向列相液晶中基于四波混频的光学相位共轭研究
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摘要
向列相液晶是一种高性能的非线性光折变材料,而且通过掺杂染料可使其性能大为改良。由于向列相液晶大的非线性系数,使得利用向列相液晶产生光学相位共轭波称为可能。从19世纪80年代起,已经有很多学者在这种材料中进行了光学相位共轭实验。本论文主要用简并四波混频的方法产生光学相位共轭波,对掺杂甲基红(MR)和掺杂C60的向列相液晶E7中的光学相位共轭特性进行了理论与实验的研究。
我们利用向列相液晶中在相干光入射下形成的折射率光栅结合麦克斯韦方程组,参考相关文献推导了向列相液晶中四束光相互作用的四波耦合方程。并依据材料吸收系数的大小求得了方程的解析结果和数值结果,分别适合对不同样品的分析。
我们制作了实验所需的E7+1%MR和E7+0.5%C60液晶盒,从理论上定性分析了两种样品各自的取向光折变的特点。搭建了用来产生光学相位共轭光的简并四波混频光路,测量了样品的基本光学特性,对两种样品都成功观察到了光学相位共轭波的产生。对不同实验条件下产生的相位共轭波进行了测量,得到了最佳的实验条件包括:样品厚度、入射光夹角、入射光偏振态等。
在确定以上实验条件的前提下,两种样品在入射光强影响下的光学相位共轭波的变化和响应时间特性被详细测量。发现相位共轭光随入射光功率的变化存在饱和效应,并且E7+1%MR样品中形成了永久光栅,E7+0.5%C60样品中形成了瞬时光栅。另外还详细的研究了E7+0.5%C60样品的外加电压特性,得到了产生相位共轭光的阈值电压和最佳电压。并对比数值结果与理论结果分析讨论以上的测量数据,发现数值方法与实验结果符合很好。
Nematic liquid crystal (NLC) is an excellent nonlinear photorefractive material with high performance. The properties of materials are improved greatly by doping them with dye. Nematic liquid crystal has a large non-linear coefficient, so it is possible to produce optical phase conjugation (OPC) wave in right condition. Since 1980s, a number of scholars have done optical phase conjugation experiment using liquid crystals. In this paper, degenerate four-wave mixing method is adopted to produce OPC wave. OPC properties of Methyl red-doped and C60-doped nematic liquid crystal are researched by theoretical and experimental studies.
Four-wave coupled equations in nematic liquid crystal have been derived using combination of the refractive index grating formed by incident coherent light and Maxwell's equations. According to the magnitude of absorption coefficient, analytical solution and numerical solution have been obtained.
E7+1%MR and E7+0.5%C60 LC cell were prepared in our experiments. The photorefractive orientationnal properties of two samples have been analyzed. Optical circuit for degenerate four-wave mixing used in phase conjugation has been set up. OPC wave was measured in different experimental conditions including the sample thickness, probe and pump light angle, incident light polarization, applied voltage and so on. And the best experimental conditions have been obtained.
Based on the best experimental conditions,the change of OPC wave and response time characteristics were measured in detail under the influence of the variation of optical power. Saturation effect was found in OPC changing with incident light power. And permanent grating was formed in E7+1%MR samples, transient grating was formed in E7 +0.5%C60 samples. Voltage characteristics of E7 +0.5%C60 samples have also been researched. And experiment data has been discussed compared to numerical and analytical results.
