD backlight unit is needed to improve the low efficiency, light illuminance and uniformity by optimizing the structures on the light bar to control the diffraction directions and eliminate the dark region or hot spots in this viewing direction. The first stage is to turn the Red/Green/Blue incident rays into uniformly and normally output white light with high illuminance from the surface of a light guide. The next stage is designed to replace conventional dye color filters for color LCDs. The light bar generates color rays by transmitting them from side-lit color light-emitting diodes (LEDs) through the sub-micron grating. These angular color rays are then redirected using a V-grooved light guide, and converged using a lens array to map to corresponding sub-pixel positions to efficiently display color images. The final application presents the design and simulation results of a high-precision low-cost refractometer that demonstrates the main advantage of a wide measurement range. The proposed design is based on the diffractive properties of sub-micron gratings and Snell’s Law. The precision and uncertainty factors of the proposed system were tested and analyzed, revealing that the proposed refractometer demonstrates a wide measurement range with high measurement accuracy.

CHAPTER ONE 1
INTRODUCTION 1
CHAPTER TWO LITERATURE REVIEW 11
2.1 MOLD FABRICATION FOR MICRON STRUCTURES 11
2.2 VARIOUS APPROACHES TO PRODUCE MICRO STRUCTURES 19
2.3 THE USE OF THE SUB-MICRON GRATING FOR BACKLIGHT ILLUMINANCE AND UNIFORMITY 25
2.4 THE USE OF THE SUB-MICRON GRATING FOR THE COLOR-SEPARATION 29
2.5 THE APPLICATIONS OF MEASUREMENT OF REFRACTIVE INDEX 36
CHAPTER THREE OBJECTIVES AND PROPOSED PROCESS 42
3.1 DESIGN PROCESS METHOD FOR PROPOSED MODULE 43
3.2 PROPOSED MANUFACTURING PROCESS FOR DESIGNED MODULE 46
CHAPTER FOUR FABIRCATION OF SUB-MICRON GRATING 53
4.1. OPTICAL PERFORMANCE OF SUB-MICRON GRATING 54
4.2. EXPERIMENTAL SET-UP, DESIGN, RESULTS AND DISCUSSIONS 57
CHAPTER FIVE BACKLIGHT MODULE 68
5-1 DESIGN OF MODULE TO REDUCE COUPLING LENGTH 68
5-2 DESIGN OF MODULE FOR COLOR-SEPARATION 90
CHAPTER SIX REFRACTIVE INDEX MEASURING DEVICE 112
6-1 DESIGN AND SIMULATIONS 112
6-2 THE GRATING DESIGN 119
6-3 TEST RESULTS AND DISCUSSIONS 121
CHAPTER SEVEN CONCLUSIONS 124
. 132
REFERENCES 133

. Kimmel, "Review Paper: Diffractive backlight technologies for mobile applications,"J SOC INF DISPLAY 20(5), 245–258,(2012).
[2] S. R. Park, O. J. Kwon, D. Shin, S.-H. Song, H.-S. Lee, and H. Y. Choi, "Grating micro-dot patterned light guide plates for LED backlights," Opt. Express 15, 2888-2899 (2007).
[3] W. L. Barnes1, A. Dereux, and T. W. Ebbesen,"Surface plasmon subwavelength optics," Nature 424, 824-830, (2013).
[4] Y. Kanamori, E. Roy, Y. Chen, "Antireflection sub-wavelength gratings fabricated by spin-coating replication," Microelectronic Engineering 78–79, 287-293, (2005)
[5] C. Chevallier, N. Fressengeas, F. Genty, and J. Jacquet,"Optimized sub-wavelength grating mirror design for mid-infrared wavelength range,"Applied Physics A 103(4),1139-1144, (2011).
[6] G. Zhou, Y. Du, Q. Zhang, H. Feng and F. S. Chau,"High-speed, high-optical-efficiency laser scanning using a MEMS-based in-plane vibratory sub-wavelength diffraction grating,"J. Micromech. Microeng. 18, 134-144, (2008).
