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通过测量铌酸锂（LN）单模波导在不同波长下的半波电压，结合半波电压与电光重叠积分因子的依赖关系，实验发现了LN单模波导电光重叠积分因子随波长增大而迅速减小. 另一方面，通过数值求解法分别得出了LN单模波导在不同波长的导模场分布和调制电场分布以及二者的重叠积分因子，在理论上获得了与实验数据十分近似的结果. 进一步的仿真分析指出LN单模波导电光重叠积分因子随波长增大而减小的规律主要来自于导模的光场中心随波长增大逐渐远离波导表面，向低电场强度区域靠近. 这种电光重叠积分因子的波长依赖特性是导致LN波导半波电压随波长增大而非线性上升的原因之一，它将为基于LN波导的器件的设计和优化提供重要参考.Wavelength dependence of the electro-optic overlap integral factor (Γ) for a single-mode LiNbO3 (LN) channel waveguide was analyzed experimentally and theoretically. By measuring the half-wave voltage (Vπ) of the LN waveguide at different wavelengths and then substituting the measured values into a formula that describes the relationship between Vπ and Γ, the quantitative dependence of Γ on wavelength was obtained; and it showed that Γ rapidly decreases with increasing wavelength. On the other hand, numerical simulations of the modulating electric field distribution, the modal field distribution, and Γ at different wavelengths were carried out; the calculated relationship between Γ and wavelength is in good agreement with the measured results. Further simulations indicate that as the wavelength increases, the center of the modal field profile gradually moves toward the weak electric field side from the waveguide surface, thus leading to a smaller Γ at a longer wavelength. Such a relationship between Γ and wavelength is partially responsible for the nonlinear dependence of Vπ on wavelength obtained experimentally. This would be useful for designing and optimization of LN waveguide-based devices.
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Keywords:
- LiNbO3 waveguide /
- electro-optic overlap integral factor /
- half-wave voltage /
- wavelength dependence
[1] Wooten E L, Kissa K M, Yi-Yan A, Murphy E J, Lafaw D A, Hallemeier P F, Maack D, Attanasio D V, Fritz D J, McBrien G J, Bossi D E 2000 IEEE J.Sel. Top. Quantum Electron. 6 69
[2] Lee Y L, Eom T J, Shin W, Yu B A, Ko D K, Kim W K, Lee H Y 2009 Opt. Express 17 10718
[3] Xue T, Yu J, Yang T X, Ni W J, Li S C 2002 Acta Phys. Sin. 51 1521 (in Chinese)[薛挺, 于建, 杨天新, 倪文俊, 李世忱2002 51 1521]
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[7] Wei Z J, Wan W, Wang J D, Liao C J, Liu S H 2011 Acta Phys. Sin. 60 094216 (in Chinese)[魏正军, 万伟, 王金东, 廖常俊, 刘颂豪2011 60 094216]
[8] Bentini G G, Bianconi M, Cerutti A, Chiarini M, Pennestr G, Sada C, Argiolas N, Bazzan M, Mazzoldi P 2007 Opt. Laser Eng. 45 368
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[19] Lee H Y, Yang W S, Kim W K 2004 J. Opt. Soc. Korea 8 90
[20] Marcuse D 1982 IEEE J. Quantum Electron. QE-18 393
[21] Kim C M, Ramaswamy R V 1989 J. Lightwave Technol. 7 1063
[22] Becker R A, Kincaid B E 1993 J. Lightwave Technol. 11 2076
[23] Chang S J, Tsai C L, Lin Y B, Liu J F, Wang W S 1999 J. Lightwave Technol. 17 843
[24] Wu Y K, Wang W S 2008 J. Lightwave Technol. 26 286
[25] Yonekura K, Jin L, Takizawa K 2008 Jpn. J. Appl. Phys. 47 5503
[26] Toro J A de, Serrano M D, Cabañes A G, Cabrera J M 1998 Opt. Commun. 154 23
[27] He H Y 2004 Calculation Method for Electro-magnetic Field in Matlab (Wuhan: Huazhong University of Science & Technology Press) p100 (in Chinese) [何红雨2004 电磁场数值计算法与Matlab 实现(武汉: 华中科技大学出版社) 第100 页]
[28] Chen J J, Li Z, Zhang J S, Gong Q H 2008 Acta Phys. Sin. 57 5893 (in Chinese)[陈建军, 李智, 张家森, 龚旗煌 2008 57 5893]
