在本工作中，我們研製適用於兆赫波段的電控可調式液晶消色差四分之一波長波片，並驗證其消色差及消色差範圍可調性之表現。
根據理論模型及模擬結果，我們可預測三片與四片液晶組成消色差四分之一波片之表現。考慮穿透率，我們所設計的元件由三片兆赫波段下的液晶(MDA-00-3461)相位調制器所組成。根據理論，我們設計每片液晶相位調制器所需的厚度及雙折射率。樣品中使用銦錫氧化物奈米晶鬚作為兆赫波段之透明電極，以量測之電壓-相位特性曲線推估樣品所需外加之電壓。同時改變每片樣品之等效雙折射率能使消色差範圍平移，由此實現本設計之可調性。
此外，我們建立了可量測兆赫波之偏振態的兆赫波時域光譜儀，以量測及計算兆赫波之史托克參數。實驗結果顯示我們所設計的兆赫波消色差四分之一波長波片在0.30~0.45 THz範圍有消色差的表現，並且可移動至0.35~0.50 THz之範圍，與理論預測結果大致符合。

In this work, we constructed a liquid-crystal-based electrically tunable terahertz (THz) achromatic quarter-waveplate (AQWP), and demonstrated its performance in achromatism and the tunability of its achromatic range.
According to the theoretical model and the simulation results, the expected performance of AQWP composed of three LC and four LC cells are compared. For better transmittance, we choose the design with three LC(MDA-00-3461) THz phase shifters. Using the Jones matrix formulism by a simple algorithm, we designed thickness and bias of each LC cell. ITO nanowhiskers (NWhs),highly transparent in the THz frequency band, is used as the transparent electrode of our LC cells. The voltage applied to each cell is estimated by the characteristic bias-phase shift curve of each cell. We demonstrated that by judiciously changing the effective birefringence of each cell, achromatic range of the AQWP can be tuned.
Besides, we set up a polarization-resolved THz time-domain spectroscopy (TDS). The Stokes parameters of the THz wave can be determined. The experimental results show that our AQWP design achieve achromatism in the frequency range of 0.30~0.45 THz. Furthermore, the achromatic range can be shifted to 0.35~0.50 THz. The results are in general agreement with the theoretical predictions.

[1] Terahertz Science Group University of Fukui (FIR-FU). (2011). What is THz-TDS? Available: http://fir.u-fukui.ac.jp/thzlab/index_E.html
[2] D. Auston, K. Cheung, and P. Smith, "Picosecond photoconducting Hertzian dipoles," Applied physics letters, vol. 45, pp. 284-286, 1984.
[3] A. Rice, Y. Jin, X. F. Ma, X. C. Zhang, D. Bliss, and e. al., "Terahertz optical rectification from <110> zincblende crystals," Applied Physics Letters, vol. 64, pp. 1324-1326, 1994.
[4] X. C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, "Generation of femtosecond electromagnetic pulses from semiconductor surfaces," Applied Physics Letters, vol. 56, pp. 1011-1013, 1990.
[5] R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, et al., "Terahertz semiconductor heterostructure laser," Nature, vol. 417, pp. 156-159, 2002.
[6] Q. Wu and X. C. Zhang, "Free-space electro-optic sampling of terahertz beams," Applied Physics Letters, vol. 67, pp. 3523-3525, 1995.
[7] D. E. Spence, J. M. Evans, W. E. Sleat, and W. Sibbett, "Regeneratively initiated self-mode-locked Ti:sapphire laser," Optics Letters, vol. 16, pp. 1762-1764, 1991.
[8] J. V. Rudd, J. L. Johnson, and D. M. Mittleman, "Cross-polarized angular emission patterns from lens-coupled terahertz antennas," Journal of the Optical Society of America B, vol. 18, pp. 1524-1533, 2001.
[9] C. A. Schmuttenmaer, "Exploring Dynamics in the Far-Infrared with Terahertz Spectroscopy," Chemical Reviews, vol. 104, pp. 1759-1780, 2004.
[10] C.-S. Yang, M.-H. Lin, C.-H. Chang, P. Yu, J.-M. Shieh, C.-H. Shen, et al., "Non-Drude Behavior in indium-tin-oxide nanowhiskers and thin films investigated by transmission and reflection THz time-domain spectroscopy," Quantum Electronics, IEEE Journal of, vol. 49, pp. 677-690, 2013.
[11] X.-w. Lin, J.-b. Wu, W. Hu, Z.-g. Zheng, Z.-j. Wu, G. Zhu, et al., "Self-polarizing terahertz liquid crystal phase shifter," AIP Advances, vol. 1, p. 032133, 2011.