我们利用向列相液晶中在相干光入射下形成的折射率光栅结合麦克斯韦方程组,参考相关文献推导了向列相液晶中四束光相互作用的四波耦合方程。并依据材料吸收系数的大小求得了方程的解析结果和数值结果,分别适合对不同样品的分析。
我们制作了实验所需的E7+1%MR和E7+0.5%C60液晶盒,从理论上定性分析了两种样品各自的取向光折变的特点。搭建了用来产生光学相位共轭光的简并四波混频光路,测量了样品的基本光学特性,对两种样品都成功观察到了光学相位共轭波的产生。对不同实验条件下产生的相位共轭波进行了测量,得到了最佳的实验条件包括:样品厚度、入射光夹角、入射光偏振态等。
在确定以上实验条件的前提下,两种样品在入射光强影响下的光学相位共轭波的变化和响应时间特性被详细测量。发现相位共轭光随入射光功率的变化存在饱和效应,并且E7+1%MR样品中形成了永久光栅,E7+0.5%C60样品中形成了瞬时光栅。另外还详细的研究了E7+0.5%C60样品的外加电压特性,得到了产生相位共轭光的阈值电压和最佳电压。并对比数值结果与理论结果分析讨论以上的测量数据,发现数值方法与实验结果符合很好。
Nematic liquid crystal (NLC) is an excellent nonlinear photorefractive material with high performance. The properties of materials are improved greatly by doping them with dye. Nematic liquid crystal has a large non-linear coefficient, so it is possible to produce optical phase conjugation (OPC) wave in right condition. Since 1980s, a number of scholars have done optical phase conjugation experiment using liquid crystals. In this paper, degenerate four-wave mixing method is adopted to produce OPC wave. OPC properties of Methyl red-doped and C60-doped nematic liquid crystal are researched by theoretical and experimental studies.
Four-wave coupled equations in nematic liquid crystal have been derived using combination of the refractive index grating formed by incident coherent light and Maxwell's equations. According to the magnitude of absorption coefficient, analytical solution and numerical solution have been obtained.
E7+1%MR and E7+0.5%C60 LC cell were prepared in our experiments. The photorefractive orientationnal properties of two samples have been analyzed. Optical circuit for degenerate four-wave mixing used in phase conjugation has been set up. OPC wave was measured in different experimental conditions including the sample thickness, probe and pump light angle, incident light polarization, applied voltage and so on. And the best experimental conditions have been obtained.
Based on the best experimental conditions,the change of OPC wave and response time characteristics were measured in detail under the influence of the variation of optical power. Saturation effect was found in OPC changing with incident light power. And permanent grating was formed in E7+1%MR samples, transient grating was formed in E7 +0.5%C60 samples. Voltage characteristics of E7 +0.5%C60 samples have also been researched. And experiment data has been discussed compared to numerical and analytical results.
引文
1 G. S. He. Optical Phase Conjugation: Principles, Techniques and Application. Progress in Quantum Electronics, 2002, 26: 131~191
2陈军.光学位相共轭及其应用.科学出版社, 1999: 1~10
3 I. C. Khoo. Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena. John Wiley & Sons, INC, 1995: 47~48
4 S. P. Almeida, S. P. Varmit. Phase Conjugation By Four-Wave in Nematic Liquid Crystals. Proc SPIE, 1991, 1500: 34~35
5陈世伟,钟鸣,欧群飞等.向列相液晶四波混频的若干问题.激光与光电子学进展, 2007, 44(9): 55~59
6 I. C. Khoo, Y. Liang. Stimulated Orientational and Thermal Scatterings and Self-starting Optical Phase Conjugation with Nematic Liquid Crystals. Phys. Rev. E, 2000, 62(5): 6722~6733
7尚庆虎.光学相位共轭与四波混频.光学与光电子技术, 2003, 1(3): 9~11
8 X. D. Sun, Y. B. Pei, F. F. Yao, J. L. Zhang, C. F. Hou. AC Electric Field Assisted Orientaonal Photorefractive Effect in C60-Doped Nematic Liquid Crystal. J. Phys. D: Appl. Phys, 2007, (40): 3348~3351
9 O. Koysal, S. Eren. Effect on Response Time and Diffraction Efficiency of Co-usage Azo Dye and Carbon Nanoparticle in Nematic Liquid Crystal. Syntheic Metals, 2008, 158: 527~531
10 L. Z. Ruan, F. Yang, J. R. Sambles. Voltage Dependent Director of a Homeotropic Negative Liquid Crystal Cell. AppL. Phys. Lett, 2008, 93(3): 1~3
11 S. Yilmaz. Optical Properties of Some Mixed Nematic Liquid Crystals in Electric Field. Materials Chemistry and Physics, 2008, 110: 140~144
