光孤子传输特性的研究
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摘要
本论文研究光孤子的传输特性,对时间孤子和空间孤子都进行了研究。研究时间光孤子的传输特性对于设计和实现高速光孤子通信系统具有重要的理论意义和现实意义。光学空间孤子在全光开关、光波导、光显示、光计算等方面有应用潜力,同时也在相关的物理理论的研究、验证等方面有重要的意义。
在研究时间孤子时,详细讨论了一种解光纤中非线性薛定谔方程的数值方法—对称分步傅里叶法。研究了三阶色散效应对基态孤子传输的影响,发现正、负三阶色散都会使基态孤子在传输过程中产生畸变。针对研究高阶孤子情况较少的情况,研究了高阶孤子对间的相互作用,发现高阶孤子对与一阶孤子对的传输特性不同,高阶孤子对会在中间周期性的产生衍生孤子,在相同的传输距离内,三阶孤子对产生的衍生孤子多于二阶孤子对。
本论文在研究光学格子中的带隙光孤子时,获得一维、二维光学格子的布洛赫带结构都是用平面波展开法,在计算孤子形状时,一维情况用打靶法,二维情况用改进的平方算子迭代法,模拟孤子传输时,都是用分步傅里叶法。
研究了饱和非线性介质中一维超晶格光学格子中的带隙空间光孤子,对其传输特性进行了详细的研究。发现带隙孤子只存在于半无穷带隙,而且只能在低功率区域稳定传输。
研究了饱和介质中正方形的二维光学格子中的空间缺陷带隙孤子,研究发现对于负缺陷,孤子可以存在于第一带隙,随着负缺陷的增大,缺陷孤子不再是在第一带隙都能稳定传输,而是只能在中等功率范围内稳定传输;而在半无穷带隙,随着缺陷深度的增加,孤子在整个半无穷带隙都不能稳定传输。对于正缺陷,缺陷孤子只存在于半无穷带隙,而且只能在低功率范围内稳定传输。
本论文还对三角形格子中的缺陷孤子进行了研究,研究发现,对于正缺陷,孤子只存在于半无穷带隙,而且只能在低功率范围内稳定传输。而对于负缺陷,孤子不但能存在于半无穷带隙,而且能存在于第一带隙,随着负缺陷的加深,孤子将在整个半无穷带隙内不稳定,在第一带隙内,将经历低功率不稳定,高功率和低功率不稳定,直至整个第一带隙不稳定的过程。
最后对克尔介质中正方形二维光学格子中的带隙空间光孤子的稳定性进行了讨论。发现,在半无穷带隙内离散孤子和涡旋孤子在靠近带边时都不能稳定传输。
The paper has researched the transmission characteristics of solitons. Time solitons and spatial solitons have been studied. Researching for time solitons has theoretical and practical significance for designing and implementing high-speed optical solitons communication. Spatial optical solitons have the potential applications in all-optical switching, optical waveguide, optical display, optical computing, etc. At the same time,the spatial optical solitons also have the important significance in related theoretical researching and validation of physics
When researched the time solitons, A form of symmetric split-step Fourier method is carefully discussed. Researched the influence of third-order dispersion on state-ground solitons transmission, found the state-ground solitons pulse will be distorted by the third-order dispersion. The case of researching the two high-order solitons are less, We have studied the interaction between two high-order solitons, found that the transmission characteristics of the two second-order solitons and the two third-order solitons are significantly different from the two first-order solitons, the two second-order solitons and the two third-order solitons will not attract and collide periodically, the interaction between the two second-order solitons and the two third-order solitons will periodically produce ramification solitons in the middle, in same transmission distance, the third-order soliton-pair produce more derivative solitons than the second-order soliton-pair.
When researched gap solitons in optical lattices, get the blouch band structures of one-dimensional and two-dimensional lattices both by the plane wave expansion method. To calculate the numerical gap solitons solution of one-dimension optical lattices, used the shooting method, and used The modified squared-operator method to calulate the numerical gap solitons solution of two-dimension optical lattices. When simulated spatial optical solitons transmit, used symmetric split-step Fourier method.
The paper has researched gap solitons in superlattice, the propagation characteristics of these solitons were carefully discussed. It is found that these gap solitons only transmit stably in low power region.
