全息聚合物分散液晶Bragg光栅的机理研究与性能优化
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摘要
聚合物单体由于光敏感性好、折射率调制度大和分辨率高等优点在全息聚合物光栅、光了晶体和光相位调制器等器件中得到广泛的应用。在形成器件的过程中,单体的扩散能力和聚合能力对器件的性能具有很大的影响。因此,如何确定单体的扩散速率和聚合速率系数在优化器件性能方面至关重要。所以提出一种方法可通用的并且便利的确定不同条件下单体的扩散速率和聚合速率系数就成了一项重要的任务。另外,在衡量全息聚合物分散液晶Bragg体光栅的性能时,高的衍射效率、低的阈值和关闭电压和快的效应速度是必要的参考指标。因而,本论文的工作主要围绕以下两个方面：
1.理论上,根据Zhao和Mouroulis的一维反应扩散模型并结合严格的双波耦合理论推导出扩散速率系数和聚合速率系数的解析表达式。用该表达式确定扩散速率系数和聚合速率系数不仅与理论预测的参数范围符合很好,而且对于同一条件多次重复实验取得的数据一致性也很好,说明了该方法的可行性。之后,我们根据隐性中心差分方法对一维反应扩散模型进行求解,通过人为改变衰减系数,模拟光栅衍射效率建立过程。由于后聚合效应,我们将模拟分为聚合和后聚合两个过程,并对衰减系数加以区别。模拟结果显示,在适当选择衰减系数后,模拟曲线与实验实时记录曲线匹配很好。更进一步,修正一维反应扩散模型,将反应对光强的依赖性修正为其对活性单体浓度和寿命的依赖性,从而理论上给予后聚合效应很好的解释；
2.实验上,利用后聚合效应,通过优化曝光时间制得衍射效率为96%的光栅,并通过在配方中引入紫外固化胶NOA65将光栅的阈值电压和关闭电压分别降至1.5V/μm和3.5V/μm。响应时间下降沿和上升沿经测量分别为153ms和250ms。最后通过光学偏光显微镜和共聚焦显微镜对液晶分了的排列取向定性的进行了分析研究。
Good photon sensitivity, large index modulation and high resolution make monomer in a number of applications such as holographic polymer grating, photonic crystal and light phase modulator. In fabrication of such devices, diffusablity and reaction of monomer have a great effect on the performance of devices. Hence, how to determine the diffusion and reaction coefficients is of significance on the improvement of devices performance. Thus, it is desirable to determine the diffusion and reaction coefficients of monomer universally under convenient conditions. Besides, high diffraction efficiency, low threshold and turn-off voltages and fast response time are necessary gauges to evaluate the holographic polymer dispersed liquid crystal Bragg volume grating. Therefore, this article can be summarized into the following two sides:
1. Theoretically, analytical expressions of diffusion and reaction coefficients were derived according to Zhao and Mouroulis's one dimensional diffusion-reaction model and in combination with two-wave coupling theory. Small discrepancies among parameters values determined in multiple experiments under same condition and good agreement with theoretical prediction suggested the feasibility of this method. Thereafter, simulations of the build-up of grating diffraction efficiency were conducted by adjusting the decay constants through solving the finite difference equations under implicit scheme. Taking post curing into account, decay constants were specific for curing and post curing processes. The results showed great agreement between the simulated curves and experimental real-time traces. Moreover, the one dimensional diffusion-reaction model was revised by introducing the radicals' concentration and lives instead of the reaction dependence on recording beam intensity, which interpreted theoretically the post curing very well.
2. Experimentally, grating with diffraction efficiency as high as 96% was fabricated by optimizing the recording time making use of post curing effect. In addition, threshold and turn-off voltages of the grating were reduced to 1.5 V/μm and 3.5 V/μm respectively by means of introducing some amount of NOA65 into the recipe. Response times of the up and down slopes were measured to be 250ms and 153 ms respectively. In the end, alignment of liquid crystal molecules was investigated through optically polarized microscope and confocal microscope.
