磁光非线性光纤中光脉冲传播与分步傅里叶计算
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摘要
随着人们对各种高非线性光纤的相继开发,基于光纤非线性的光子信息处理器件备受关注。磁光非线性光纤是一类具有高磁光效应和光纤非线性效应的特种光纤,在磁场传感、光通信与光信息处理领域已具有广泛应用前景。本文主要研究内容包括:
1.研究了磁光光纤中光脉冲的非线性传播,介绍了磁光非线性光纤的微扰理论和基本的研究方法。将磁光效应与非线性效应视为微扰,并用附加电极化强度表示,然后根据麦克斯韦方程推导出磁光光纤中光脉冲的非线性耦合模方程。
2.根据磁光光纤中的椭圆双折射特性,推导了导波光脉冲演化的本征型和非本征型非线性耦合模方程,分析了各种坐标系下修正分步傅里叶算法(SSFM)的精度。研究表明,本征型非线性耦合模方程对分步傅里叶算法的适应性最好。
3.分析了光脉冲的自相位调制(SPM)特性,给出了磁光光纤等效非线性系数与本征椭圆偏振光椭圆率的关系。自相位调制引起的最大非线性相移会随着外加磁场的增加而减小,从而揭示了非线性光纤器件的磁控机理。
4.通过修正分步傅里叶算法(SSFM)计算了磁光光纤中光脉冲的传播特性。研究表明,脉冲频谱会随着外加磁场的增加而展宽,磁场有助于减弱光纤非线性的偏振依赖性。
With development of a variety of highly nonlinear optical fiber, photonic information processing devices based on fiber nonlinear effects are concerned. Magneto-optical nonlinear fibers, as a class of special fibers, possess high magneto-optical effects and nonlinear effects with wide application prospects in magnetic field sensing, optical communication and optical information processing field. The research works are as follows:
1. Nonlinear propagation of optical pulses in magneto-optical fibers is described according to the perturbation theory. The magneto-optical effect and nonlinearity are regarded as the perturbation expressed by the additional electrical polarization. And then, the magneto-optical and nonlinear coupled mode equations of optical pulses can be derived from Maxwell's equations.
2. According to the characteristics of elliptical birefringence in magneto-optical fiber, we put forward the eigen and non-eigen nonlinear coupled-mode equations for guided optical waves and analyze the accuracy of the modified split-step Fourier method (SSFM). It shows that the eigen nonlinear coupled mode equations are fit for the modified split-step Fourier method.
3. For the self-phase modulation (SPM) characteristics, the relationship between the equivalent nonlinear coefficient and the ellipticity of eigen elliptical polarized light is obtained. The maximum of nonlinear phase shift induced by SPM increases with the decrease of applied magnetic field, and then the magnetic control mechanism of nonlinearity is opened out.
4. The modified split-step Fourier method (SSFM) is also used to calculate the propagation characteristics of light pulses in the fibers. With the increase of magnetic field, the pulse spectrum can be broadened and the polarization dependency of nonlinearity reduces.
1.研究了磁光光纤中光脉冲的非线性传播,介绍了磁光非线性光纤的微扰理论和基本的研究方法。将磁光效应与非线性效应视为微扰,并用附加电极化强度表示,然后根据麦克斯韦方程推导出磁光光纤中光脉冲的非线性耦合模方程。
2.根据磁光光纤中的椭圆双折射特性,推导了导波光脉冲演化的本征型和非本征型非线性耦合模方程,分析了各种坐标系下修正分步傅里叶算法(SSFM)的精度。研究表明,本征型非线性耦合模方程对分步傅里叶算法的适应性最好。
3.分析了光脉冲的自相位调制(SPM)特性,给出了磁光光纤等效非线性系数与本征椭圆偏振光椭圆率的关系。自相位调制引起的最大非线性相移会随着外加磁场的增加而减小,从而揭示了非线性光纤器件的磁控机理。
4.通过修正分步傅里叶算法(SSFM)计算了磁光光纤中光脉冲的传播特性。研究表明,脉冲频谱会随着外加磁场的增加而展宽,磁场有助于减弱光纤非线性的偏振依赖性。
With development of a variety of highly nonlinear optical fiber, photonic information processing devices based on fiber nonlinear effects are concerned. Magneto-optical nonlinear fibers, as a class of special fibers, possess high magneto-optical effects and nonlinear effects with wide application prospects in magnetic field sensing, optical communication and optical information processing field. The research works are as follows:
1. Nonlinear propagation of optical pulses in magneto-optical fibers is described according to the perturbation theory. The magneto-optical effect and nonlinearity are regarded as the perturbation expressed by the additional electrical polarization. And then, the magneto-optical and nonlinear coupled mode equations of optical pulses can be derived from Maxwell's equations.