[12] C.-Y. Chen, C.-L. Pan, C.-F. Hsieh, Y.-F. Lin, and R.-P. Pan, "Liquid-crystal-based terahertz tunable Lyot filter," Applied Physics Letters, vol. 88, p. 101107, 2006.
[13] H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature, vol. 444, pp. 597-600, 2006.
[14] B. Scherger, C. Jördens, and M. Koch, "Variable-focus terahertz lens," Optics Express, vol. 19, pp. 4528-4535, 2011.
[15] S.-T. Wu, U. Efron, and L. D. Hess, "Birefringence measurements of liquid crystals," Applied Optics, vol. 23, pp. 3911-3915, 1984.
[16] F. Yang and J. R. Sambles, "Microwave liquid crystal wavelength selector," Applied Physics Letters, vol. 79, p. 3717, 2001.
[17] L. Wang, X.-w. Lin, X. Liang, J.-b. Wu, W. Hu, Z.-g. Zheng, et al., "Large birefringence liquid crystal material in terahertz range," Optical Materials Express, vol. 2, pp. 1314-1319, 2012.
[18] N. Vieweg, M. K. Shakfa, and M. Koch, "BL037: A nematic mixture with high terahertz birefringence," Optics Communications, vol. 284, pp. 1887-1889, 2011.
[19] T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, "Terahertz time-domain spectroscopy studies of the optical constants of the nematic liquid crystal 5CB," Applied Optics, vol. 42, pp. 2372-2376, 2003.
[20] C.-S. Yang, C.-J. Lin, R.-P. Pan, C. T. Que, K. Yamamoto, M. Tani, et al., "The complex refractive indices of the liquid crystal mixture E7 in the terahertz frequency range," Journal of the Optical Society of America B, vol. 27, pp. 1866-1873, 2010.
[21] C.-C. S. Cheng-Pin Ku, Chia-Jen Lin, Ru-Pin Pan and Ci-Ling Pan, "THz Optical Constants of the Liquid Crystal MDA-00-3461," Molecular Crystals and Liquid Crystals, vol. 541, pp. 65/[303]-70/[308], 2011.
[22] C.-S. Yang, T.-T. Tang, P.-H. Chen, R.-P. Pan, P. Yu, and C.-L. Pan, "Voltage-controlled liquid-crystal terahertz phase shifter with indium-tin-oxide nanowhiskers as transparent electrodes," Optics Letters, vol. 39, pp. 2511-2513, 2014.
[23] C.-F. Hsieh, R.-P. Pan, T.-T. Tang, H.-L. Chen, and C.-L. Pan, "Voltage-controlled liquid-crystal terahertz phase shifter and quarter-wave plate," Optics Letters, vol. 31, pp. 1112-1114, 2006.
[24] C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, "Magnetically tunable room-temperature 2 pi liquid crystal terahertz phase shifter," Optics Express, vol. 12, pp. 2625-2630, 2004.
[25] Y. Wu, X. Ruan, C.-H. Chen, Y. J. Shin, Y. Lee, J. Niu, et al., "Graphene/liquid crystal based terahertz phase shifters," Optics Express, vol. 21, pp. 21395-21402, 2013.
[26] H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, "Electrically tunable room-temperature 2 pi liquid crystal terahertz phase shifter," Ieee Photonics Technology Letters, vol. 18, pp. 1488-1490, 2006.
[27] K. Altmann, M. Reuter, K. Garbat, M. Koch, R. Dabrowski, and I. Dierking, "Polymer stabilized liquid crystal phase shifter for terahertz waves," Optics Express, vol. 21, pp. 12395-12400, 2013.
[28] R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, "Liquid crystal based electrically switchable Bragg structure for THz waves," Optics Express, vol. 17, pp. 7377-7382, 2009.
[29] C.-J. Lin, Y.-T. Li, C.-F. Hsieh, R.-P. Pan, and C.-L. Pan, "Manipulating terahertz wave by a magnetically tunable liquid crystal phase grating," Optics Express, vol. 16, pp. 2995-3001, 2008.
[30] H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, "A metamaterial solid-state terahertz phase modulator," Nature Photonics, vol. 3, pp. 148-151, 2009.
[31] C.-F. Hsieh, Y.-C. Lai, R.-P. Pan, and C.-L. Pan, "Polarizing terahertz waves with nematic liquid crystals," Optics Letters, vol. 33, pp. 1174-1176, 2008.
[32] E. Hecht, "Optics," ed: Addison-Wesley, 2001.
