铌酸锂弹光晶体的频率—温度特性研究
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摘要
弹光调制干涉具作为弹光调制傅里叶变换光谱仪的核心部件，是由弹光晶体和压电晶体组成的弹光调制器构成。而作为弹光调制器组成部分的弹光晶体的选择广泛，其中铌酸锂晶体由于具有机械性能稳定、耐高温、抗腐蚀，成本低、易加工、易于生产大尺寸晶体的特点以及优良的光弹、非线性光学、压电等物理特性，被广泛地应用到弹光调制器中。但弹光调制器自身的谐振特性，会导致晶体温度-频率的漂移，从而造成系统工作的不稳定，因而降低铌酸锂晶体的温度系数是亟待解决的问题。
为解决铌酸锂晶体的温度系数这一问题，同时满足弹光调制器中温度控制与补偿的需要，根据铌酸锂晶体的性能与晶体切型有关这一特征，本研究分析了铌酸锂晶体谐振器( xyt ) 1切型长度伸缩振动模式下的频率温度特性。并推导了温度与铌酸锂晶体的密度、杨氏模量和膨胀等材料性质的关系，计算出铌酸锂晶体的一级弹性温度系数、一级线膨胀系数和一级密度温度系数。结果表明相对于铌酸锂的一级频率温度系数而言，铌酸锂的高级频率温度系数可以忽略。此外，研究将频率温度特性方程与频率方程相结合，用计算机计算出铌酸锂晶体( xyt ) 1切型长度伸缩振动模式的一级频率温度系数a 0与切角1之间的关系曲线，对这一关系曲线进行分析研究，得出铌酸锂晶体( xyt ) 1切型长度伸缩振动模式没有零温度系数，为铌酸锂晶体切型的进一步研究和弹光调制器温度补偿控制以及消除频率温度的漂移提供理论依据。
Photo-elastic modulation interferometer, as the core component of photo-elasticmodulation Fourier transform spectrometer, consists of photo-elastic modulator which iscomposed of photo-elastic crystal and piezoelectric crystal. As part of photo-elastic modulator,elastic-photo crystal has a wide selection, among which lithium niobate crystal has theproperties of stable mechanical properties, high temperature resistance, corrosion resistance,excellent nonlinear optical effect, photo-elasticity and piezoelectricity, as well as easyproducing crystal with large size, easy processing and low cost, thus is widely applied inphoto-elastic modulator. However, resonance characteristics of photo-elastic modulatorcauses the drift of temperature-frequency of crystal, thus resulting in instability when systemis running. Therefore lowering the temperature coefficient of lithium niobate crystal is animportant problem demanding prompt solution.
To solve the problem of higher temperature coefficient of lithium niobate crystal,meanwhile controlling and compensating for temperature in elastic-optic modulator,according to the characteristics of the properties of lithium niobate crystal relate to crystalcut ,the present study analyzes the frequency temperature characteristic of lithium niobatecrystal resonator in (xyt)φ1cut-length extension vibration mode, deduces the relationshipof temperature with Density of lithium niobate crystals, young's modulus and expansioncoefficient, and figures out the level temperature coefficient of elasticity, level coefficient oflinear expansion and level density temperature coefficient. The results show that thehigher-order frequency- temperature coefficient can be ignored compared with level-ordertemperature coefficient. Besides, the study gets relationship of first temperature coefficient offrequency of lithium niobate crystal a0and tangent anglesφ1by combining frequency temperature characteristic equation with the frequency equation in (xyt)φ1cut-lengthextension vibration mode. By analysing this curve, the author gets the conclusion that thereexists no zero temperature coefficient in (xyt)φ1cut-length extension vibration mode, whichprovides a theoretical basis for the further study of cut type of lithium niobate crystal,elastic-optic modulator control and compensation of temperature, as well as the eliminatingthe drift of frequency temperature.
