旋光-电光晶体的电光调制特性及π-电压
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摘要
分析旋光-电光晶体的电光相位以及强度调制特性,并定义晶体的π-电压。对于具有旋光性的电光晶体,以往半波电压的概念不能准确描述其电光偏振、强度调制的周期性,因而引入π-电压这一概念,并将其定义为此类晶体的椭圆双折射相位延迟变化量等于π时所需要的调制电压。对于置于两个偏振器之间的旋光-电光晶体强度调制器,旋光性可以为电光强度调制提供光学偏置,但调制光强度是调制电压的偶函数,只有当检偏器的主透光方向平行或垂直于晶体出射线偏振光波的偏振方向时,才能实现完全的电光开关。当将此类晶体用于电光开关时,可定义能够实现完全开关状态转换所需要的最大调制电压为开关电压。通过实验测量了一块尺寸为6 mm×4 mm×2.9 mm的硅酸铋(Bi_(12)SiO_(20))晶体的π/4-电压,对于635 nm的光波长,π/4-电压约为3 kV。对于具有旋光性的弹光调制器,可以引入π-应力和π-应变的概念。
This study investigates the electro-optical phase and intensity modulation characteristics of the optically active and electro-optical crystal and defines its π-voltage. For electro-optic crystals with optical activity, the former concept of half-wave voltage cannot accurately describe the periodical characteristics of electro-optic polarization and intensity modulation. Thus, the π-voltage concept is introduced and defined as the modulation voltage required for the elliptical birefringence phase-delay variation of such a crystal to be equal to π. As for an optically active and electro-optical crystal intensity modulator inserted between two polarizers, the optical activity can provide optical bias for electro-optical intensity modulation. However, the modulated light intensity is an even function of the modulation voltage, and an electro-optical switch can be fully used only when the transmission direction of the analyzer is parallel or perpendicular to the polarization direction of the emerging light from the crystal. As for an electro-optical switcher based on such a crystal, the maximum modulation voltage required to achieve a full switching-state transition can be defined as its switching voltage. The π/4-voltage of a bismuth silicate(Bi_(12)SiO_(20)) crystal with dimensions of 6 mm×4 mm×2.9 mm is experimentally measured and found to be approximately 3 kV for a wavelength of 635 nm. Similarly, the concepts of π-stress and π-strain can be defined for the elasto-optic modulator with optical activity.
This study investigates the electro-optical phase and intensity modulation characteristics of the optically active and electro-optical crystal and defines its π-voltage. For electro-optic crystals with optical activity, the former concept of half-wave voltage cannot accurately describe the periodical characteristics of electro-optic polarization and intensity modulation. Thus, the π-voltage concept is introduced and defined as the modulation voltage required for the elliptical birefringence phase-delay variation of such a crystal to be equal to π. As for an optically active and electro-optical crystal intensity modulator inserted between two polarizers, the optical activity can provide optical bias for electro-optical intensity modulation. However, the modulated light intensity is an even function of the modulation voltage, and an electro-optical switch can be fully used only when the transmission direction of the analyzer is parallel or perpendicular to the polarization direction of the emerging light from the crystal. As for an electro-optical switcher based on such a crystal, the maximum modulation voltage required to achieve a full switching-state transition can be defined as its switching voltage. The π/4-voltage of a bismuth silicate(Bi_(12)SiO_(20)) crystal with dimensions of 6 mm×4 mm×2.9 mm is experimentally measured and found to be approximately 3 kV for a wavelength of 635 nm. Similarly, the concepts of π-stress and π-strain can be defined for the elasto-optic modulator with optical activity.
引文
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[18] Li C S.Mutual compensation property of electrooptic and magnetooptic effects and its application to sensor[J].Acta Physica Sinica,2015,64(4):047801.李长胜.电光与磁光效应的互补特性及其传感应用[J].物理学报,2015,64(4):047801.
[19] Li C S,Cui X.Review of optical electric-power sensor[J].Acta Optica Sinica,2018,38(3):0328011.李长胜,崔翔.光学电功率传感器研究综述[J].光学学报,2018,38(3):0328011.
[20] Yin X,Wang J Y,Zhang S J.The study of the electrooptic effect of the optical active crystals in the polarized light interferometric experiment[J].Acta Optica Sinica,2003,23(12):1484-1488.尹鑫,王继扬,张少军.旋光晶体在偏光干涉实验中电光效应的研究[J].光学学报,2003,23(12):1484-1488.