1.理论上,根据Zhao和Mouroulis的一维反应扩散模型并结合严格的双波耦合理论推导出扩散速率系数和聚合速率系数的解析表达式。用该表达式确定扩散速率系数和聚合速率系数不仅与理论预测的参数范围符合很好,而且对于同一条件多次重复实验取得的数据一致性也很好,说明了该方法的可行性。之后,我们根据隐性中心差分方法对一维反应扩散模型进行求解,通过人为改变衰减系数,模拟光栅衍射效率建立过程。由于后聚合效应,我们将模拟分为聚合和后聚合两个过程,并对衰减系数加以区别。模拟结果显示,在适当选择衰减系数后,模拟曲线与实验实时记录曲线匹配很好。更进一步,修正一维反应扩散模型,将反应对光强的依赖性修正为其对活性单体浓度和寿命的依赖性,从而理论上给予后聚合效应很好的解释；
2.实验上,利用后聚合效应,通过优化曝光时间制得衍射效率为96%的光栅,并通过在配方中引入紫外固化胶NOA65将光栅的阈值电压和关闭电压分别降至1.5V/μm和3.5V/μm。响应时间下降沿和上升沿经测量分别为153ms和250ms。最后通过光学偏光显微镜和共聚焦显微镜对液晶分了的排列取向定性的进行了分析研究。
Good photon sensitivity, large index modulation and high resolution make monomer in a number of applications such as holographic polymer grating, photonic crystal and light phase modulator. In fabrication of such devices, diffusablity and reaction of monomer have a great effect on the performance of devices. Hence, how to determine the diffusion and reaction coefficients is of significance on the improvement of devices performance. Thus, it is desirable to determine the diffusion and reaction coefficients of monomer universally under convenient conditions. Besides, high diffraction efficiency, low threshold and turn-off voltages and fast response time are necessary gauges to evaluate the holographic polymer dispersed liquid crystal Bragg volume grating. Therefore, this article can be summarized into the following two sides:
1. Theoretically, analytical expressions of diffusion and reaction coefficients were derived according to Zhao and Mouroulis's one dimensional diffusion-reaction model and in combination with two-wave coupling theory. Small discrepancies among parameters values determined in multiple experiments under same condition and good agreement with theoretical prediction suggested the feasibility of this method. Thereafter, simulations of the build-up of grating diffraction efficiency were conducted by adjusting the decay constants through solving the finite difference equations under implicit scheme. Taking post curing into account, decay constants were specific for curing and post curing processes. The results showed great agreement between the simulated curves and experimental real-time traces. Moreover, the one dimensional diffusion-reaction model was revised by introducing the radicals' concentration and lives instead of the reaction dependence on recording beam intensity, which interpreted theoretically the post curing very well.
2. Experimentally, grating with diffraction efficiency as high as 96% was fabricated by optimizing the recording time making use of post curing effect. In addition, threshold and turn-off voltages of the grating were reduced to 1.5 V/μm and 3.5 V/μm respectively by means of introducing some amount of NOA65 into the recipe. Response times of the up and down slopes were measured to be 250ms and 153 ms respectively. In the end, alignment of liquid crystal molecules was investigated through optically polarized microscope and confocal microscope.