Gap solitons in two-demensional square lattices in focusing saturable nonlinearity have been researshed, we constructed a defect in the square lattices. It is found that for the negative defect, the defect gap solitons not only exist in the semi-infinite gap, but also exist in the first gap, increasing the defect depth, the stable region only in the moderate power region in the first gap; In the semi-infinite gap, with the increasing of defect depth, defect solitons will unstably transmit in the entire gap. Forpositive defect, gap solitons only exist in semi-infinite gap, and these solitons only can stably transmit in low power region and unstably transmit in high power region. The paper also has researshed the defect gap solitons in triangular optical lattices.
For the negative defect, solitons only exist in semi-infinite gap, and it can stably transmit only in the lower power region. For the negative defect, solitons not only exist in the semi-infinte gap, but also exist in the first gap, with the increasing of thedefect depth, the solitons will unstable in the whole semi-infinte gap, and in the first gap, it will be unstable in lower power region, high power region and lower power region, untill the whole first gap region.
Finally, the paper has researched the gap solitons’stability in kerr nonlinearity, it is found that in the semi-infinite gap, vortex and discrete solitons near the band can not stably transmit.
在研究时间孤子时,详细讨论了一种解光纤中非线性薛定谔方程的数值方法—对称分步傅里叶法。研究了三阶色散效应对基态孤子传输的影响,发现正、负三阶色散都会使基态孤子在传输过程中产生畸变。针对研究高阶孤子情况较少的情况,研究了高阶孤子对间的相互作用,发现高阶孤子对与一阶孤子对的传输特性不同,高阶孤子对会在中间周期性的产生衍生孤子,在相同的传输距离内,三阶孤子对产生的衍生孤子多于二阶孤子对。
本论文在研究光学格子中的带隙光孤子时,获得一维、二维光学格子的布洛赫带结构都是用平面波展开法,在计算孤子形状时,一维情况用打靶法,二维情况用改进的平方算子迭代法,模拟孤子传输时,都是用分步傅里叶法。
研究了饱和非线性介质中一维超晶格光学格子中的带隙空间光孤子,对其传输特性进行了详细的研究。发现带隙孤子只存在于半无穷带隙,而且只能在低功率区域稳定传输。
研究了饱和介质中正方形的二维光学格子中的空间缺陷带隙孤子,研究发现对于负缺陷,孤子可以存在于第一带隙,随着负缺陷的增大,缺陷孤子不再是在第一带隙都能稳定传输,而是只能在中等功率范围内稳定传输;而在半无穷带隙,随着缺陷深度的增加,孤子在整个半无穷带隙都不能稳定传输。对于正缺陷,缺陷孤子只存在于半无穷带隙,而且只能在低功率范围内稳定传输。
本论文还对三角形格子中的缺陷孤子进行了研究,研究发现,对于正缺陷,孤子只存在于半无穷带隙,而且只能在低功率范围内稳定传输。而对于负缺陷,孤子不但能存在于半无穷带隙,而且能存在于第一带隙,随着负缺陷的加深,孤子将在整个半无穷带隙内不稳定,在第一带隙内,将经历低功率不稳定,高功率和低功率不稳定,直至整个第一带隙不稳定的过程。
最后对克尔介质中正方形二维光学格子中的带隙空间光孤子的稳定性进行了讨论。发现,在半无穷带隙内离散孤子和涡旋孤子在靠近带边时都不能稳定传输。
The paper has researched the transmission characteristics of solitons. Time solitons and spatial solitons have been studied. Researching for time solitons has theoretical and practical significance for designing and implementing high-speed optical solitons communication. Spatial optical solitons have the potential applications in all-optical switching, optical waveguide, optical display, optical computing, etc. At the same time,the spatial optical solitons also have the important significance in related theoretical researching and validation of physics
When researched the time solitons, A form of symmetric split-step Fourier method is carefully discussed. Researched the influence of third-order dispersion on state-ground solitons transmission, found the state-ground solitons pulse will be distorted by the third-order dispersion. The case of researching the two high-order solitons are less, We have studied the interaction between two high-order solitons, found that the transmission characteristics of the two second-order solitons and the two third-order solitons are significantly different from the two first-order solitons, the two second-order solitons and the two third-order solitons will not attract and collide periodically, the interaction between the two second-order solitons and the two third-order solitons will periodically produce ramification solitons in the middle, in same transmission distance, the third-order soliton-pair produce more derivative solitons than the second-order soliton-pair.
