4.2-1 Temperature Effect on Real Refractive Indices
4.4 Temperature Dependence of Gradient of Refractive Indices
So far, the temperature gradient of n is negative for most of the LC. By the different LC e materials and operating temperature, however, the temperature gradient of n will change o from negative to positive by any possibility.
We can derive the Eq. (4.5) and Eq. (4.6) by temperature derivatives of Eq. (3.33) and Eq.
(3.34) respectively [64].
73
Here, we have to check the three parameters ( B ,β ,(Δn)0), and all of them can be determined by fitting average refractive indices (< >n ) and birefringence (Δn). From the
Fig. 4.15, we find the dne
dT for E7 is negative throughout its nematic range because n e decreases with the temperature increasing in the entire nematic phase. On the other hand, the
result of dno
dT is shown as Fig. 4.16. We can find the E7 exhibits a negative dno
dT at room temperature and change into large positive number. In the other words, there is a transition
temperature which lets the dno 0
dT = . Here, the transition temperature is defined as cross-over temperature. We show the results clearly as the Fig. 4.17.
300 305 310 315 320 325 330
-0.012
305 306 307 308 309
-0.0015 -0.0010
dne/dT
Temperature(oC)
Fig. 4.15 Temperature-dependent dne
dT of E7 at different frequencies (0.34, 0.41, 0.53, 0.70, 0.80, 0.89, 0.98, 1.10, 1.19, 1.29 and 1.40 THz), respectively.
74
300 305 310 315 320 325 330
0.000 0.001 0.002 0.003 0.004 0.005
dn o/dT
Temperature(oC)
0.34THz 0.41THz 0.53THz 0.70THz 0.80THz 0.89THz 0.98THz 1.10THz 1.19THz 1.29THz 1.40THz
305 306 307 308 309 310 311 312 313
0.0000 0.0002 0.0004
dno/dT
Temperature(oC)
Fig. 4.16Temperature-dependent dno
dT of E7 at different frequencies (0.34, 0.41, 0.53, 0.70, 0.80, 0.89, 0.98, 1.10, 1.19, 1.29 and 1.40 THz), respectively.
Fig. 4.17 Temperature-dependent dno
dT of E7 at 0.41(THz).
75
Chapter 5 Conclusions
Here, we investigate the optical constants of E7 depending on temperature (26°C ~69°C) and frequency (0.2~1.4THz) in the nematic and isotropic phase, respectively. At 26°C the real parts of indices distribute with ne = 1.71 ± 0.01, no = 1.57 ± 0.02, giving rise to a birefringence of 0.14 ± 0.01 and the index of isotropic phase fall at 1.61 ± 0.01 in the 0.2 to 1.4 THz range.
The order parameter extracted from temperature-dependent birefringence of E7 coincides approximately with the results in visible region (589 nm). On the other hand, for the imaginary part of the refractive indices, we note that κe = 0.014 ± 0.002, κo = 0.036 ± 0.004 and κ in the isotropic phase is 0.030 ± 0.005. Most of all, the extended Cauchy equations describing the temperature dependence of refractive indices of liquid crystal is confirmed completely in this study.
76
References
1. Ernst Lueder, Liquid Crystal Displays Addressing Schemes and Electro-optical Effect (Wiley, 2001)
2. K. C. Lim, J. D. Margerum and A. M. Lackner, Appl. Phys. Lett. 62 (10) (1993) 3. F. Yang, J. R. Sambles, Appl. Phys. Lett. 79, 3717-3719 (2001)
4. Eric R. Mueller, The Industrial Physicist 27, Aug./Sept. (2003)
5. Daniel Mittleman, Sensing with Terahertz Radiation, 1st ed. (Spring, New York, 2002)
6. D. Spence, P. Kean and W. Sibbett. Opt. Lett. 16, 42 (1991)
7. M. van Exter, Ch. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 55, 337 (1989)
8. M. van Exter, D. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990)
9. X.-C. Zhang, B. Hu, J. Darrow and D. Auston. Appl. Phys. Lett 56, 1011 (1990)
10. Q. Wu, X. –C. Zhang, Appl. Phys. Lett. 68, 1604-1606 (1996)
11. Iam-Choon Khoo, Liquid Crystals Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995)
12. P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, New York, 1983).
13. Jun Li, Student, Chien-Hui Wen, Sebastian Gauza, Ruibo Lu, and Shin-Tson Wu, J.
Display Technol. 1, 51-61 (2005)
14. Eugene Hecht, Optics 3rd ed. (Addison Wesley Longman, New York, 1998)
77
15. K. C. Lim, J. D. Margerum, A. M. Lackner, Appl. Phys. Lett. 62 (10) (1993)
16. Chao-Yuan Chen, Cho-Fan Hsieh, Yea-Feng Lin, Ru-Pin Pan and Ci-Ling Pan, Opt.
Express 12 (12) (2004)
17. C. F. Hsieh, R. P. Pan, T. T. Tang, H. L. Chen and C. L. Pan, Opt. Lett. 31, 1112-1114 (2006)
18. I. H. Libon, S. Baumgä, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch and P.
Dawson, Appl. Phys. Lett. 76, 2821-2823 (2000)