[29] Li J Y, Yao Y Q, Wu J J, Qi Z M 2013 Acta Optica Sinica 33 196 (in Chinese) [李金洋, 要彦清, 吴建杰, 祁志美2013 光学学报33 196]
[30] Kawano K, Kitoh T 2001 Introduction to Optical Waveguide Analysis(New York: John Wiley & Sons) pp117-164
[31] Cao Z Q 2007 Wave guiding Optics (Beijing: Science Press) p26 (in Chinese) [曹庄琪2007 导波光学(北京: 科学出版社) 第26 页]
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[1] Wooten E L, Kissa K M, Yi-Yan A, Murphy E J, Lafaw D A, Hallemeier P F, Maack D, Attanasio D V, Fritz D J, McBrien G J, Bossi D E 2000 IEEE J.Sel. Top. Quantum Electron. 6 69
[2] Lee Y L, Eom T J, Shin W, Yu B A, Ko D K, Kim W K, Lee H Y 2009 Opt. Express 17 10718
[3] Xue T, Yu J, Yang T X, Ni W J, Li S C 2002 Acta Phys. Sin. 51 1521 (in Chinese)[薛挺, 于建, 杨天新, 倪文俊, 李世忱2002 51 1521]
[4] Li G H, Jiang H L, Xu X Y 2011 Chin. Phys. B 20 064201
[5] Lin H Y, Ning J P, Geng F 2004 Chin. Opt. Lett. 2 89
[6] Wang D L, Sun J Q, Wang J 2008 Acta Phys. Sin. 57 252 (in Chinese)[汪大林, 孙军强, 王健2008 57 252]
[7] Wei Z J, Wan W, Wang J D, Liao C J, Liu S H 2011 Acta Phys. Sin. 60 094216 (in Chinese)[魏正军, 万伟, 王金东, 廖常俊, 刘颂豪2011 60 094216]
[8] Bentini G G, Bianconi M, Cerutti A, Chiarini M, Pennestr G, Sada C, Argiolas N, Bazzan M, Mazzoldi P 2007 Opt. Laser Eng. 45 368
[9] Chen F, Liu R P, Qi Z M 2011 Acta Optica Sinica 31 513001 (in Chinese) [陈方, 刘瑞鹏, 祁志美2011 光学学报 31 513001]
[10] Grusemann U, Zeitner B, Rottschalk M, Ruske J P, Tnnermann A, Rasch A 2002 Appl. Opt. 41 6211
[11] Yim Y S, Shin S Y 1998 Opt. Commun. 152 225
[12] Miyakawa T, Nishikawa K, Nishida K 2005 Electron. Comn. Jpn. Part 2 88(4) 18
[13] Yang Y J, Chen F S, Sun B 2006 Chin. Opt. Lett. 4 110643
[14] Jung H S 2012 J. Opt. Soc. Korea 16 47
[15] Strake E, Bava G P, Montrosset I 1988 J. Lightwave Technol. 6 1126
[16] Fouchet S, Carenco A, Daguet C, Guglielmi R, Riviere L 1987 J. Lightwave Technol. LT-5 700
[17] Zelmon D E, Small D L, Jundt D 1997 J. Opt. Soc. Am. B 14 3319
[18] Lang T, Thévenaz L, Ren Z B, Robert P 1994 Meas. Sci. Technol. 5 1124
[19] Lee H Y, Yang W S, Kim W K 2004 J. Opt. Soc. Korea 8 90
[20] Marcuse D 1982 IEEE J. Quantum Electron. QE-18 393
[21] Kim C M, Ramaswamy R V 1989 J. Lightwave Technol. 7 1063
[22] Becker R A, Kincaid B E 1993 J. Lightwave Technol. 11 2076
[23] Chang S J, Tsai C L, Lin Y B, Liu J F, Wang W S 1999 J. Lightwave Technol. 17 843
[24] Wu Y K, Wang W S 2008 J. Lightwave Technol. 26 286
[25] Yonekura K, Jin L, Takizawa K 2008 Jpn. J. Appl. Phys. 47 5503
[26] Toro J A de, Serrano M D, Cabañes A G, Cabrera J M 1998 Opt. Commun. 154 23
[27] He H Y 2004 Calculation Method for Electro-magnetic Field in Matlab (Wuhan: Huazhong University of Science & Technology Press) p100 (in Chinese) [何红雨2004 电磁场数值计算法与Matlab 实现(武汉: 华中科技大学出版社) 第100 页]
[28] Chen J J, Li Z, Zhang J S, Gong Q H 2008 Acta Phys. Sin. 57 5893 (in Chinese)[陈建军, 李智, 张家森, 龚旗煌 2008 57 5893]
[29] Li J Y, Yao Y Q, Wu J J, Qi Z M 2013 Acta Optica Sinica 33 196 (in Chinese) [李金洋, 要彦清, 吴建杰, 祁志美2013 光学学报33 196]
[30] Kawano K, Kitoh T 2001 Introduction to Optical Waveguide Analysis(New York: John Wiley & Sons) pp117-164
[31] Cao Z Q 2007 Wave guiding Optics (Beijing: Science Press) p26 (in Chinese) [曹庄琪2007 导波光学(北京: 科学出版社) 第26 页]
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