引文
[1]R. Jakubiak, T. J. Bunning, R. A. Varia, L. V. Natarajan, and V. P. Tondiglia, One-Dimensional Polymeric Resonators from Holographic Photopolymerization:A New Approach for Active Photonic Bandgap Materials[J],Adv. Mater.2003,15 (3):241-244
[2]V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, D. Tomlin, and T. J. Bunning, Holographic Formation of Electro-Optical Polymer CLiquid Crystal Photonic Crystal [J],Adv. Mater.2002,14(3):187-191
[3]R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, S. Chandra, D. Tomlin, and T. J. Bunning, Switchable Orthorhombic F Photonic Crystals Formed by Holographic Polymerization-induced Phase Separation of Liquid Crystal [J], Opt. Express. 2002,10(20):1074-1082
[4]H. Ono, A. Emoto, and N. Kawatsuki, Anisotropic Photonic Gratings Formed in Photocross-Linkable Polymer Liquid Crystals[J], J. Appl. Phys.2006,100(1): 261918:1-3
[5]S. T. Wu and AYG Fuh,2005 Conference on Lasers & Electro-Optics (CLEO)[C], Baltimore, MD,2005,MAY 22-27
[6]M. J. Escuti, J. Qi, and G. P. Crawford, Two-dimensional Tunable Photonic Crystal Formed in a Liquid-Crystal Polymer Composite:Threshold Behavior and Morphology[J], Appl. Phys. Lett.2003,83(7):1331-1333
[7]J. Qi, H.Q. Xiangyu, J. H. Liang, and G. P. Crawford, Active U-Turn Electro optic Switch Formed in Patterned Holographic Polymer-Dispersed Liquid Crystals[J], IEEE Photonics Technol. Lett.2003,15(5):685-687
[8]Y. J. Liu, X. W. Sun, J. H.Liu, H. T. Dai, and K. S. Xu, A Polarization Insensitive 2x2 Optical Switch Fabricated by Liquid Crystal Polymer Composit[J],Appl. Phys. Lett.2005,86,041115:1-3
[9]S. A. Holmstrom, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland, and T. J. Bunning, Mechanical Tuning of Holographic Polymer-Dispersed Liquid Crystal Reflection Gratings[J], Appl. Phys. Lett.2004,85(11):1949-1951
[10]R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, P. F. Lloyd, and T. J. Bunning, Coherent Diffraction and Random Scattering in Thiol-ene-based Holographic Polymer-Dispersed Liquid Crystal Reflection Gratings[J], J. Appl. Lett.2006,99, 123104:1-12
[11]L. V. Natarajan, D. P. Brown, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, P. F. Lloyd, and T. J. Bunning, Holographic Polymer Dispersed Liquid Crystal Reflection Gratings Formed by Visible Light Initiated Thiol-ene Photopolymerization[J], Polymer,2006,47:4411-4420
[12]M. J. Escuti, P. Kossyrev, G. P. Crawford,T. G. Fiske, J. Colegrove and L. D. Silverstein, Expanded Viewing-angle Reflection from Diffuse Holographic-Polymer Dispersed Liquid Crystal Films[J], Appl. Phys. Lett.2000,77(26):4262-4264
[13]GZhao and P. Mouroulis, Diffussion Model of Hologram Formation in Dry Photopolymer Materials[J], J. Mod. Opt.1994,41(10),:1929-1939
[14]V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, Quantitative Model of Volume Hologram Formation in Photopolymers[J]. J. Appl.Phys.1997,81, 5913-5923
[15]D.Engin,A.S.Kewitsch, A.Yariv, Holographic Characterization of Chain Photopolymerization[J], J. Opt. Soc. Am. B.1999,16(8):1213-1219
[16]G.M.Karpov,V.V.Obukhovsky,T.N.Smirnova,V.V.Lemeshko, Spatial Transfer of Matter as a Matter of Holographic Recording in Photoformers[J], Optics Communications,2000,174:391-404
[17]R. Caputo, A. V. Sukhov, C. Umeton and R.F. Ushakov,Dynamics of Mass Transfer Caused by the Photoinduced Spatially Inhomogeneous Modulation of Mobility in a Multicomponent Medium[J], J. Exp. Theor. Phys.,2001,92(1):28-36