19. F. Yang, J. R. Sambles, Appl. Phys. Lett. 79, 3717-3719 (2001)
20. H. Nemec, P. Kuzel, L. Duvillaret, A. Pashkin, M. Dressel and M. T. Sebastian, Opt.
Lett. 30, 549-551 (2005)
21. Chao-Yuan Chen, Ci-Ling Pan, Cho-Fan Hsieh, Yea-Feng Lin and Ru-Pin Pan, Appl.
Phys. Lett. 88, 101107 (2006)
22. I-Chen Ho, Ci-Ling Pan, Cho-Fan Hsieh and Ru-Pin Pan, Opt. Lett. 33 (2008)
23. Martin van Exter, Ch. Fattinger, and D. Grischkowsky, Optical Letter 14, 20 (1989)
24. A. S. Krishnagopal, V. Kumar, Radiat. Phys. Chem. 70, 559 (2004)
25. H. P. Freund, G. R. Neil, Proceedings of IEEE 87, 782 (1999)
26. R. Kompfner, N. T. Williams, Proc. IRE 41, 1602 (1953)
27. T. Y. Chang, T. J. Bridges, Opt. Commun. 1, 423 (1970)
78
28. M. Inguscio, G. Moruzzi, K. M. Evenson and D. A. Jennings, J. Appl. Phys. 60, 161 (1986)
29. M. Bass, Phys. Rev. Lett. 9, 446 (1962)
30. A. Bonvalet, Appl. Phys. Lett. 67, 2907 (1995)
31. O. S. Heavens, R. W. Ditchburn, Insight into Optics (1987)
32. Justin T. Darrow, Xi-Cheng Zhang, David H. Austion and Jeffrey D Morse, IEEE J.
Quantum electron 28, 1607 (1992)
33. M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, M. Haiml, U. Seifner, and U.
Keller, Appl. Phys. Let. 74, 1993 (1999)
34. M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, and Jo. Schneider, Appl. Phys.
Let. 58, 1881 (1991)
35. M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, M. Haiml, U. Seifner, and U.
Keller, Appl. Phys. Let. 74, 1993 (1999)
36. B. Salem, D. Morris, V. Aimez, J Veerens, J Beauvais and D Houde., J. Phys.:
Condens. Matter 17 7327-7333 (2005)
37. M. Mikulics, E. A. Michael, M. Marso, M. Lepsa, A. van der Hart, and H. Lüth, A.Dewald, S. Stanček and M. Mozolik and P. Kordoš, Appl. Phys. Lett. 89, 071103, (2006)
38. S. Kono, M. Tani and K. Sakai, IEE, Proc. Optoelectron. 149, 105-109 (2002)
79
39. Sang-Gyu Park, Michael R. Melloch and Andrew M. Weiner, IEEE J. Quantum Electronics. 35, 810-819 (1999)
40. S Kono, Masahiko Tani and Kiyomi Sakai, Appl. Phys. Lett. 79, 898-900 (2001)
41. S. E. Ralph, D. Grischkowsky, Appl. Phys. Lett. 60, 1070 (1992)
42. Q. Wu, X.-C. Zhang, Appl. Phys. Lett. 70, 1784 (1997)
43. Q. Wu, X.-C. Zhang, Appl. Phys. Lett. 71, 1285 (1997)
44. F. G. Sun, G. A. Wagoner and X.-C. Zhang, Appl. Phys. Lett. 67, 1656 (1995)
45. J. Bromage, I.A. Walmsley and C.R.Stroud, Appl. Phys. Lett. 75, 2181 (1999)
46. S. Kono, M. Tani, G. Ping and K. Sakai, Appl. Phys. Lett. 77, 4104 (2000)
47. Tsung-Ta Tang, Ru-Pin Pan, Yi-Chao Wang and Ci-Ling Pan, Ferroelectrics 364, 72-77 (2008)
48. Jun Li, Student, Chien-Hui Wen, Sebastian Gauza, Ruibo Lu, and Shin-Tson Wu,
J. Display Technol. 1, 51-61 (2005)
49. Jun Li, Shin-Tson Wu, Stefano Brugioni, Riccardo Meucci, and Sandro Faetti, J. Appl.
Phys. 97, 073501 (2005)
50. S. Brugioni, R. Meucci, Infrared Physics & Technology 49, 210–212 (2007)
51. Shin-Tson Wu, Phys. Rev. A 33, 1270-1274 (1986)
52. S. Brugioni, R. Meucci, Infrared Physics & Technology 46, 17–21 (2004)
80
53. Fuzi Yang, J. R. Sambles, Appl. Phys. Lett. 79 No. 22, 26 (2001)
54. Fuzi Yang, J. R. Sambles, Appl. Phys. Lett. 81, No. 11, 9 (2002)
55. Fuzi Yang, J. R. Sambles, Liq. Cryst. 30, No. 5, 599-602 (2003)
56. M. Koeberle, T. Göbel, D. Schönherr, S. Mueller, R. Jakoby, P. Meissner and H.-L.
Hartnagel, German Microwave Conference (2008)
57. H. Mada and S. Kobayashi, Mol. Cryst. Liq. Cryst. 33, 47 (1976)
58. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1962)
59. Kittel, Introduction to Solid State Physics, 7th ed (Wiley)
60. M. F. Vuks, Opt. Spectrosc. 20, 644 (1966)
61. Jun Li ,Shin-Tson Wu, Journal of Applied Physics 96, 6253-6258 (2004)
62. Jun Li, Sebastian Gauza, and Shin-Tson Wu, Journal of Applied Physics 96, 19-24 (2004)
63. A. D. Buckingham, Molecular Electro-optics, (Marcel Dekker, New York, 1976) 64. Jun Li, Sebastian Gauzia, and Shin-Tson Wu, Optics Express 12, 2002-2010 (2004)