[7] H. Lochbihler, "Colored images generated by metallic sub-wavelength gratings," Opt. Express 17, 12189-12196, (2009)
[8] H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, "Efficient light coupling into in-plane semiconductor nanomembrane photonic devices utilizing a sub-wavelength grating coupler," Opt. Express 20, 20659-20665 (2012)
[9] P. J. Bock, P. Cheben, A. Delâge, J. H. Schmid, D.-X. Xu, S. Janz, and T. J. Hall, "Demultiplexer with blazed waveguide sidewall grating and sub-wavelength grating structure," Opt. Express 16, 17616-17625 (2008)
[10] Moharam M. G., Grann E. B., and Pommet D. A., “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 5, 1068-1076 (1995).
[11] X.H. Rao, J.G. Cai, G.T. Shen, B.C. Yang, Z.Q. Zhang, J.H Zheng and S.L. Zhuang, “Study on the zero order reflection efficiency of sub-wavelength grating,” J. University of Shanghai for Science and Technology 29(3), 245-249 (2007).
[12] S.Y. Lee, “Technical trends and requirements/Specifications for LCD TV backlights,” John Wiley & Sons, Ltd, 2009.
[13] Kondo, “Technological trends of LED backlight units,” John Wiley & Sons, Ltd, 2009.
[14] J. S. Kim, Y. B. Ko, C. J. Hwang, J. D. Kim and K. H. Yoon, “A study on the fabrication method of middle size LGP using continuous micro-lenses made by LIGA reflow,” Vol. 19, No. 3 pp. 171-176, November 2007.
[15] J. Yuan, S. Ji, D. Wen and M. Chen, “Ultra-Precision Machining Technologies,” Advanced Materials Research, Volumes 69 – 70, 2009.
[16] G. D. Kim, B. G. Loh, “An ultrasonic elliptical vibration cutting device for micro V-groove machining: Kinematical analysis and micro V-groove machining characteristics,” Journal of Materials Processing Technology 190 p. 181–188, 2007.
[17] D. S. Park, M. W. Chob, H. H. Lee, W. S. Cho, “Micro-grooving of glass using micro-abrasive jet machining,” Journal of Materials Processing Technology 146 P. 234–240, 2004.
[18] Z. Lu, T. Yoneyama, “Micro cutting in the micro lathe turning system,” International Journal of Machine Tools & Manufacture 39,p. 1171–1183, 1999.
[19] F. Z. Fang, H. Wu, Y. C. Liu and S. T. Ng, “Burr Formation in Fly-cutting,” STR/03/022/MT, 2003.
[20] W. Ehrfeld, Micro System Technologies, (ed. H.Reichl), Springer-Verlag, Heidelberg, 1990.
[21] W. Bacher, K. Bade, B. Matthis, M. Saumer, R. Schwarz, “Fabrication of LIGA mold inserts,” Microsystem Technologies 4 P. 117~119, 1998.
[22] R. A. Turner, “TAPERED LIGA MOLD INSERT,” A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College In partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering in The Department of Mechanical Engineering, December, 2002.
[23] H. H. Yang and C. T. Pan “Analogous Micro-optical Components Fabricated Using Excimer Laser Ablation” Tamkang Journal of Science and Engineering, Vol. 6, No. 3, pp.145-150, 2003.
[24] H. L. Yuan, S. Gao, M. N. Dai, C. L. Zong, D. Günther,G. H. Fontaine, X. M. Liu, C. R. Diwu, “Simultaneous determinations of U–Pb age, Hf isotopes and trace element compositions of zircon by excimer laser-ablation quadrupole and multiple-collector ICP-MS,” Chemical Geology 247 100–118,2008.
[25] L. K. Chen, “Mechanism and Modeling of Ring Pattern Formation for Electron Beam Exposure on Zwitterresist,” Lpn. J. Appl. Phys. Part1, Vol.42 No. 6B, 3838-841, 2003.
[26] [30] A.M. Sukhadia, A. Datta, and D.G. Baird, Int’l Polym. Proc., VII (3), 218, 1992.
[27] P. K. Wright, “21st century manufacturing,”2001.
[28] C. H. Hung, T. H. Yu, J. A. Cheng, C. H. Chang, Y. H. Hsiau and C. H. Tien, “Micro lens Array by Ink-Jet Technology for LCD Backlight Applications” SID ’08 Digest 1553-1555, 2008.
[29] Y. Ishii, S. Koike, Y. Arai and Y. Ando, “Ink-Jet Fabrication of Polymer Microlens for Optical-I/O Chip Packaging,” Jpn. J. Appl. Phys. Vol. 39 pp. 1490–1493, 2000.