[18]A. Veltri, R. Caputo, C. Umeton and A. V. Sukhov, Model for the Photoinduced Formation of Diffraction Gratings in Liquid Crystalline Composite Materials[J], Appl. Phys.Lett.2004,84,3492-3494
[19]John T. Sheridan and Justin R. Lawrence, Nonlocal-Response Diffusion Model of Holographic Recording in Photopolymer[J], J. Opt. Soc. Am. B,2000,17(6): 1106-1114
[20]Justin R. Lawrence, Feidhlim T. O'Neill and John T. Sheridana, Photopolymer Holographic Recording Material Parameter Estimation Using a Nonlocal Diffusion Based Model[J], J. Appl.Phys.,2001,90(7):3142-3148
[21]John V. Kelly, Feidhlim T. O'Neill, and John T. Sheridan, Holographic Photopolymer Materials:Nonlocal Polymerization-Driven Diffusion under Nonideal Kinetic Conditions[J], J. Opt. Soc. Am. B,2005,22(2):407-416
[22]Michael R. Gleeson, John V. Kelly, Dusan Sabol, Ciara E. Close, Shui Liu, and John T. Sheridanan, Modeling the Photochemical Effects Present During Holographic Grating Formation in Photopolymer Materials[J], J. Appl. Phys.,2007,102:023108-9
[23]P.A.Kossyrev and GP.Crawford, Formation Dynamics of Diffraction Gratings in Reactive Liquid Crystals[J], Appl. Phys.Lett.2001,79(3):296-298
[24]刘思敏,郭儒,许京军,光折变非线性光学及其应用[M],北京：科学出版社,2004
[25]JuYeonWoo, EunHeeKim, SungSubShim, ByungKyuKim, High Dielectric Anisotropy Compound Doped Transmission Gratings of HPDLC[J], Opt. Commun.,2008,281:2167-2172
[26]R.Caputo,L.D.Sio,A.Veltri,C.Umeton and A.V.Sukhov, Development of a New Kind of Switchable Holographic Grating Made of Liquid Crystal Films Separated by Slices of Polymeric Material[J], Opt.Lett.2004,29(11):1261-1263
[27]A.d'Alessandro,R.Asquini, C.Gizzi, R.Caputo,C.Umeton,A.Veltri and A.V. Sukhov, Electro-Optic Properties of Switchable Gratings Made of Polymer and Nematic Liquid Crystal slices[J], Opt.Lett.,2004,29(12):1405-1407
[28]B.GWu, J.H.Erdmann, J.W.Doane, Response Times and Voltages for PDLC Light Shutters[J]. Liq. Cryst.,1989,5:1453-67
[29]Pochi Yeh, Claire Gu, Optics of Liquid Crystal Displays [M], New York:Wiley, c1999.
[30]V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, Volume Holographic Image Storage and Electrooptical Readout in a Polymer-Dispersed Liquid-Crystal Film[J], Opt.Lett.,1995,20(11),1325-1237
[31]P. C. Hiemenz and T. P. Lodge, Polymer Chemistry[M],2nd ed,CRC Press, Boca Raton,2007.
[32]A. Yariv and P. Yeh., Optical waves in crystals, propagation and control of laser radiation[M]. John Wiley &Sons, Inc 1984:.
[33]P. R. Gerber, Measurement of the Rotational Viscosity of Nematic Liquid Crystals[J], Appl. Phys.1981, A26:139-142
[34]C. Decker and K. Moussa, Real-Time Kinetic Study of Laser-Induced Polymerization[J], Macromolecules,1989,22(12):4455-4462
[35]刘言军,新型液晶全息光交换开关的研究[D],上海：复旦大学,2003
[36]C.C.Bowley and G..P.Crawford,Diffusion Kinetics of Formation of Holographic Polymer-Dispersed Liquid Crystal Display Materials[J], Appl.Phys.Lett. 2000,76,16(17):2235-2237
[37]BrendaJ.Luther,GeraldH.Springer,andDanielA.Higgins, Templated Droplets and Ordered Arrays in Polymer-DispersedLiquid-CrystalFilms[J], Chem.Mater.2001, 13(7):2281-2287
[38]DanielA.Higgin sand BrendaJ.Luther,Watching Molecules Reorient in Liquid Crystal Droplets with Multiphoton-Excited Fluorescence Microscopy[J], J. Chem. Phys.,2003,19(15):3935-3942