为解决铌酸锂晶体的温度系数这一问题，同时满足弹光调制器中温度控制与补偿的需要，根据铌酸锂晶体的性能与晶体切型有关这一特征，本研究分析了铌酸锂晶体谐振器( xyt ) 1切型长度伸缩振动模式下的频率温度特性。并推导了温度与铌酸锂晶体的密度、杨氏模量和膨胀等材料性质的关系，计算出铌酸锂晶体的一级弹性温度系数、一级线膨胀系数和一级密度温度系数。结果表明相对于铌酸锂的一级频率温度系数而言，铌酸锂的高级频率温度系数可以忽略。此外，研究将频率温度特性方程与频率方程相结合，用计算机计算出铌酸锂晶体( xyt ) 1切型长度伸缩振动模式的一级频率温度系数a 0与切角1之间的关系曲线，对这一关系曲线进行分析研究，得出铌酸锂晶体( xyt ) 1切型长度伸缩振动模式没有零温度系数，为铌酸锂晶体切型的进一步研究和弹光调制器温度补偿控制以及消除频率温度的漂移提供理论依据。
Photo-elastic modulation interferometer, as the core component of photo-elasticmodulation Fourier transform spectrometer, consists of photo-elastic modulator which iscomposed of photo-elastic crystal and piezoelectric crystal. As part of photo-elastic modulator,elastic-photo crystal has a wide selection, among which lithium niobate crystal has theproperties of stable mechanical properties, high temperature resistance, corrosion resistance,excellent nonlinear optical effect, photo-elasticity and piezoelectricity, as well as easyproducing crystal with large size, easy processing and low cost, thus is widely applied inphoto-elastic modulator. However, resonance characteristics of photo-elastic modulatorcauses the drift of temperature-frequency of crystal, thus resulting in instability when systemis running. Therefore lowering the temperature coefficient of lithium niobate crystal is animportant problem demanding prompt solution.
To solve the problem of higher temperature coefficient of lithium niobate crystal,meanwhile controlling and compensating for temperature in elastic-optic modulator,according to the characteristics of the properties of lithium niobate crystal relate to crystalcut ,the present study analyzes the frequency temperature characteristic of lithium niobatecrystal resonator in (xyt)φ1cut-length extension vibration mode, deduces the relationshipof temperature with Density of lithium niobate crystals, young's modulus and expansioncoefficient, and figures out the level temperature coefficient of elasticity, level coefficient oflinear expansion and level density temperature coefficient. The results show that thehigher-order frequency- temperature coefficient can be ignored compared with level-ordertemperature coefficient. Besides, the study gets relationship of first temperature coefficient offrequency of lithium niobate crystal a0and tangent anglesφ1by combining frequency temperature characteristic equation with the frequency equation in (xyt)φ1cut-lengthextension vibration mode. By analysing this curve, the author gets the conclusion that thereexists no zero temperature coefficient in (xyt)φ1cut-length extension vibration mode, whichprovides a theoretical basis for the further study of cut type of lithium niobate crystal,elastic-optic modulator control and compensation of temperature, as well as the eliminatingthe drift of frequency temperature.
引文
[1]林利.教学用自组式傅里叶变换光谱仪的研制.天津：南开大学，2005.
[2] Michelson A A. On the Application of Interference Methods to SpectroscopicMeasurements[J]. Publications of the Astronomical Society of the Pacific.1991,28:559-566.
[3] Zhao Haitao, Pei Yanjun. Fourier transform imaging spectrometer for chemical agentdetection[J]. Ship Science and Technology. 2006, 28(2): 80-83.
[4] ACOST A E, CHAMADOIRA S, BLENDOWSKE R. Modified point diffractioninterferometer for inspection and evaluation of ophthalmic components[J]. JOSA A,2006,23(3):632-637.
[5] KOMISARE K D, REICHARD K, MERDES D, et al. High performance non scanningFourier transform spectrometer that uses a Wollaston prism array[J]. Appl Opt,2004,43(20):3983-3987.
[6] Lv Qunbo, Yuan Yan, Xiang Libin. Fourier Transform Imaging Spectral DataCompression[J]. Acta Photonica Sinica, 2008, 37(3):573-576.
[7]刘智超,张记龙,王志斌.静态傅里叶变换干涉具在大视场探测中的应用[J].光子学报, 2009, 11( 5):2839-2843.
[8]张跃国.基于弹光效应的静态傅里叶变换干涉具设计.太原：中北大学，2011.
[9]曾爱军，王向朝，董作人，等.光弹调制器在偏振方向调制中的应用[J].中国激光，2005，32（8）：1063-1067.
[10]周军.光弹调制器应用的Mueller矩阵分析[J].常熟高等学报，2001，15（4）：19-22.
[11]孔勇发，许京军，张光寅，等.多功能光电材料——铌酸锂晶体[M].北京.科学出版社. 2005：1-17.
[12]蒋民华.人工晶体研究进展及应用前景[J].硅酸盐通报，1995，4:82-89.
[13]牟晓东，张恒利，孔庆宇，等.近红外半导体激光器的切伦科夫波导倍频研究[J].人工晶体学报, 1997,26（1）：15-19.