[30] J. H. Hwang, S. G. Lee, D. M. Shin, W. C. Kim, C. W. Park, and W. I. Kang, J. H. Seo, S. J. Lee, J. R. Koo, G. W. H., and Y. K. Kim, “Reflection Pattern Printing for Light Guide Using an Ink-Jet Coating Method,” SID 08 DIGEST, 2008.
[31] C.H. Hung, T.-H. Yu, J. A. Cheng, C.-H. Chang, Y. H. Hsiau, T.-Y. Li, C. N. Mo, and C. H. Tien, “Microlens Array by Ink-Jet Technology for LCD Backlight Applications,” SID 08 DIGEST, 2008.
[32] S. Ahn, J. Cha, H. Myung, S. M. Kim,“ Continuous ultraviolet roll nanoimprinting process for replicating large-scale nano- and micropatterns” Appl. Phys. Lett. 89, 213101 , 2006.
[33] S. Ahn, M. Choi, H. Bae, J. Lim, H. Myung, H. Kim, and S. Kang, “Design and Fabrication of Micro Optical Film by Ultraviolet Roll Imprinting,” Japanese Journal of Applied Physics Vol. 46, No. 8B, pp. 5478–5484, 2007.
[34] A. Nagasawa, T. Eguchi, Y. Sanai and K. Fujisawa “A Slim and Bendable Backlight System Manufactured by a Roll-to-Roll Continuous Process,” IDW‘06 945-948, 2006.
[35] V. W. Jones, S. Theiss, M. Gardiner, J. Clements and J. Florczak, “Roll to Roll manufacturing of subwavelength optics,” Proc. of SPIE Vol. 7205 72050T-1.
[36] Y.J. Jung, L. J. Lee, and K. W. Koelling, “Hot Embossing in Micro fabrication. Part I: Experimental,” POLYMER ENGINEERING AND SCIENCE, Vol. 42, No. 3, MARCH 2002.
[37] S. Lan, H. J. Lee, E. H. Kim, J. Ni, S. H. Lee, X. Lai, J. H. Song, N. K. Lee, M. G. Lee, “A parameter study on the micro hot-embossing process of glassy polymer for pattern replication,” Microelectronic Engineering 86 2369–2374, 2009.
[38] M.G. Lee, H.W. Choi, J.H. Min, J.S. Choi, J.H. Kim, S.M. Lee, “Optical Characteristics of Holographic Light-Guide Plate for LCD,” EURODISPLAY 2002, 2002.
[39] S. M. Lee, H. W. Choi, M. G. Lee, J. H. Min, J. S. Choi, J. H. Kim, S. I.Kim, Y. S. Choi, and K. H. Lee, “New Concept for Improvement of White Color Balance in Hologram Back-light Units,” SID 03 Digest 49,pp. 1361-1363 , 2003.
[40] H. S. Lee, S. M. Lee, J. S. Choi, J. H. Min, K. Y. Kim, Y. S. Choi, J. H. Yu, J. H. Kim, and H. Y. Choi, “Improvement of Color Dispersion in Holographic Back-Light Units Using Beat Patterns,” IDW/AD ’05, 2005.
[41] E. Miyamoto, S. Maruyama, A. Nagano, L. M. Murillo-Mora, “Novel diffraction grating light guide for LED backlight,” Proc. of SPIE Vol. 6488, 2007.
[42] http://www.nanogate.de/en/
[43] LightTools software products, Optical Research Associates, http://www.opticalres.com/lt/ltprodds_f.html
[44] Y. Taira, D. Nakano, H. Numata, A. Nishikai, S. Ono, and F. Yamada, M. Suzuki, and M. Noguchi, R. Singh, and E. G. Colgan,“Low-power LCD using a novel optical system,” SID 02 Digest 50,1313-1315 (2002).
[45] F.Yamada, S.Ono, and Y.Taira “Dual Layered Very Thin Flat Surface Micro Prism Array Directly Molded in an LCD Cell,” EURODISPLAY 2002, 2002.
[46] Y. Taira, H. Numata, D. Nakano, K. Sueoka, F. Yamada, M. Suzuki, M. Noguchi, R. Singh, and Evan G. Colgan, “Color Filterless Liquid Crystal Display Illuminated with LEDs,” SID 03 Digest 34, 1250–1253(2003).