[21] Tian Z B,Zhang S J,Li S C.Study of propagation of light in active crystal La3Ga5SiO14 with electric field added[J].Chinese Journal of Lasers,2005,32(11):1539-1542.田召兵,张少军,李世忱.加电旋光晶体La3Ga5SiO14中光的传播方程的研究[J].中国激光,2005,32(11):1539-1542.
[22] Yin X,Wang J Y.Interaction of the optical activity and electro-optic effect and its influence on the optically active crystal electro-optic Q switcher[J].Acta Physica Sinica,2004,53(10):3565-3570.尹鑫,王继扬.旋光性与电光效应交互作用及其对旋光晶体电光Q开关的影响[J].物理学报,2004,53(10):3565-3570.
[23] Yin X,Wang J Y,Zhang S J.Study on electro-optic Q switch of La3Ga5SiO14 single crystal[J].Chinese Journal of Lasers,2004,31(1):29-32.尹鑫,王继扬,张少军.La3Ga5SiO14晶体电光Q开关的研究[J].中国激光,2004,31(1):29-32.
[24] Tabor W J,Chen F S.Electromagnetic propagation through materials possessing both Faraday rotation and birefringence:experiments with ytterbium orthoferrite[J].Journal of Applied Physics,1969,40(7):2760-2765.
[25] Kaminsky W.Experimental and phenomenological aspects of circular birefringence and related properties in transparent crystals[J].Reports on Progress in Physics,2000,63(10):1575-1640.
[26] Li C S,Cui X.Coupled-wave analysis on the electro-optic and magnetooptic interaction in BSO crystal and its application to sensors[J].Acta Photonica Sinica,1998,27(2):132-136.李长胜,崔翔.硅酸铋晶体内电光、磁光相互作用的耦合波分析及其传感应用[J].光子学报,1998,27(2):132-136.
[27] Liao Y B.Polarization optics[M].Beijing:Science Press,2003:155.廖延彪.偏振光学[M].北京:科学出版社,2003:155.
[28] Xu X W,Liao J Y.Progress in study on crystal growth of bismuth silicon oxide[J].Journal of Inorganic Materials,1994,9(2):129-138.徐学武,廖晶莹.硅酸铋(Bi12SiO20)晶体生长的研究进展[J].无机材料学报,1994,9(2):129-138.
[29] Xie K C.The optical rotation characteristics of Bi12SiO20 crystals[J].Piezoelectrics & Acoustooptics,1991,13(1):22-25,4.谢克诚.硅酸铋晶体的旋光特性[J].压电与声光,1991,13(1):22-25,4.
[30] Li C S.Optical voltage sensor using angular optical biasing in lithium niobate crystal[J].Chinese Journal of Sensors and Actuators,2007,20(7):1494-1497.李长胜.基于铌酸锂晶体自身角度光偏置的光学电压传感器[J].传感技术学报,2007,20(7):1494-1497.
[31] Li C S,Shen X L,Zeng R.Optical electric-field sensor based on angular optical bias using single β-BaB2O4 crystal[J].Applied Optics,2013,52(31):7580-7585.
[32] Maldonado T A,Gaylord T K.Accurate method to determine the eigenstates of polarization in gyrotropic media[J].Applied Optics,1989,28(11):2075-2086.
[33] Han S H,Wu J W.Polarization-interferometry measurement of the Pockels coefficient in a chiral Bi12SiO20 single crystal[J].Journal of the Optical Society of America B,2000,17(7):1205-1210.
[34] She W L,Lee W K.Wave coupling theory of linear electrooptic effect[J].Optics Communications,2001,195:303-311.
[35] Xie N,Qiu X M,Xu Q F,et al.Regulation of bismuth germanate electro-optic crystal′s half-wave voltage[J].Infrared and Laser Engineering,2018,47(4):0420003.谢楠,邱鑫茂,徐启峰,等.锗酸铋电光晶体的半波电压调控[J].红外与激光工程,2018,47(4):0420003.
[36] Montemezzani G,Pf?ndler S,Günter P.Electro-optic and photorefractive properties of Bi4Ge3O12 crystals in the ultraviolet spectral range[J].Journal of the Optical Society of America B,1992,9(7):1110-1117.
[37] Williams P A,Rose A H,Lee K S,et al.Optical,thermo-optic,electro-optic,and photoelastic properties of bismuth germanate (Bi4Ge3O12)[J].Applied Optics,1996,35(19):3562-3569.