[33] A. Saha, K. Bhattacharya, and A. K. Chakraborty, "Achromatic quarter-wave plate using crystalline quartz," Applied Optics, vol. 51, pp. 1976-1980, 2012.
[34] R. M. A. Azzam and C. L. Spinu, "Achromatic angle-insensitive infrared quarter-wave retarder based on total internal reflection at the Si-SiO2 interface," Journal of the Optical Society of America A, vol. 21, pp. 2019-2022, 2004.
[35] J.-B. Masson and G. Gallot, "Terahertz achromatic quarter-wave plate," Optics Letters, vol. 31, pp. 265-267, 2006.
[36] A. V. Samoylov and V. S. Samoylov, "Achromatic and super-achromatic zero order waveplates," in LFNM 2003: 5th International Workshop on Laser and Fiber-Optical Networks Modeling, Piscataway, N.J, 2003, pp. 119-121.
[37] S. Pancharatnam, "Achromatic combinations of birefringent plates," Proc, of the Indian Academy of Sciences, vol. 41, 1955.
[38] G. Destriau and J. Prouteau, "Réalisation d'un quart d'onde quasi achromatique par juxtaposition de deux lames cristallines de même nature," J. Phys. Radium, vol. 10, pp. 53-55, 1949.
[39] M. J. Abuleil and I. Abdulhalim, "Tunable achromatic liquid crystal waveplates," Optics Letters, vol. 39, pp. 5487-5490, 2014.
[40] S. Shen, J. She, and T. Tao, "Optimal design of achromatic true zero-order waveplates using twisted nematic liquid crystal," Journal of the Optical Society of America A, vol. 22, pp. 961-965, 2005.
[41] E. Collett, Field Guide to Polarization: SPIE PRESS, 2005.
[42] B. E. A. Saleh and M. C. Teich, "Fundamentals of Photonics," B. E. A. Saleh, Ed., ed: John Wiley & Sons, Inc., 2007.
[43] G. B. Malykin, "USE OF THE POINCARE SPHERE IN POLARIZATION OPTICS AND CLASSICAL AND QUANTUM MECHANICS. REVIEW " Radiophysics and Quantum Electronics, vol. 40, pp. 175-195, 1997.
[44] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: Cambridge University Press, 1992.
[45] H. Dong, Y. Gong, V. Paulose, and M. Hong, "Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy," Optics Communications, vol. 282, pp. 3671-3675, 2009.
[46] H. Dong, Y. Gong, and M. Olivo, "Measurement of Stokes parameters of terahertz radiation in terahertz time-domain spectroscopy," Microwave and Optical Technology Letters, vol. 52, pp. 2319-2324, 2010.
[47] Y.-S. Lee, Principles of Terahertz Science and Technology: Springer, 2009.
[48] C.-S. Yang, T.-T. Tang, R.-P. Pan, P. Yu, and C.-L. Pan, "Liquid crystal terahertz phase shifters with functional indium-tin-oxide nanostructures for biasing and alignment," Applied Physics Letters, vol. 104, 2014.
[49] C.-S. Yang, C. Kuo, C.-C. Tang, J. C. Chen, R.-P. Pan, and C.-L. Pan, "Liquid-Crystal Terahertz Quarter-Wave Plate Using Chemical-Vapor-Deposited Graphene Electrodes," IEEE Photonics Journal, vol. 7, 2015.
[50] C. Kuo, "Characterization of Graphene Layers in Liquid Crystal Terahertz Phase Shifters," Master of Engineering in Photonics Technologies, Institute of Photonics Technologie, College of Electrical Engineering and Computer Science, National Tsing Hua University, Hsinchu, Taiwan, 2014.
[51] X. Nie, H. Xianyu, R. Lu, T. X. Wu, S.-T. Wu, and Hsin-Ying, "Pretilt Angle Effects on Liquid Crystal Response Time," Journal of Display Technology, vol. 3, 2007.
[52] C.-S. Yang, C.-H. Chang, M.-H. Lin, P. Yu, O. Wada, and C.-L. Pan, "THz conductivities of indium-tin-oxide nanowhiskers as a graded-refractive-index structure," Optics Express, vol. 20, pp. A441-A451, 2012.
[53] C.-P. Lu, "Improvement on the response time of electrically tunable liquid crystal terahertz phase shifter," Master of Science in Electrophysics, Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan, 2010.
[54] Z. Chen, Y. Gong, H. Dong, T. Notake, and H. Minamide, "Terahertz achromatic quarter wave plate: Design, fabrication, and characterization," Optics Communications, vol. 311, pp. 1-5, 2013.