12 U. A. Laudyn, A. E. Miroshnichenko Observation of Light-Induced Reorientational Effects in Periodic Structures with Planar Nematic-Liquid-Crystal Defects. AppL. Phys. Lett, 2008, 92(20): 203304
13 T. Erneux, A. Gavrielides, K. Green. External Cavity Modes of Semiconductor Lasers with Phase-Conjugate Feedback. 2003, 68(6): 066205
14 A. K. Bhattachariee, G. I. Menon, R. Adhikari. Numerical Method of Lines for the Relaxational Dynamics of Nematic Liquid Crystals. Phys. Rev. E, 2008, 78(2): 026707
15 P. Xie, Z. Q. Zhang. Optical Phase Conjugation in Third-Order Nonlinear Photonic Crystals. Phys. Rev. A, 2004, 69(5): 053806
16 H. Chen, J. Zhang. Continuous-Variable Quantum Cloning of Coherent States with Phase-Conjugate Input Modes Using Linear Optics. Phys. Rev. A, 2007, 75(2): 022306
17 J. Zhang, C. Xie, and K. Peng. Continuous-Variable Telecloning with Phase-Conjugate Inputs. Phys. Rev. A, 2008, 77(2): 022316
18 M. Sabuncu, U. L. Andersen, G. Leuchs. Experimental Demonstration of Continuous Variable Cloning with Phase-Conjugate Inputs. PRL, 2007, 98(17): 170503
19 I. C. Khoo, J. Ding, Y. Zhang, K. Chen, A. Diaz. Supra-Nonlinear Photorefractive Response of Single-Walled Carbon Nanotube-and C60-Doped Nematic Liquid Crystal. AppL. Phys. Lett, 2003, 82(21): 3587~3589
20 G. Zhang, G. Montemezzani, P. Gunter. Orientational Photorefractive Effect in Nematic Liquid Crystal with Externally Applied Fields. Journal of Applied Physics, 2000, 88(4): 1709~1717
21 R. P. Aguilar, J. C. Ramirez-san-Juan, O. Baldovino-Pantaleon,etc. Polarization-Controlled Contrasted Images Using Dye-Doped Nematic Liquid Crystals. Optics Express, 2009, 17(5): 3417-3423
22 A. Me, C. Go. Electric-Field Enhancement and Modulation of Permanent Grating Diffraction in Dye and Carbon Nanotube-Doped Liquid Crystal. Journal of Nanophotonics, 2008, 2: 023510
23 Y. S. Suleiman, S. Ghosh, M. E. Abbasov, G. O. Garlisle. Optical Properties of Permanent Gratings in Liquid Crystal Doped with Dye and Carbon Nanotube. Journal of Materials Science-Materials in Electronics, 2008, 19(7): 662~668
24 Y. Liu, S. Zhang. Improvement of Soliton Communication System with Optical Phase Conjugation. International Journal of Infrared and Millimeter Wave, 1999, 20(9): 1673~1681
25 M. Peccianti, A. D. Rossi, G. Assanto. Electrically Assisted Self-Confinement and Waveguiding in Planar Nematic Liquid Crystal Cells. Appl. Phys. Lett, 2000, 77(7): 7~9
26 S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, F. Kajzar. High Gain of Light in Photoconduction Polymer-Nematic Liquid Crystal Hybrid Structures. Optics Communications, 2001, 187: 257~261
27 D. Fekete, J. Auyeung, A. Yariv. Phase-Conjugate Reflection by Degenerate Four-Wave Mixing in a Nematic Liquid Crystal in the Isotropic Phase. Opt. Lett., 1980, 5(2): 51~53
28 I. C. Khoo. Degenerate Four-Wave Mixing in the Nematic Phase of a Liquid Crystal. Appl. phys. Lett, 1980, 38(3): 123~124
29 I. C. Khoo, S. L. Zhuang. Wavefront Conjugation in Nematic Liquid Crystal Films. IEEE Journal of Quantum Electronics, 1982, 18(2): 246~249
30 I. C. Khoo, R. Normandin. Infrared to Visible Image Conversion Capability of a Nematic Liquid Crystal film. Appl. Phys. Lett, 1985, 47(4): 350~352
31 I. C. Khoo, H. Li, Y. Liang. Self-Starting Optical Phase Conjugation in Dyed Nematic Liquid Crystals with a Stimulated Thermal-Scattering Effect. Opt. Lett, 1993, 18(18): 1490~1492
32 I. C. Khoo, Y. Liang, H. Li. Observation of Stimulated Orientational Scattering and Cross-Polarized Self-Starting Phase Conjugation in a Nematic Liquid-Crystal Film. Opt. Lett, 1995, 20(2): 130~132
33 P. Meindl, R. Macdonald, H. J. Eichler, O. L. Antipov. Low Threshold Self-Pumped Phase Conjugation of an Ar+-Laser Beam in Dye-Doped Nematic Liquid Crystals. Mol. Cryst. Liq. Cryst., 1996, 282: 429~435.