When researched gap solitons in optical lattices, get the blouch band structures of one-dimensional and two-dimensional lattices both by the plane wave expansion method. To calculate the numerical gap solitons solution of one-dimension optical lattices, used the shooting method, and used The modified squared-operator method to calulate the numerical gap solitons solution of two-dimension optical lattices. When simulated spatial optical solitons transmit, used symmetric split-step Fourier method.
The paper has researched gap solitons in superlattice, the propagation characteristics of these solitons were carefully discussed. It is found that these gap solitons only transmit stably in low power region.
Gap solitons in two-demensional square lattices in focusing saturable nonlinearity have been researshed, we constructed a defect in the square lattices. It is found that for the negative defect, the defect gap solitons not only exist in the semi-infinite gap, but also exist in the first gap, increasing the defect depth, the stable region only in the moderate power region in the first gap; In the semi-infinite gap, with the increasing of defect depth, defect solitons will unstably transmit in the entire gap. Forpositive defect, gap solitons only exist in semi-infinite gap, and these solitons only can stably transmit in low power region and unstably transmit in high power region. The paper also has researshed the defect gap solitons in triangular optical lattices.
For the negative defect, solitons only exist in semi-infinite gap, and it can stably transmit only in the lower power region. For the negative defect, solitons not only exist in the semi-infinte gap, but also exist in the first gap, with the increasing of thedefect depth, the solitons will unstable in the whole semi-infinte gap, and in the first gap, it will be unstable in lower power region, high power region and lower power region, untill the whole first gap region.
Finally, the paper has researched the gap solitons’stability in kerr nonlinearity, it is found that in the semi-infinite gap, vortex and discrete solitons near the band can not stably transmit.
引文
[1]张妍.光孤子通信系统传输特性及其偏振模色散的研究[D].济南:山东大学通信与系统专业,2004
[2]王志斌.光孤子在光纤中传输的特性研究[D].秦皇岛:燕山大学测试计量技术及仪器专业,2007
[3]杨懿.二阶光纤孤子传输特性研究[D].五邑:五邑大学信息与信号处理专业,2008
[4]王建东.空间光孤子[D].合肥:中国科学技术大学光学专业博士论文,2006.
[5]陈武喝.一维光学格子中带隙光孤子的研究[D].广州:中山大学光学专业博士论文, 2007.
[6]何影记.空间孤子传输的研究[D].广州:中山大学光学工程专业博士论文, 2007.
[7]石顺祥,陈国夫,赵卫,等.非线性光学[M].西安:西安电子科技大学出版社,2003,417-448.
[8]李均,黄德修,张新亮.光纤传输模型的数值计算研究[J].光电子技术与信息,2003,16(2):9-12
[9]王志斌,李志全,刘洋.高阶孤子在光纤中传输的数值研究[J].光子学报,2007,36(9):1641-1644.
[10]雷超.基于MATLAB的非线性薛定谔方程的数值算法研究.中国科技论文在线(http://www.paper.edu.cn). 2008年11月28日.
[11]施娟.基于对称分步傅立叶算法的光孤子仿真[J].电子元器件应用,2008,10(1):73-75.
[12]曹文华,刘颂豪.负三阶色散光纤中的孤子效应脉冲压缩[J].量子电子学报,1999,16(1):9-15.
[13]黄天水,曹文华,尹新付,等.高阶色散效应对光纤中高斯光脉冲的影响[J].半导体光电,2007,28(4):564-567.
[14]吕理想,张晓萍.不同形式非线性薛定谔方程及其傅里叶法求解[J].计算物理,2007,24(3):373-377.
[15]张晓光,杨伯君,俞重远.非线性薛定谔方程数值解法中傅立叶正逆变换选取的讨论[J]计算物理,2003,20(3):267—272.
[16]李志全,王志斌,刘洋.高阶色散对光孤子传输的影响[J].光学仪器,2008,30(2):66-69
[17]方云团,范俊.二阶孤子的传输和相互作用[J].应用光学,2008,29(2):317-320.
[18] S mith D. R. , Dalichaouch R, K roll N, et al,"Photonic band structure and defects in one and twodimensions,"J .Opt.Soc.A m.B ,1993,10:314-321.
[19] Fedele F, Yang J. K. , and Chen Z.G. ,“Properties of Defect Modes in One-Dimensional Optically Induced Photonic Lattices,”Stud.Appl.Math. 115:277-299.
[20] Alexander T. J. , Desyatnikov A. S. , and Kivshar Y. S. ,“Multivortex solitons in triangular photonic lattices”Opt. Lett. 32, 1293-1295 (2007).