[47] R. Caputo, L. D. Sio, M. J.J. Jak, E. J. Hornix, D. K.G. de Boer, and H. J. Cornelissen, “Short period holographic structures for backlight display applications,” OPTICS EXPRESS, Vol. 15, No. 17 , August 2007.
[48] Martin J. J. Jak, Robert Caputo, Eefje J. Hornix, Luciano de Sio, Dick K. G. de Boer, Hugo J. Cornelissen,"Color-separating backlight for improved LCD efficiency,"Journal of the SID 16(8),803-810(2008).
[49] Dick K.G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch,Eefje J. Hornix, Martin J.J. Jak,"Diffractive grating structures for colour-separating backlights,"Proceedings of the SPIE 6196, 61960R(2006).
[50] Hui-Hsiung Lin, Chi-hung Lee, and Mao-Hong Lu, “Dye-less color filter fabricated by roll-to-roll imprinting for liquid crystal display applications,” OPTICS EXPRESS, Vol. 17, No. 15, July 2009.
[51] D. R. Selviah, K. Wang, “Modeling of a Color-Separating Backlight with Internal Mirrors,” SID 04 Digest P-64, pp.487-489, 2004.
[52] Po-Chou Chen, Hui-Hsiung Lin, Cheng-Huan Chen, Chi-Hung Lee, “Color separation system with angularly positioned light source module for pixelized backlighting,” OPTICS EXPRESS, Vol. 18, No. 2, January 2010.
[53] J. Rheims, J. Köser and T. Wriedt, “ Refractive-index measurements in the near-IR using an Abbe refractometer, ” Meas. Sci. Technol. 8, 601-605 (1997).
[54] P. P. Herrmann, “Determination of thickness, refractive index, and dispersion of waveguiding thin films with an Abbe refractometer, ” Appl. Opt. 19, 3261-3262 (1980).
[55] S.Nemoto, "Measurement of the refractive index of liquid using laser beam displacement",APPLIED OPTICS, 31 (31) , 1992.
[56] D. Donisi, R. Caputo, and G. Cennini, “Holographic grating based high sensitivity device for refractive index measurements, ” Opt. Express 18, 15236-15241 (2010).
[57] T. Tamulevičiu s, R. Šeperysa, M. Andrulevičius, V. Kopustinskas, Šarūnas Meškinis, S. Tamulevičius, V. Mikalayeva, R. Daugelavičius, “Application of holographic sub-wavelength diffraction gratings for monitoring of kinetics of bioprocesses, ” Appl. Surf. Sci. 258, 9292–9296 (2012).
[58] T. Tamulevičius, R. Šeperys, M. Andrulevičius, S. Tamulevičius., “Total internal reflection based sub-wavelength grating sensor for the determination of refractive index of liquids, ” Photonics and Nanostructures – Fundamentals and Applications 9 , 140–148(2011).
[59] D.C. Su, J.Y. Lee, M.H. Chiu, “New type of liquid refractometer, ” Opt. Eng. 37, 2795–2797 (1998).
[60] M. G. Moharam, D. A. Pommet, and E. B. Grann, Orlando, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” T. K. Gaylord Vol. 12, No. 5 J. Opt. Soc. Am. A 1077, May 1995.
[61] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” Vol. 71, No. 7 J. Opt. Soc. Am. 811, July 1981.
[62] P. S. J. Russell, “Power conservation and field structures in uniform dielectric gratings,” Vol. 1, No. 3 J. Opt. Soc. Am. A 293, March 1984.
[63] T. K. Gaylord, “Analysis and Applications of optical diffraction by gratings,” Proceedings of the IEEE 73, pp894-937, 1985.
[64] ASAP software products,, Breault Research Organization, http://www.breault.com/
[65] LightTools software products, http://www.opticalres.com/lt/ltprodds_f.html
[66] CodeV software products, Optical Research Associates, http://www.opticalres.com/lt/ltprodds_f.html
[67] G. D. Danilatos, “Foundations of environmental scanning electron microscopy,” Advances in Electronics and Electron Physics 71: 109–250, 1988.
[68] “Force measurements with the atomic force microscope: Technique, interpretation and applications.” Surface Science Reports 59: 1-152, 2005.
[69] E. Hecht, Optics (Addison Wesley Co., 2001).