34 A. Miniewicz, S. Bartkiewicz, J. Parka. Optical Phase Conjugation in Dye-Doped Nematic Liquid Crystal. Optics Communications, 1998, 149: 89~95.
35 G. P. Wiederrecht, M. R. Wasielewski. Photorefractivity in Polymer-Stabilized Nematic Liquid Crystals. Proc .SPIE, 1998, 3471: 102~109
36 K. Kitamura, H. Ono, H. Norisada et al. Optical Phase Conjugation by Four Wave Mixing in Photorefractive Mesogenic Composites. Proc. SPIE, 2001, 4279: 175~182
37 L. Lucchetti, M. Di fabrizio, M. Gentili, F. Simoni. Optical Phase Conjugation and Efficient wave Front Correction of Weak Light Beams by Dye-Doped Liquid Crystals. AppL. Phys. Lett, 2003, 83(26): 5389~5391
38 S. Bartkiewicz, J. Mysliwiec. A. Miniewicz. Applications of Photorefractive Liquid Crystals. Proc. SPIE, 2004, 5351: 158~165
39 J. Mysliwiec, S. Bartkiewicz, K. Janus. Optical Phase Conjugation in the Hybrid Polymer Liquid Crystal Panel. Optics Communications, 2007, 276: 58~61
40 I. C. Khoo, M. Y. Shih, M. V. Wood etc. Dye-doped Photorefractive Liquid Crystals for Dynamic and Storage Holographic Grating Formation and Spatial Light Modulation. Proceedings of the IEEE. 1999,87(11): 1897~1901
41 I. C. Khoo. Orientational Photorefractive Effects in Nematic Liquid Crystal Films. IEEE Journal of Quantum Electuonics. 1996, 32(3): 525~534
42 M. Eich, J. Wendorff. Laser-Induced Gratings and Spectroscopy in Monodomains of Liquid-Crystal Polymers. J. Opt. Soc Am B. 1990, (7): 1428~1431
43 I. C.Khoo, H. Li, and Y. Liang. Observation of Orientational Photorefractive Effects in Nematic Liquid Crystal. Opt. Lett, 1994, (19): 1723~1725
44刘思敏,郭儒,许京军.光折变非线性光学及其应用.科学出版社,2004: 45~70
45顾开宇.掺杂甲基红向列液晶取向光折变特性实验研究.哈尔滨工业大学硕士论文,2006: 24~27
46 Xiangyu Sun, Fuguo Xu, Shaozhi Pu, Ye Shang, Shiping Ou, Chunfeng Hou. Observation of Discrete Diffraction and Discrete Spatial Solitons in the Waveguide Array in Methyl-Red Doped Nematic Liquid Crystal. The International Conference on Nanophotonics. Harbin, China, 2009: 219
2陈军.光学位相共轭及其应用.科学出版社, 1999: 1~10
3 I. C. Khoo. Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena. John Wiley & Sons, INC, 1995: 47~48
4 S. P. Almeida, S. P. Varmit. Phase Conjugation By Four-Wave in Nematic Liquid Crystals. Proc SPIE, 1991, 1500: 34~35
5陈世伟,钟鸣,欧群飞等.向列相液晶四波混频的若干问题.激光与光电子学进展, 2007, 44(9): 55~59
6 I. C. Khoo, Y. Liang. Stimulated Orientational and Thermal Scatterings and Self-starting Optical Phase Conjugation with Nematic Liquid Crystals. Phys. Rev. E, 2000, 62(5): 6722~6733
7尚庆虎.光学相位共轭与四波混频.光学与光电子技术, 2003, 1(3): 9~11
8 X. D. Sun, Y. B. Pei, F. F. Yao, J. L. Zhang, C. F. Hou. AC Electric Field Assisted Orientaonal Photorefractive Effect in C60-Doped Nematic Liquid Crystal. J. Phys. D: Appl. Phys, 2007, (40): 3348~3351
9 O. Koysal, S. Eren. Effect on Response Time and Diffraction Efficiency of Co-usage Azo Dye and Carbon Nanoparticle in Nematic Liquid Crystal. Syntheic Metals, 2008, 158: 527~531
10 L. Z. Ruan, F. Yang, J. R. Sambles. Voltage Dependent Director of a Homeotropic Negative Liquid Crystal Cell. AppL. Phys. Lett, 2008, 93(3): 1~3