[2] Yu K X.Advanced optics[M].Beijing:Beijing University of Technology Press,2009:114.俞宽新.高等光学[M].北京:北京工业大学出版社,2009:114.
[3] Yu D Y,Tan H Y.Engineering optics[M].4th ed.Beijing:China Machine Press,2015:251.郁道银,谈恒英.工程光学[M].4版.北京:机械工业出版社,2015:251.
[4] Hecht E.Optics[M].5th ed.Beijing:Publishing House of Electronics Industry,2017:383.
[5] Mu G G,Zhan Y L.Optics[M].2nd ed.Beijing:Higher Education Press,2009:353-354.母国光,战元龄.光学[M].2版.北京:高等教育出版社,2009:353-354.
[6] Pellat-Finet P.Measurement of the electro-optic coefficient of BSO crystals[J].Optics Communications,1984,50(5):275-280.
[7] Kutsaenko V V,Potapov V T,Shpilevskii R V.Bi12SiO20 fiber-optic electric field sensor[J].Soviet Physics:Technical Physics,1985,30(7):790-793.
[8] Gorchakov V K,Kutsaenko V V,Potapov V T.Electro-optical and magneto-optical effects in bismuth silicate crystals and optical polarization sensors using such crystals[J].International Journal of Optoelectronics,1990,5(3):235-250.
[9] Zhang J Z,Dong X Y,Sheng Q Q,et al.Experimental research of electro-optic effect in BSO crystals[J].Chinese Journal of Lasers,1991,18(7):531-534.张建忠,董孝义,盛秋琴,等.BSO晶体电光效应的实验研究[J].中国激光,1991,18(7):531-534.
[10] Li C S,Zeng Z,He X L.Optical voltage sensor using bismuth silicate crystal grown by hydrothermal method[J].Journal of Optoelectronics·Laser,2014,25(2):239-245.李长胜,曾张,何小玲.基于水热法生长的硅酸铋晶体光学电压传感器[J].光电子·激光,2014,25(2):239-245.
[11] Vachss F,Hesselink L.Measurement of the electrogyratory and electro-optic effects in BSO and BGO[J].Optics Communications,1987,62(3):159-165.
[12] Li C S,Zeng Z,He X L.Simultaneous measurement of alternating voltage and current using single bismuth silicate crystal[J].Infrared and Laser Engineering,2014,43(9):3036-3041.李长胜,曾张,何小玲.利用单块硅酸铋晶体同时测量交流电压和电流[J].红外与激光工程 2014,43(9):3036-3041.
[13] Li C S.Linear electrooptic and electrogyration intensity modulation using crystalline quartz[J].Acta Optica Sinica,2012,32(1):0123002.李长胜.利用石英晶体的线性电光和电致旋光强度调制[J].光学学报,2012,32(1):0123002.
[14] Li C S,Cui H,Zhang X.Optical magnetic field sensor based on electrogyratory and electrooptic compensation in single quartz crystal[J].IEEE Sensors Journal,2018,18(4):1427-1434.
[15] Li C S,Yoshino T.Simultaneous measurement of current and voltage by use of one bismuth germanate crystal[J].Applied Optics,2002,41(25):5391-5397.
[16] Li C S,Cui X,Yoshino T.Optical electric-power sensor by use of one bismuth germanate crystal[J].Journal of Lightwave Technology,2003,21(5):1328-1333.
[17] Li C S,Yoshino T.Single-crystal magneto-optic sensor with electrically adjustable sensitivity[J].Applied Optics,2012,51(21):5119-5125.
[18] Li C S.Mutual compensation property of electrooptic and magnetooptic effects and its application to sensor[J].Acta Physica Sinica,2015,64(4):047801.李长胜.电光与磁光效应的互补特性及其传感应用[J].物理学报,2015,64(4):047801.
[19] Li C S,Cui X.Review of optical electric-power sensor[J].Acta Optica Sinica,2018,38(3):0328011.李长胜,崔翔.光学电功率传感器研究综述[J].光学学报,2018,38(3):0328011.
[20] Yin X,Wang J Y,Zhang S J.The study of the electrooptic effect of the optical active crystals in the polarized light interferometric experiment[J].Acta Optica Sinica,2003,23(12):1484-1488.尹鑫,王继扬,张少军.旋光晶体在偏光干涉实验中电光效应的研究[J].光学学报,2003,23(12):1484-1488.
