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The birefringence is one of the most important properties of all kinds of optical materials. and is widely used in many basic researches and industrial fields. By utilizing high birefringent materials or waveguides, a variety of unique and interesting optical features or functions can be achieved, such as in manipulating the polarization of an optical beam in a miniaturized way and providing the organic electro-luminescence display. Crystals, liquid crystals, semiconductor, silicon, ferroelectric material and polymer can exhibit their birefringences. While polymer materials are commonly used to fabricate optical films and waveguides, most polymer materials show relatively weak birefringences, and thus they are restricted in realizing novel functional photonics devices. In the past, such a weak birefringence has been roughly characterized in experiment. There is a lack of systematic method to theoretically calculate the birefringences of polymer materials, especially at a molecular level. This restricts the research on enhancing the birefringences of polymer materials. To study the birefringences in fluorinated polymers and find the way to enhance them, the origin of the birefringence in fluorinated polymer should be investigated in depth and the birefringence should be exactly calculated. In this paper, a theoretical method is established to calculate the birefringence of polymer systematically from the monomer unit to the molecular chain. Based on this method, the limiting factor that leads to a weak birefringence in polymer material is investigated. Taking the polymethyl methacrylate（PMMA) for example, the density functional theory（DFT) is first used to study the intrinsic birefringence of PMMA, where the intrinsic birefringence value is indeed the birefringence of the monomer unit and is also a maximum birefringence of the polymer material when the molecular chains are fully oriented. In the DFT, a stable structure of the PMMA monomer unit is constructed, and the intrinsic birefringence of this PMMA monomer unit structure is calculated. The calculation result shows that the intrinsic birefringence of PMMA monomer unit can reach up to 0.0738, the dispersion curve of the average birefringence of the monomer unit is also given. Furthermore, the molecular dynamics is used to study the material birefringence of the PMMA material consisting of 20 molecular chains. The calculation results show that although the intrinsic birefringence is much larger, the material birefringence of the PMMA is only 0.00052, due to the low degree of orientation of molecular chain in the PMMA. It is found that the molecular structure and the molecular orientation of the polymer are the two main factors influencing the birefringence. The theoretical method established in this work and the calculation results provide a research basis for enhancing the birefringences of polymer materials.
[1] Beeckman J, James R, Fernández A F 2009 J. Lightwave. Technol. 27 3812
[2] Niculescu E C, Burileanu L M, Radu A 2011 J. Lumin. 131 1113
[3] Timoshenko V Y, Osminkina L A, Efimova A I 2003 Phys. Rev. B 67 113405
[4] Xu Y 2013 Ferroelectric Materials and Their Applications (North-Holland:Elsevier) pp73-99
[5] Elser J, Wangberg R, Podolskiy V A 2006 Appl. Phys. Lett. 89 261102
[6] Zhan Q 2009 Adv. Opt. Photon. 1 1
[7] Arabanian A S, Massudi R 2013 Appl. Opt. 52 4212
[8] Smalley D E, Smithwick Q Y J, Bove V M 2013 Nature 498 313
[9] Arakawa Y, Kuwahara H, Sakajiri K 2015 Liq. Cryst. 42 1419
[10] álvarez J, Bettotti P, Kumar N, Suárez I, Hill D, Martínez-Pastor J 2012 SPIE BiOS San Francisco, USA, January 21-22, 2012 p821209
[11] Ma H, Jen A K Y, Dalton L R 2002 Adv. Mater. 14 1339