2. According to the characteristics of elliptical birefringence in magneto-optical fiber, we put forward the eigen and non-eigen nonlinear coupled-mode equations for guided optical waves and analyze the accuracy of the modified split-step Fourier method (SSFM). It shows that the eigen nonlinear coupled mode equations are fit for the modified split-step Fourier method.
3. For the self-phase modulation (SPM) characteristics, the relationship between the equivalent nonlinear coefficient and the ellipticity of eigen elliptical polarized light is obtained. The maximum of nonlinear phase shift induced by SPM increases with the decrease of applied magnetic field, and then the magnetic control mechanism of nonlinearity is opened out.
4. The modified split-step Fourier method (SSFM) is also used to calculate the propagation characteristics of light pulses in the fibers. With the increase of magnetic field, the pulse spectrum can be broadened and the polarization dependency of nonlinearity reduces.
引文
[1]刘鹏,WDM光纤通信系统中非线性影响及其仿真研究:[硕士学位论文].哈尔滨:哈尔滨工程大学,2008
[2]邱昆,王冕,邱琪.光纤通信系统.成都:电子科技大学出版社, 2005,1-2,117(03):3-11
[3]伦秀君,黄永清,张瑞康,任晓敏.全光3R再生原理与技术,光通信研究,2003,3-8
[4]吴铭,刘海荣,黄德修.光子晶体光纤色散与非线性特性的研究,光学学报,2008,28(03):539-542
[5]董方.用光纤XPM实现全光3R中再整形的研究[学位论文]-南京邮电大学2008
[6]王新兵.超快非线性干涉仪(UNI)的理论和实验研究[学位论文]-天津大学2005
[7]张勇,吴重庆,李保海,尚玉峰.光3R再生技术,通讯世界2003-9(1)
[8]董方,陈鹤鸣.利用光子晶体光纤交叉相位调制和自相位调制实现40Gb/s全光3R在整形.全国第十三次光纤通信暨第十四届集成光学学术会议.2007-11
[9]王剑.吴波. F-P滤波器和SOA在全光帧始终提取中的分析和试验[学术期刊].中国民航大学学报.2008-2
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[12] Johnson C, Demarest K, Allen C, et al. Multiwavelength all -optical clock recovery .IEEE Photonics Techonol Lett, 1999,117, 11(7): 895~897 .
[13] Shelby J.Savage, Bryan S.Robinson, Scott A.Hamilton,et al, A wavelength-maintaining polarization-insensitive all-optical 3R regenerator, 2006 Optical Fiber Communication Conference, and the 2006 National Fiber Optic Engineers Conference, v 2006, Proceedings-Thirteenth International Symposium on Temporal Representation and Reasoning, TIME 2006, 2006
[14] T. Otani, T.Miyazaki, S.Yamamoto, Optical 3R regenerator using wavelength converters basedon electroabsorption modulator for all-optical network applications, IEEE Photonics Technilogy Letters,v 12,n4, Apr, 2000,p 431-433
[15]鲍振武,王林斗.光纤中的磁性光学效应.天津大学学报,1994,27(4): 403-411
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[18] Mao.T.C.,Chen J.C., Hu C.C.. Effect of the pulling rate on the quality of cerium-substituted YIG single-crystal fibers by LHPG. J Crystal Growth, 2006, 296: 110–116
[19]武保剑,组合磁光光纤光栅的磁场敏感性分析.电子科技大学学报,2009,38(5):634-638
[20] N. G. Roderick, D. Taverner, D. J. Richardson, etc. J. Opt. Soc. Am. B17, 345(2000)
[21] Bahuguna R, Mina M, Weber R J, Magneto-optic based fiber switch for optical communication. 2006 International Conference on Magnetics, Page(s):456-456
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[23]翁梓华.基于磁光光纤光纤和高速磁场的全光磁光开关研究:[博士学位论文].杭州:浙江大学,2005
[24]殷海荣,章春香,刘立营.高Verdet常数法拉第玻璃磁光理论及其应用.硅酸盐通报,2008,27(4): 748-753
[25]殷海荣,汪涛,董继先. Tb 3+ / Dy 3+共掺杂磁光玻璃的备制及性能研究.电子元件与材料. 2010, 29(11):61-64
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[28]刘志华,刘瑞金.关于正常塞曼效应现象的理论解释.山东理工大学学报(自然科学版), 2006,(05) .