11 S. Yilmaz. Optical Properties of Some Mixed Nematic Liquid Crystals in Electric Field. Materials Chemistry and Physics, 2008, 110: 140~144
12 U. A. Laudyn, A. E. Miroshnichenko Observation of Light-Induced Reorientational Effects in Periodic Structures with Planar Nematic-Liquid-Crystal Defects. AppL. Phys. Lett, 2008, 92(20): 203304
13 T. Erneux, A. Gavrielides, K. Green. External Cavity Modes of Semiconductor Lasers with Phase-Conjugate Feedback. 2003, 68(6): 066205
14 A. K. Bhattachariee, G. I. Menon, R. Adhikari. Numerical Method of Lines for the Relaxational Dynamics of Nematic Liquid Crystals. Phys. Rev. E, 2008, 78(2): 026707
15 P. Xie, Z. Q. Zhang. Optical Phase Conjugation in Third-Order Nonlinear Photonic Crystals. Phys. Rev. A, 2004, 69(5): 053806
16 H. Chen, J. Zhang. Continuous-Variable Quantum Cloning of Coherent States with Phase-Conjugate Input Modes Using Linear Optics. Phys. Rev. A, 2007, 75(2): 022306
17 J. Zhang, C. Xie, and K. Peng. Continuous-Variable Telecloning with Phase-Conjugate Inputs. Phys. Rev. A, 2008, 77(2): 022316
18 M. Sabuncu, U. L. Andersen, G. Leuchs. Experimental Demonstration of Continuous Variable Cloning with Phase-Conjugate Inputs. PRL, 2007, 98(17): 170503
19 I. C. Khoo, J. Ding, Y. Zhang, K. Chen, A. Diaz. Supra-Nonlinear Photorefractive Response of Single-Walled Carbon Nanotube-and C60-Doped Nematic Liquid Crystal. AppL. Phys. Lett, 2003, 82(21): 3587~3589
20 G. Zhang, G. Montemezzani, P. Gunter. Orientational Photorefractive Effect in Nematic Liquid Crystal with Externally Applied Fields. Journal of Applied Physics, 2000, 88(4): 1709~1717
21 R. P. Aguilar, J. C. Ramirez-san-Juan, O. Baldovino-Pantaleon,etc. Polarization-Controlled Contrasted Images Using Dye-Doped Nematic Liquid Crystals. Optics Express, 2009, 17(5): 3417-3423
22 A. Me, C. Go. Electric-Field Enhancement and Modulation of Permanent Grating Diffraction in Dye and Carbon Nanotube-Doped Liquid Crystal. Journal of Nanophotonics, 2008, 2: 023510
23 Y. S. Suleiman, S. Ghosh, M. E. Abbasov, G. O. Garlisle. Optical Properties of Permanent Gratings in Liquid Crystal Doped with Dye and Carbon Nanotube. Journal of Materials Science-Materials in Electronics, 2008, 19(7): 662~668
24 Y. Liu, S. Zhang. Improvement of Soliton Communication System with Optical Phase Conjugation. International Journal of Infrared and Millimeter Wave, 1999, 20(9): 1673~1681
25 M. Peccianti, A. D. Rossi, G. Assanto. Electrically Assisted Self-Confinement and Waveguiding in Planar Nematic Liquid Crystal Cells. Appl. Phys. Lett, 2000, 77(7): 7~9
26 S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, F. Kajzar. High Gain of Light in Photoconduction Polymer-Nematic Liquid Crystal Hybrid Structures. Optics Communications, 2001, 187: 257~261
27 D. Fekete, J. Auyeung, A. Yariv. Phase-Conjugate Reflection by Degenerate Four-Wave Mixing in a Nematic Liquid Crystal in the Isotropic Phase. Opt. Lett., 1980, 5(2): 51~53