[12] Brown D, Clarke J H R 1991 Macromolecules 24 2075
[13] Hayakawa D, Ueda K 2015 Carbohydr. Res. 402 146
[14] Iwasaki S, Satoh Z, Shafiee H, Tagaya A, Koike Y 2013 J. Appl. Polym. Sci. 130 138
[15] Iwasaki S, Satoh Z, Shafiee H, Tagaya A, Koike Y 2012 Polymer 53 3287
[16] Hahn B R, Wendorff J H 1985 Polymer 26 1619
[17] Grimme S, Antony J, Ehrlich S 2010 J. Chem. Phys. 132 154104
[18] Parr R G, Yang W 1989 Density-functional Theory of Atoms and Molecules (New York:Oxford University Press) pp101-103
[19] Salahub D R, Zerner M C 1989 The Challenge of d and f Electrons (Washington:ACS) pp165-179
[20] Kusanagi H, Chatani Y, Tadokoro H 1994 Polymer 35 2028
[21] Blythe A R, Bloor D 2005 Electrical Properties of Polymers (Cambridge:Cambridge University Press) pp37-58
[22] Foresman J, Frish E 1996 Exploring Chemistry with Electronic Structure Methods (USA:Pittsburg) pp39-40
[23] Luo Q Q, Zheng C T, Huang X L, Wang X B, Zhang D M, Wang Y D 2015 Acta Photon. Sin. 44 0713001(in Chinese)[罗倩倩, 郑传涛, 黄小亮, 王希斌, 张大明, 王一丁2015光子学报44 0713001]
[24] Balamurugan N, Charanya C, Sampath Krishnan S 2015 Spectrochim. Acta Part A 137 1374
[25] Kasarova S N, Sultanova N G, Ivanov C Di, Nikolov I D 2007 Opt. Mater. 29 1481
[26] Turzi S S 2011 J. Math. Phys. 52 053517
[27] Zhang H Y, Wang Y Y, Tao G Q 2011 Acta Chim. Sin. 69 2053(in Chinese)[张宏玉, 王艳艳, 陶国强2011化学学报69 2053]
[28] Jones D M, Brown A A, Huck W T S 2002 Langmuir 18 1265
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[1] Beeckman J, James R, Fernández A F 2009 J. Lightwave. Technol. 27 3812
[2] Niculescu E C, Burileanu L M, Radu A 2011 J. Lumin. 131 1113
[3] Timoshenko V Y, Osminkina L A, Efimova A I 2003 Phys. Rev. B 67 113405
[4] Xu Y 2013 Ferroelectric Materials and Their Applications (North-Holland:Elsevier) pp73-99
[5] Elser J, Wangberg R, Podolskiy V A 2006 Appl. Phys. Lett. 89 261102
[6] Zhan Q 2009 Adv. Opt. Photon. 1 1
[7] Arabanian A S, Massudi R 2013 Appl. Opt. 52 4212
[8] Smalley D E, Smithwick Q Y J, Bove V M 2013 Nature 498 313
[9] Arakawa Y, Kuwahara H, Sakajiri K 2015 Liq. Cryst. 42 1419
[10] álvarez J, Bettotti P, Kumar N, Suárez I, Hill D, Martínez-Pastor J 2012 SPIE BiOS San Francisco, USA, January 21-22, 2012 p821209
[11] Ma H, Jen A K Y, Dalton L R 2002 Adv. Mater. 14 1339
[12] Brown D, Clarke J H R 1991 Macromolecules 24 2075
[13] Hayakawa D, Ueda K 2015 Carbohydr. Res. 402 146
[14] Iwasaki S, Satoh Z, Shafiee H, Tagaya A, Koike Y 2013 J. Appl. Polym. Sci. 130 138
[15] Iwasaki S, Satoh Z, Shafiee H, Tagaya A, Koike Y 2012 Polymer 53 3287
[16] Hahn B R, Wendorff J H 1985 Polymer 26 1619
[17] Grimme S, Antony J, Ehrlich S 2010 J. Chem. Phys. 132 154104
[18] Parr R G, Yang W 1989 Density-functional Theory of Atoms and Molecules (New York:Oxford University Press) pp101-103
[19] Salahub D R, Zerner M C 1989 The Challenge of d and f Electrons (Washington:ACS) pp165-179
[20] Kusanagi H, Chatani Y, Tadokoro H 1994 Polymer 35 2028
[21] Blythe A R, Bloor D 2005 Electrical Properties of Polymers (Cambridge:Cambridge University Press) pp37-58
[22] Foresman J, Frish E 1996 Exploring Chemistry with Electronic Structure Methods (USA:Pittsburg) pp39-40
[23] Luo Q Q, Zheng C T, Huang X L, Wang X B, Zhang D M, Wang Y D 2015 Acta Photon. Sin. 44 0713001(in Chinese)[罗倩倩, 郑传涛, 黄小亮, 王希斌, 张大明, 王一丁2015光子学报44 0713001]
[24] Balamurugan N, Charanya C, Sampath Krishnan S 2015 Spectrochim. Acta Part A 137 1374
[25] Kasarova S N, Sultanova N G, Ivanov C Di, Nikolov I D 2007 Opt. Mater. 29 1481
[26] Turzi S S 2011 J. Math. Phys. 52 053517
[27] Zhang H Y, Wang Y Y, Tao G Q 2011 Acta Chim. Sin. 69 2053(in Chinese)[张宏玉, 王艳艳, 陶国强2011化学学报69 2053]
[28] Jones D M, Brown A A, Huck W T S 2002 Langmuir 18 1265
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