[39]AifangXie,TakashiIto,andDanielA.Higgins,Fabrication and Characterization of Polymer/Liquid Crystal Composite Diffractive Optics by Multiphoton Methods[J], Adv.Funct.Mater.2007,17:1515-1522
[2]V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, D. Tomlin, and T. J. Bunning, Holographic Formation of Electro-Optical Polymer CLiquid Crystal Photonic Crystal [J],Adv. Mater.2002,14(3):187-191
[3]R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, S. Chandra, D. Tomlin, and T. J. Bunning, Switchable Orthorhombic F Photonic Crystals Formed by Holographic Polymerization-induced Phase Separation of Liquid Crystal [J], Opt. Express. 2002,10(20):1074-1082
[4]H. Ono, A. Emoto, and N. Kawatsuki, Anisotropic Photonic Gratings Formed in Photocross-Linkable Polymer Liquid Crystals[J], J. Appl. Phys.2006,100(1): 261918:1-3
[5]S. T. Wu and AYG Fuh,2005 Conference on Lasers & Electro-Optics (CLEO)[C], Baltimore, MD,2005,MAY 22-27
[6]M. J. Escuti, J. Qi, and G. P. Crawford, Two-dimensional Tunable Photonic Crystal Formed in a Liquid-Crystal Polymer Composite:Threshold Behavior and Morphology[J], Appl. Phys. Lett.2003,83(7):1331-1333
[7]J. Qi, H.Q. Xiangyu, J. H. Liang, and G. P. Crawford, Active U-Turn Electro optic Switch Formed in Patterned Holographic Polymer-Dispersed Liquid Crystals[J], IEEE Photonics Technol. Lett.2003,15(5):685-687
[8]Y. J. Liu, X. W. Sun, J. H.Liu, H. T. Dai, and K. S. Xu, A Polarization Insensitive 2x2 Optical Switch Fabricated by Liquid Crystal Polymer Composit[J],Appl. Phys. Lett.2005,86,041115:1-3
[9]S. A. Holmstrom, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland, and T. J. Bunning, Mechanical Tuning of Holographic Polymer-Dispersed Liquid Crystal Reflection Gratings[J], Appl. Phys. Lett.2004,85(11):1949-1951
[10]R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, P. F. Lloyd, and T. J. Bunning, Coherent Diffraction and Random Scattering in Thiol-ene-based Holographic Polymer-Dispersed Liquid Crystal Reflection Gratings[J], J. Appl. Lett.2006,99, 123104:1-12
[11]L. V. Natarajan, D. P. Brown, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, P. F. Lloyd, and T. J. Bunning, Holographic Polymer Dispersed Liquid Crystal Reflection Gratings Formed by Visible Light Initiated Thiol-ene Photopolymerization[J], Polymer,2006,47:4411-4420
[12]M. J. Escuti, P. Kossyrev, G. P. Crawford,T. G. Fiske, J. Colegrove and L. D. Silverstein, Expanded Viewing-angle Reflection from Diffuse Holographic-Polymer Dispersed Liquid Crystal Films[J], Appl. Phys. Lett.2000,77(26):4262-4264
[13]GZhao and P. Mouroulis, Diffussion Model of Hologram Formation in Dry Photopolymer Materials[J], J. Mod. Opt.1994,41(10),:1929-1939
[14]V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, Quantitative Model of Volume Hologram Formation in Photopolymers[J]. J. Appl.Phys.1997,81, 5913-5923
[15]D.Engin,A.S.Kewitsch, A.Yariv, Holographic Characterization of Chain Photopolymerization[J], J. Opt. Soc. Am. B.1999,16(8):1213-1219
[16]G.M.Karpov,V.V.Obukhovsky,T.N.Smirnova,V.V.Lemeshko, Spatial Transfer of Matter as a Matter of Holographic Recording in Photoformers[J], Optics Communications,2000,174:391-404
[17]R. Caputo, A. V. Sukhov, C. Umeton and R.F. Ushakov,Dynamics of Mass Transfer Caused by the Photoinduced Spatially Inhomogeneous Modulation of Mobility in a Multicomponent Medium[J], J. Exp. Theor. Phys.,2001,92(1):28-36
[18]A. Veltri, R. Caputo, C. Umeton and A. V. Sukhov, Model for the Photoinduced Formation of Diffraction Gratings in Liquid Crystalline Composite Materials[J], Appl. Phys.Lett.2004,84,3492-3494