28 I. C. Khoo. Degenerate Four-Wave Mixing in the Nematic Phase of a Liquid Crystal. Appl. phys. Lett, 1980, 38(3): 123~124
29 I. C. Khoo, S. L. Zhuang. Wavefront Conjugation in Nematic Liquid Crystal Films. IEEE Journal of Quantum Electronics, 1982, 18(2): 246~249
30 I. C. Khoo, R. Normandin. Infrared to Visible Image Conversion Capability of a Nematic Liquid Crystal film. Appl. Phys. Lett, 1985, 47(4): 350~352
31 I. C. Khoo, H. Li, Y. Liang. Self-Starting Optical Phase Conjugation in Dyed Nematic Liquid Crystals with a Stimulated Thermal-Scattering Effect. Opt. Lett, 1993, 18(18): 1490~1492
32 I. C. Khoo, Y. Liang, H. Li. Observation of Stimulated Orientational Scattering and Cross-Polarized Self-Starting Phase Conjugation in a Nematic Liquid-Crystal Film. Opt. Lett, 1995, 20(2): 130~132
33 P. Meindl, R. Macdonald, H. J. Eichler, O. L. Antipov. Low Threshold Self-Pumped Phase Conjugation of an Ar+-Laser Beam in Dye-Doped Nematic Liquid Crystals. Mol. Cryst. Liq. Cryst., 1996, 282: 429~435.
34 A. Miniewicz, S. Bartkiewicz, J. Parka. Optical Phase Conjugation in Dye-Doped Nematic Liquid Crystal. Optics Communications, 1998, 149: 89~95.
35 G. P. Wiederrecht, M. R. Wasielewski. Photorefractivity in Polymer-Stabilized Nematic Liquid Crystals. Proc .SPIE, 1998, 3471: 102~109
36 K. Kitamura, H. Ono, H. Norisada et al. Optical Phase Conjugation by Four Wave Mixing in Photorefractive Mesogenic Composites. Proc. SPIE, 2001, 4279: 175~182
37 L. Lucchetti, M. Di fabrizio, M. Gentili, F. Simoni. Optical Phase Conjugation and Efficient wave Front Correction of Weak Light Beams by Dye-Doped Liquid Crystals. AppL. Phys. Lett, 2003, 83(26): 5389~5391
38 S. Bartkiewicz, J. Mysliwiec. A. Miniewicz. Applications of Photorefractive Liquid Crystals. Proc. SPIE, 2004, 5351: 158~165
39 J. Mysliwiec, S. Bartkiewicz, K. Janus. Optical Phase Conjugation in the Hybrid Polymer Liquid Crystal Panel. Optics Communications, 2007, 276: 58~61
40 I. C. Khoo, M. Y. Shih, M. V. Wood etc. Dye-doped Photorefractive Liquid Crystals for Dynamic and Storage Holographic Grating Formation and Spatial Light Modulation. Proceedings of the IEEE. 1999,87(11): 1897~1901
41 I. C. Khoo. Orientational Photorefractive Effects in Nematic Liquid Crystal Films. IEEE Journal of Quantum Electuonics. 1996, 32(3): 525~534
42 M. Eich, J. Wendorff. Laser-Induced Gratings and Spectroscopy in Monodomains of Liquid-Crystal Polymers. J. Opt. Soc Am B. 1990, (7): 1428~1431
43 I. C.Khoo, H. Li, and Y. Liang. Observation of Orientational Photorefractive Effects in Nematic Liquid Crystal. Opt. Lett, 1994, (19): 1723~1725
44刘思敏,郭儒,许京军.光折变非线性光学及其应用.科学出版社,2004: 45~70
45顾开宇.掺杂甲基红向列液晶取向光折变特性实验研究.哈尔滨工业大学硕士论文,2006: 24~27
46 Xiangyu Sun, Fuguo Xu, Shaozhi Pu, Ye Shang, Shiping Ou, Chunfeng Hou. Observation of Discrete Diffraction and Discrete Spatial Solitons in the Waveguide Array in Methyl-Red Doped Nematic Liquid Crystal. The International Conference on Nanophotonics. Harbin, China, 2009: 219