[14]蒋民华.从电子材料到光子材料[J].材料导报，1999，13（6）：5-9.
[15]蒋民华.从电子、光子材料的发展展望人工晶体的前景[J].人工晶体学报，2000,29(5):1.
[16]蒋民华.面向新世纪的人工晶体[J].人工晶体学报，2001，30(1):1-9.
[17]蒋民华.人工晶体发展动向的探讨[J].人工晶体学报，2002,31(3):177-181.
[18] Mohlecke M, Corradi G, Betzler K. Optical Methods to Characterize theComposition and Homogeneity of Lithium Niobate Single Crystals[J]. Appl. Phys. B.1996, 63:323-327.
[19] Iyi N, Kitamura K, Izumi F, et al. Comparative Study of Defect Structure in LithiumNiobate with Different Compositions[J]. J. Solid State Chem. 1992, 101:340-352.
[20] Fay H, Alford W J, Dess H M. Dependence of Second Harmonic Phase-matchingTemperature in LiNb03Crystals on Melt-composition[J]. Appl. Phys. Lett. 1968, 12:69-71.
[21] Lerner P, Legras C, Dumas J. Stoechiometrie des Monocristaux de Metaniobate deLithium[J]. J. Crystal Growth. 1986, 3/4: 231-235.
[22] Peterson G, Carnevale A. 93Nb NMR Line widths in Nonstiochiometric LithiumNiobate[J]. J. Chem. Phys. 1972, 56: 4848-4852.
[23] Abrahams S, Marsh P. Defect Structure Dependence on Composition in LithiumNiobate[J]. Acta Crystallogr. Sect. B. 1986, 42: 61-64.
[24] Wilkinson A., Cheetharm A., Jarman R. The Defect Structure of CongruentlyMelting Lithium Niobate[J]. J. Appl. Phys. 1993, 74: 3080-3087.
[25] Donnerberg H, Tomlinson S, Catlow C. Defects in LiNb03-II.ComputerSimulation[J]. J.Phys.Chem. Solids. 1991，52: 201-205.
[26] lyi N, Kitamura K, Izumi F, et al. Comparative Study of Defect Structure in LithiumNiobate with Different Compositions[J]. J. Solid State Chem. 1992,101:340-352.
[27] Zotov N, Boysen H, Frey F, et al. Cation Substitution Models of Congruent LiNb03Investigated by X-Ray and Neutron Powder Diffraction[J].J. Phys. Chem.Solids.1994,55:145-152.
[28] Blumel J, Born E., Metzger T, et al. Solid State NMR Study Supporting the LithiumVacancy Defect Model in Congruent Lithium Niobate[J]. J.Phys.Chem.Solids.1994,55:589-593.
[29]赁敦敏，肖定全，朱建国，余萍，鄢洪建. LiNbO3基无铅压电陶瓷的研究与进展[J].功能材料. 2004,35（1）：18-20.
[30] Ballman A A. Growth of Piezoelectric and Ferroelectric Materials by the CzochraIskiTechnique[J]. Journal of the American Ceramic Society,1965, 48（2）:112-113.
[31] Abrahams S C, Hamilton W C, Reddy J M. Ferroelectric lithium nibate. 4. Single crystalX-ray diffraction study at 24℃and 1200℃[J]. J. Phys. Chem. Solids, 1966,27: 1019.
[32] Abrahams S C, Buehler E, Hamilton W C, et al. Ferroelectric lithiumtantalate-Ⅲ. temperature dependence of the structure in the ferroelectric phase and thepara-electric structure at 940 K[J].J Phys Chem Solids,1973,34(3):521-532.
[33] Reisman A, Holtzberg F. Reactions of the Group VB Pentoxides with Alkali Oxides andCarbonates. VII. Heterogeneous Equilibria in the System Na2O or Na2CO3-Nb2O5[J].The Journal of Physical Chemistry, 1958,80（1）：37-42.
[34] Reisman A, Holtzberg F. Heterogeneous Equilibria in the Systems Li2O-, Ag2O-Nb2O5and Oxide-Models[J]. The Journal of Physical Chemistry, 1958,80（24）：6503-6507.
[35] Bergman J G, A. Askin, Ballman A A, Dziedzic J M, Levenstein H Jand Smith R G..Curie temperature, birefringence, and irefringence, and phase-matching temperaturevariations in LiNbO3as a function of melt stoichiometry[J]. Appl. Phys. Lett., 1968,12:92-95.
[36]强亮生.铌酸锂晶体改性及温度系数与切型相关性研究.哈尔滨：哈尔滨工业大学.2005.