[29] Yinlan Ruan, Ruth A. Jarvis, Andrei V. Rode, Steve Madden, Barry Luther-Davies. Wavelength dispersion of Verdet constants in chalcogenide glasses for magneto-optical waveguide devices. Optics Communication,2005, 252: 39-45
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[34]武保剑.微波磁光理论与磁光信号处理.成都:电子科技大学出版社,2009,190-217
[35]邱昆,武保剑,文峰.磁光光纤Bragg光栅中圆偏振光的非线性传输特性.物理学报,2009,58(3):1726-1729
[36] Toshihiko Yoshino. Theory for the Faraday effect in optical fiber. J. Opt. Soc. Am. B, 2005, 22(9): 1856–1860
[37] Haus H A, Huang W. Coupled-mode theory. Proc. IEEE, 1991,79(10):1505-1518.
[38]钱景仁.耦合模理论及其在光纤光学中的应用.光学学报, 2009,29(5):1188-1192
[39]黄海泉.光子晶体光纤的理论与实验研究:[硕士毕业论文].浙江:浙江大学,2006
[40] Baojian Wu, Fen Liu, Shuo Liu, Wei Huang. Research on transmission spectra of one-dimensional magneto-photonic crystals. Optoelectronics Letters, 2009, 5(4):0268-0271
[41] G. P. Agrawal. Nonlinear Fiber Optics. 3rd ed, Elservier(Singapore) Pte Ltd, 2005
[42] Ju Han Lee and Kazuro Kikuchi. All-fiber 80-Gbit/s wavelength converter using 1-m-long Bismuth Oxide-based nonlinear optical fiber with a nonlinearityγof 1100 /W/km. Optics express., 2005, 13(8): 3144–3149
[43] M. J. Holmes, D. L. Williams, R. J. Manning. Highly nonlinear optical fiber for all optical processing applications. Photonics Technology Letters, IEEE. 2002, 7(9): 1045～1047
[44]董建绩,张新亮,黄德修.基于半导体光放大器四波混频效应的多种调制格式的波长转换实验.光学学报,2008,28(7):1327～1332
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[2]邱昆,王冕,邱琪.光纤通信系统.成都:电子科技大学出版社, 2005,1-2,117(03):3-11
[3]伦秀君,黄永清,张瑞康,任晓敏.全光3R再生原理与技术,光通信研究,2003,3-8
[4]吴铭,刘海荣,黄德修.光子晶体光纤色散与非线性特性的研究,光学学报,2008,28(03):539-542
[5]董方.用光纤XPM实现全光3R中再整形的研究[学位论文]-南京邮电大学2008
[6]王新兵.超快非线性干涉仪(UNI)的理论和实验研究[学位论文]-天津大学2005
[7]张勇,吴重庆,李保海,尚玉峰.光3R再生技术,通讯世界2003-9(1)
[8]董方,陈鹤鸣.利用光子晶体光纤交叉相位调制和自相位调制实现40Gb/s全光3R在整形.全国第十三次光纤通信暨第十四届集成光学学术会议.2007-11
[9]王剑.吴波. F-P滤波器和SOA在全光帧始终提取中的分析和试验[学术期刊].中国民航大学学报.2008-2
[10] Yikai Su, Lijun Wang, Anjali Agarwal and Prem Kumar. Wavelength-tunable all-optical clock recovery using a fiber-optic parametric oscillator .Optics Communications, 2000,184, 184 (1-4):151-156 .
[11] L.Billes, J.C.Simon, B.Kowalski,et al, 20Gbit/s optical 3R regenerator using SOA based Mach-Zehnder interferometer gate, Proceedings of the 1997 11th International Conference on Integrated Optics and Optical Fibre Communications and 23rd European Conference on Optical Communication, IOOC-ECOC’97. Part2 (of 5), 1997, 09: 22-25
[12] Johnson C, Demarest K, Allen C, et al. Multiwavelength all -optical clock recovery .IEEE Photonics Techonol Lett, 1999,117, 11(7): 895~897 .