[21] Tian Z B,Zhang S J,Li S C.Study of propagation of light in active crystal La3Ga5SiO14 with electric field added[J].Chinese Journal of Lasers,2005,32(11):1539-1542.田召兵,张少军,李世忱.加电旋光晶体La3Ga5SiO14中光的传播方程的研究[J].中国激光,2005,32(11):1539-1542.
[22] Yin X,Wang J Y.Interaction of the optical activity and electro-optic effect and its influence on the optically active crystal electro-optic Q switcher[J].Acta Physica Sinica,2004,53(10):3565-3570.尹鑫,王继扬.旋光性与电光效应交互作用及其对旋光晶体电光Q开关的影响[J].物理学报,2004,53(10):3565-3570.
[23] Yin X,Wang J Y,Zhang S J.Study on electro-optic Q switch of La3Ga5SiO14 single crystal[J].Chinese Journal of Lasers,2004,31(1):29-32.尹鑫,王继扬,张少军.La3Ga5SiO14晶体电光Q开关的研究[J].中国激光,2004,31(1):29-32.
[24] Tabor W J,Chen F S.Electromagnetic propagation through materials possessing both Faraday rotation and birefringence:experiments with ytterbium orthoferrite[J].Journal of Applied Physics,1969,40(7):2760-2765.
[25] Kaminsky W.Experimental and phenomenological aspects of circular birefringence and related properties in transparent crystals[J].Reports on Progress in Physics,2000,63(10):1575-1640.
[26] Li C S,Cui X.Coupled-wave analysis on the electro-optic and magnetooptic interaction in BSO crystal and its application to sensors[J].Acta Photonica Sinica,1998,27(2):132-136.李长胜,崔翔.硅酸铋晶体内电光、磁光相互作用的耦合波分析及其传感应用[J].光子学报,1998,27(2):132-136.
[27] Liao Y B.Polarization optics[M].Beijing:Science Press,2003:155.廖延彪.偏振光学[M].北京:科学出版社,2003:155.
[28] Xu X W,Liao J Y.Progress in study on crystal growth of bismuth silicon oxide[J].Journal of Inorganic Materials,1994,9(2):129-138.徐学武,廖晶莹.硅酸铋(Bi12SiO20)晶体生长的研究进展[J].无机材料学报,1994,9(2):129-138.
[29] Xie K C.The optical rotation characteristics of Bi12SiO20 crystals[J].Piezoelectrics & Acoustooptics,1991,13(1):22-25,4.谢克诚.硅酸铋晶体的旋光特性[J].压电与声光,1991,13(1):22-25,4.
[30] Li C S.Optical voltage sensor using angular optical biasing in lithium niobate crystal[J].Chinese Journal of Sensors and Actuators,2007,20(7):1494-1497.李长胜.基于铌酸锂晶体自身角度光偏置的光学电压传感器[J].传感技术学报,2007,20(7):1494-1497.
[31] Li C S,Shen X L,Zeng R.Optical electric-field sensor based on angular optical bias using single β-BaB2O4 crystal[J].Applied Optics,2013,52(31):7580-7585.
[32] Maldonado T A,Gaylord T K.Accurate method to determine the eigenstates of polarization in gyrotropic media[J].Applied Optics,1989,28(11):2075-2086.
[33] Han S H,Wu J W.Polarization-interferometry measurement of the Pockels coefficient in a chiral Bi12SiO20 single crystal[J].Journal of the Optical Society of America B,2000,17(7):1205-1210.
[34] She W L,Lee W K.Wave coupling theory of linear electrooptic effect[J].Optics Communications,2001,195:303-311.
[35] Xie N,Qiu X M,Xu Q F,et al.Regulation of bismuth germanate electro-optic crystal′s half-wave voltage[J].Infrared and Laser Engineering,2018,47(4):0420003.谢楠,邱鑫茂,徐启峰,等.锗酸铋电光晶体的半波电压调控[J].红外与激光工程,2018,47(4):0420003.
[36] Montemezzani G,Pf?ndler S,Günter P.Electro-optic and photorefractive properties of Bi4Ge3O12 crystals in the ultraviolet spectral range[J].Journal of the Optical Society of America B,1992,9(7):1110-1117.
[37] Williams P A,Rose A H,Lee K S,et al.Optical,thermo-optic,electro-optic,and photoelastic properties of bismuth germanate (Bi4Ge3O12)[J].Applied Optics,1996,35(19):3562-3569.