[37] IRE Committee for Piezoelectric Standards, IRE Standards on Piezoelectric Crystals[J].Proc.IRE,1949,37(10) :1378.
[38] Weis R S., Gaylord T K. Lithium niobate: Summary of physical properties and crystalstructure[J]. Applied Physics. Section A: Materials Science and Processing. 1985,37（4）：191-203.
[39]秦自楷.压电石英晶体[M].北京：国防工业出版社,1980,69-72,146-165,265-275.
[40]陈纲,廖理几.晶体物理学基础[M].北京：科学出版社，2007,202-221.
[41]田文杰,路峻岭,张福学,等. AT切石英谐振器频率温度系数的研究[J].电子元件与材料,2002,21（9）：1-3.
[42]马廷锋,张超,张志甜,等.石英晶体横向场激励压电传感器的频率温度特性[J].仪表技术与传感器,2009,增刊：25-27.
[43] Zhdanova V V, Klyuev V P, Lemanov V V, et al. The thermal properties of lithiumniobate [J]. Fizika Tverdogo Tela,1968,10:1725.
[44] Prokhorov A M., Kuz’minov Yu S. Physics and chemistry of crystalline lithiumniobate[J]. IOP Publishing Ltd, Adam Hilger,1990.
[2] Michelson A A. On the Application of Interference Methods to SpectroscopicMeasurements[J]. Publications of the Astronomical Society of the Pacific.1991,28:559-566.
[3] Zhao Haitao, Pei Yanjun. Fourier transform imaging spectrometer for chemical agentdetection[J]. Ship Science and Technology. 2006, 28(2): 80-83.
[4] ACOST A E, CHAMADOIRA S, BLENDOWSKE R. Modified point diffractioninterferometer for inspection and evaluation of ophthalmic components[J]. JOSA A,2006,23(3):632-637.
[5] KOMISARE K D, REICHARD K, MERDES D, et al. High performance non scanningFourier transform spectrometer that uses a Wollaston prism array[J]. Appl Opt,2004,43(20):3983-3987.
[6] Lv Qunbo, Yuan Yan, Xiang Libin. Fourier Transform Imaging Spectral DataCompression[J]. Acta Photonica Sinica, 2008, 37(3):573-576.
[7]刘智超,张记龙,王志斌.静态傅里叶变换干涉具在大视场探测中的应用[J].光子学报, 2009, 11( 5):2839-2843.
[8]张跃国.基于弹光效应的静态傅里叶变换干涉具设计.太原：中北大学，2011.
[9]曾爱军，王向朝，董作人，等.光弹调制器在偏振方向调制中的应用[J].中国激光，2005，32（8）：1063-1067.
[10]周军.光弹调制器应用的Mueller矩阵分析[J].常熟高等学报，2001，15（4）：19-22.
[11]孔勇发，许京军，张光寅，等.多功能光电材料——铌酸锂晶体[M].北京.科学出版社. 2005：1-17.
[12]蒋民华.人工晶体研究进展及应用前景[J].硅酸盐通报，1995，4:82-89.
[13]牟晓东，张恒利，孔庆宇，等.近红外半导体激光器的切伦科夫波导倍频研究[J].人工晶体学报, 1997,26（1）：15-19.
[14]蒋民华.从电子材料到光子材料[J].材料导报，1999，13（6）：5-9.
[15]蒋民华.从电子、光子材料的发展展望人工晶体的前景[J].人工晶体学报，2000,29(5):1.
[16]蒋民华.面向新世纪的人工晶体[J].人工晶体学报，2001，30(1):1-9.
[17]蒋民华.人工晶体发展动向的探讨[J].人工晶体学报，2002,31(3):177-181.
[18] Mohlecke M, Corradi G, Betzler K. Optical Methods to Characterize theComposition and Homogeneity of Lithium Niobate Single Crystals[J]. Appl. Phys. B.1996, 63:323-327.
[19] Iyi N, Kitamura K, Izumi F, et al. Comparative Study of Defect Structure in LithiumNiobate with Different Compositions[J]. J. Solid State Chem. 1992, 101:340-352.
[20] Fay H, Alford W J, Dess H M. Dependence of Second Harmonic Phase-matchingTemperature in LiNb03Crystals on Melt-composition[J]. Appl. Phys. Lett. 1968, 12:69-71.
[21] Lerner P, Legras C, Dumas J. Stoechiometrie des Monocristaux de Metaniobate deLithium[J]. J. Crystal Growth. 1986, 3/4: 231-235.