[13] Shelby J.Savage, Bryan S.Robinson, Scott A.Hamilton,et al, A wavelength-maintaining polarization-insensitive all-optical 3R regenerator, 2006 Optical Fiber Communication Conference, and the 2006 National Fiber Optic Engineers Conference, v 2006, Proceedings-Thirteenth International Symposium on Temporal Representation and Reasoning, TIME 2006, 2006
[14] T. Otani, T.Miyazaki, S.Yamamoto, Optical 3R regenerator using wavelength converters basedon electroabsorption modulator for all-optical network applications, IEEE Photonics Technilogy Letters,v 12,n4, Apr, 2000,p 431-433
[15]鲍振武,王林斗.光纤中的磁性光学效应.天津大学学报,1994,27(4): 403-411
[16]卜胜利.磁光玻璃光纤的磁致旋光效应及其在全光纤电流传感器中的应用研究:[硕士学位论文].合肥:安徽大学,2003
[17] Lim Han-Jin, Demattei R. C, Feigelson R. S. Growth of single crystal YIG fibers by the laser heated pedestal growth method. Materials Research Society Symposium Proceedings, 1998,481: 83-88
[18] Mao.T.C.,Chen J.C., Hu C.C.. Effect of the pulling rate on the quality of cerium-substituted YIG single-crystal fibers by LHPG. J Crystal Growth, 2006, 296: 110–116
[19]武保剑,组合磁光光纤光栅的磁场敏感性分析.电子科技大学学报,2009,38(5):634-638
[20] N. G. Roderick, D. Taverner, D. J. Richardson, etc. J. Opt. Soc. Am. B17, 345(2000)
[21] Bahuguna R, Mina M, Weber R J, Magneto-optic based fiber switch for optical communication. 2006 International Conference on Magnetics, Page(s):456-456
[22]马静.磁光玻璃光纤的偏振特性及其在电流传感器上的应用:[硕士学位论文].合肥:安徽大学,2002
[23]翁梓华.基于磁光光纤光纤和高速磁场的全光磁光开关研究:[博士学位论文].杭州:浙江大学,2005
[24]殷海荣,章春香,刘立营.高Verdet常数法拉第玻璃磁光理论及其应用.硅酸盐通报,2008,27(4): 748-753
[25]殷海荣,汪涛,董继先. Tb 3+ / Dy 3+共掺杂磁光玻璃的备制及性能研究.电子元件与材料. 2010, 29(11):61-64
[26]张国营,张学龙,王明泉.关于磁线光折射偏振模式的讨论.第十六次全国原子、原子核物理研讨会暨全国近代物理研究会第九届年会. 2006
[27]刘公强,吴蓓,虞志强,刘湘林.克尔磁光效应的经典理论分析.光学学报. 1990, 10(1): 67-73
[28]刘志华,刘瑞金.关于正常塞曼效应现象的理论解释.山东理工大学学报(自然科学版), 2006,(05) .
[29] Yinlan Ruan, Ruth A. Jarvis, Andrei V. Rode, Steve Madden, Barry Luther-Davies. Wavelength dispersion of Verdet constants in chalcogenide glasses for magneto-optical waveguide devices. Optics Communication,2005, 252: 39-45
[30]李婧,欧阳雪琼,卢安贤.磁光玻璃的研究进展.材料导报, 2008, 12(22): 219-222
[31] M. J. Holmes, D. L. Williams, R. J. Manning. Highly nonlinear optical fiber for all optical processing applications. Photonics Technology Letters, IEEE. 2002, 7(9): 1045–1047
[32] Bao-jian Wu, Xiao Liu, Kun Qiu. Characteristics of magneto-optic fiber Bragg grating for use in optical signal. Optical Fiber Technology, 2009, 15:165–171
[33] G. P. Agrawal. Nonlinear Fiber Optics. 3rd ed, Elsevier (Singapore) Pte Ltd, 2005
[34]武保剑.微波磁光理论与磁光信号处理.成都:电子科技大学出版社,2009,190-217
[35]邱昆,武保剑,文峰.磁光光纤Bragg光栅中圆偏振光的非线性传输特性.物理学报,2009,58(3):1726-1729
[36] Toshihiko Yoshino. Theory for the Faraday effect in optical fiber. J. Opt. Soc. Am. B, 2005, 22(9): 1856–1860
[37] Haus H A, Huang W. Coupled-mode theory. Proc. IEEE, 1991,79(10):1505-1518.
[38]钱景仁.耦合模理论及其在光纤光学中的应用.光学学报, 2009,29(5):1188-1192
[39]黄海泉.光子晶体光纤的理论与实验研究:[硕士毕业论文].浙江:浙江大学,2006
[40] Baojian Wu, Fen Liu, Shuo Liu, Wei Huang. Research on transmission spectra of one-dimensional magneto-photonic crystals. Optoelectronics Letters, 2009, 5(4):0268-0271
[41] G. P. Agrawal. Nonlinear Fiber Optics. 3rd ed, Elservier(Singapore) Pte Ltd, 2005
[42] Ju Han Lee and Kazuro Kikuchi. All-fiber 80-Gbit/s wavelength converter using 1-m-long Bismuth Oxide-based nonlinear optical fiber with a nonlinearityγof 1100 /W/km. Optics express., 2005, 13(8): 3144–3149
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