[19]John T. Sheridan and Justin R. Lawrence, Nonlocal-Response Diffusion Model of Holographic Recording in Photopolymer[J], J. Opt. Soc. Am. B,2000,17(6): 1106-1114
[20]Justin R. Lawrence, Feidhlim T. O'Neill and John T. Sheridana, Photopolymer Holographic Recording Material Parameter Estimation Using a Nonlocal Diffusion Based Model[J], J. Appl.Phys.,2001,90(7):3142-3148
[21]John V. Kelly, Feidhlim T. O'Neill, and John T. Sheridan, Holographic Photopolymer Materials:Nonlocal Polymerization-Driven Diffusion under Nonideal Kinetic Conditions[J], J. Opt. Soc. Am. B,2005,22(2):407-416
[22]Michael R. Gleeson, John V. Kelly, Dusan Sabol, Ciara E. Close, Shui Liu, and John T. Sheridanan, Modeling the Photochemical Effects Present During Holographic Grating Formation in Photopolymer Materials[J], J. Appl. Phys.,2007,102:023108-9
[23]P.A.Kossyrev and GP.Crawford, Formation Dynamics of Diffraction Gratings in Reactive Liquid Crystals[J], Appl. Phys.Lett.2001,79(3):296-298
[24]刘思敏,郭儒,许京军,光折变非线性光学及其应用[M],北京：科学出版社,2004
[25]JuYeonWoo, EunHeeKim, SungSubShim, ByungKyuKim, High Dielectric Anisotropy Compound Doped Transmission Gratings of HPDLC[J], Opt. Commun.,2008,281:2167-2172
[26]R.Caputo,L.D.Sio,A.Veltri,C.Umeton and A.V.Sukhov, Development of a New Kind of Switchable Holographic Grating Made of Liquid Crystal Films Separated by Slices of Polymeric Material[J], Opt.Lett.2004,29(11):1261-1263
[27]A.d'Alessandro,R.Asquini, C.Gizzi, R.Caputo,C.Umeton,A.Veltri and A.V. Sukhov, Electro-Optic Properties of Switchable Gratings Made of Polymer and Nematic Liquid Crystal slices[J], Opt.Lett.,2004,29(12):1405-1407
[28]B.GWu, J.H.Erdmann, J.W.Doane, Response Times and Voltages for PDLC Light Shutters[J]. Liq. Cryst.,1989,5:1453-67
[29]Pochi Yeh, Claire Gu, Optics of Liquid Crystal Displays [M], New York:Wiley, c1999.
[30]V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, Volume Holographic Image Storage and Electrooptical Readout in a Polymer-Dispersed Liquid-Crystal Film[J], Opt.Lett.,1995,20(11),1325-1237
[31]P. C. Hiemenz and T. P. Lodge, Polymer Chemistry[M],2nd ed,CRC Press, Boca Raton,2007.
[32]A. Yariv and P. Yeh., Optical waves in crystals, propagation and control of laser radiation[M]. John Wiley &Sons, Inc 1984:.
[33]P. R. Gerber, Measurement of the Rotational Viscosity of Nematic Liquid Crystals[J], Appl. Phys.1981, A26:139-142
[34]C. Decker and K. Moussa, Real-Time Kinetic Study of Laser-Induced Polymerization[J], Macromolecules,1989,22(12):4455-4462
[35]刘言军,新型液晶全息光交换开关的研究[D],上海：复旦大学,2003
[36]C.C.Bowley and G..P.Crawford,Diffusion Kinetics of Formation of Holographic Polymer-Dispersed Liquid Crystal Display Materials[J], Appl.Phys.Lett. 2000,76,16(17):2235-2237
[37]BrendaJ.Luther,GeraldH.Springer,andDanielA.Higgins, Templated Droplets and Ordered Arrays in Polymer-DispersedLiquid-CrystalFilms[J], Chem.Mater.2001, 13(7):2281-2287
[38]DanielA.Higgin sand BrendaJ.Luther,Watching Molecules Reorient in Liquid Crystal Droplets with Multiphoton-Excited Fluorescence Microscopy[J], J. Chem. Phys.,2003,19(15):3935-3942
[39]AifangXie,TakashiIto,andDanielA.Higgins,Fabrication and Characterization of Polymer/Liquid Crystal Composite Diffractive Optics by Multiphoton Methods[J], Adv.Funct.Mater.2007,17:1515-1522
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