[22] Peterson G, Carnevale A. 93Nb NMR Line widths in Nonstiochiometric LithiumNiobate[J]. J. Chem. Phys. 1972, 56: 4848-4852.
[23] Abrahams S, Marsh P. Defect Structure Dependence on Composition in LithiumNiobate[J]. Acta Crystallogr. Sect. B. 1986, 42: 61-64.
[24] Wilkinson A., Cheetharm A., Jarman R. The Defect Structure of CongruentlyMelting Lithium Niobate[J]. J. Appl. Phys. 1993, 74: 3080-3087.
[25] Donnerberg H, Tomlinson S, Catlow C. Defects in LiNb03-II.ComputerSimulation[J]. J.Phys.Chem. Solids. 1991，52: 201-205.
[26] lyi N, Kitamura K, Izumi F, et al. Comparative Study of Defect Structure in LithiumNiobate with Different Compositions[J]. J. Solid State Chem. 1992,101:340-352.
[27] Zotov N, Boysen H, Frey F, et al. Cation Substitution Models of Congruent LiNb03Investigated by X-Ray and Neutron Powder Diffraction[J].J. Phys. Chem.Solids.1994,55:145-152.
[28] Blumel J, Born E., Metzger T, et al. Solid State NMR Study Supporting the LithiumVacancy Defect Model in Congruent Lithium Niobate[J]. J.Phys.Chem.Solids.1994,55:589-593.
[29]赁敦敏，肖定全，朱建国，余萍，鄢洪建. LiNbO3基无铅压电陶瓷的研究与进展[J].功能材料. 2004,35（1）：18-20.
[30] Ballman A A. Growth of Piezoelectric and Ferroelectric Materials by the CzochraIskiTechnique[J]. Journal of the American Ceramic Society,1965, 48（2）:112-113.
[31] Abrahams S C, Hamilton W C, Reddy J M. Ferroelectric lithium nibate. 4. Single crystalX-ray diffraction study at 24℃and 1200℃[J]. J. Phys. Chem. Solids, 1966,27: 1019.
[32] Abrahams S C, Buehler E, Hamilton W C, et al. Ferroelectric lithiumtantalate-Ⅲ. temperature dependence of the structure in the ferroelectric phase and thepara-electric structure at 940 K[J].J Phys Chem Solids,1973,34(3):521-532.
[33] Reisman A, Holtzberg F. Reactions of the Group VB Pentoxides with Alkali Oxides andCarbonates. VII. Heterogeneous Equilibria in the System Na2O or Na2CO3-Nb2O5[J].The Journal of Physical Chemistry, 1958,80（1）：37-42.
[34] Reisman A, Holtzberg F. Heterogeneous Equilibria in the Systems Li2O-, Ag2O-Nb2O5and Oxide-Models[J]. The Journal of Physical Chemistry, 1958,80（24）：6503-6507.
[35] Bergman J G, A. Askin, Ballman A A, Dziedzic J M, Levenstein H Jand Smith R G..Curie temperature, birefringence, and irefringence, and phase-matching temperaturevariations in LiNbO3as a function of melt stoichiometry[J]. Appl. Phys. Lett., 1968,12:92-95.
[36]强亮生.铌酸锂晶体改性及温度系数与切型相关性研究.哈尔滨：哈尔滨工业大学.2005.
[37] IRE Committee for Piezoelectric Standards, IRE Standards on Piezoelectric Crystals[J].Proc.IRE,1949,37(10) :1378.
[38] Weis R S., Gaylord T K. Lithium niobate: Summary of physical properties and crystalstructure[J]. Applied Physics. Section A: Materials Science and Processing. 1985,37（4）：191-203.
[39]秦自楷.压电石英晶体[M].北京：国防工业出版社,1980,69-72,146-165,265-275.
[40]陈纲,廖理几.晶体物理学基础[M].北京：科学出版社，2007,202-221.
[41]田文杰,路峻岭,张福学,等. AT切石英谐振器频率温度系数的研究[J].电子元件与材料,2002,21（9）：1-3.
[42]马廷锋,张超,张志甜,等.石英晶体横向场激励压电传感器的频率温度特性[J].仪表技术与传感器,2009,增刊：25-27.
[43] Zhdanova V V, Klyuev V P, Lemanov V V, et al. The thermal properties of lithiumniobate [J]. Fizika Tverdogo Tela,1968,10:1725.
[44] Prokhorov A M., Kuz’minov Yu S. Physics and chemistry of crystalline lithiumniobate[J]. IOP Publishing Ltd, Adam Hilger,1990.