[21] Wang J. D and Yang J. K. , Chen Z. G. ,“Two-dimensional defect modes in optically induced photonic lattices,”Phys. Rev. A 76 013828 (2007)
[22] Yang J. K. , and Chen Z. G. ,“Defect solitons in photonic lattices,”Phys. Rev. E 73 026609 (2006)
[23] Yang J. K. and Lakoba T. I. ,“Universally-Convergent Squared-Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations,”Stud. Appl. Math. 118, 153-197 (2007).
[24] Yang J. K. ,“Newton-conjugate gradient methods for solitary wave computations,”J. Comp. Phys. 228, 7007-7024 (2009).
[25] Fleischer J. W. , Segev M, Efremidis N. K, et al,“Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,”Nature 422, 147-150 (2003).
[26] Ablowitz M. J. , Ilan B, Schonbrun E. , et al,“Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,”Phys. Rev. E 74, 035601 (2006).
[27] Chen W. , He Y. , and Wang H. ,“Defect superlattice solitons,”Opt. Express 15, 14498–14503 (2007).
[28] Wang J. D. and Yang J. K. ,“Families of vortex solitons in periodic media,”Phys. Rev. A 77, 033834 (2008).
[29] Kartashov Y.V. , Vysloukh V. A. , and Torner L. ,“Surface gap solitons,”Phys. Rev. Lett. 96, 073901(2006).
[30] Kivshar Y. S. ,“Self-localization in arrays of defocusing waveguides,”Opt. Lett. 18, 1147-1149(1993).
[31] Lou C. , Wang X. , Xu J. , Chen Z. , et al,“Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structure,”Phys. Rev. Lett. 98, 213903(2007).
[32] Chen W. , He Y. , and Wang H. ,“Surface defect superlattice solitons,”J Opt. Soc. Am. B 24, 2584-2588(2007).
[33] Fleischer J. W. , Carmon T. , Segev M. , et al“Observation of discrete solitons in optically induced real time waveguide arrays,”Phys.Rev. Lett. 90, 023902 (2003).
[34] Chen Z. and Mccarthy K. ,“Spatial soliton pixels from partially incoherent light,”Opt. Lett. 27, 2019-2021 (2002).
[35] Kartashov Y. V. , Vysloukh V. , and Torner L. ,“Soliton trains in photonic lattices,”Opt. Express 12, 2831-2837 (2004).
[36] Yang J. K. and Musslimani Z. ,“Fundamental and vortex solitons in two-dimensional optical lattices,”Opt. Lett. 28, 2094-2096 (2003).
[37] Peleg O. , Bartal G. , Freedman B. , et al, M. Segev, and D. N. Christodoulides,“Conical Diffraction and Gap Solitons in Honeycomb Photonic Lattices,”Phys. Rev. Lett. 98, 103901 (2007).
[38] Tang L. , Lou C. , Wang X. , et al,“Observation of dipole-like gap solitons in self-defocusing waveguide lattices,”Opt. Lett. 32, 3011-3013 (2007).
[39] Wang X. , Bezryadina A. , and Chen Z. ,“Observation of Two-Dimensional Surface Solitons,”Phys. Rev. Lett. 98, 123903 (2007).
[40] Makasyuk I. , Chen Z. G. , and Yang J. K. ,“Band-gap guidance in optically induced photonic lattices with a negative defect,”Phys.Rev. Lett. 96, 223903 (2006).
[41] Szameit A. , Kartashov Y. V. , Herinrich M. , et al,“Observation of two-dimensional defect surface solitons,”Opt. Lett. 34, 797-799 (2009).
[42] Yang J. K. ,“Iteration methods for stability spectra of solitary waves,”J. Comp. Phys. 227, 6862-6876 (2008).
[43] Li Y. , Pang W. , Chen Y. , et al,“Defect-mediated discrete solitons in optically induced photorefractive lattices,”Phys. Rev. A 80, 043824 (2009).
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[45] Law. K. J. H, Suanto. H, and Keverkidis,“Solitons and vortices in honeycomb defcousing photonic lattices,”Phys. Rev. A 78, 033802 (2008).
[46] Efremidis N.K. , Hudock J. , Christodoulides D.N. ,et al ,“Two-Dimensional Optical Lattice Solitons,”Phys Rev. Let,2003,91(21):213906
[2]王志斌.光孤子在光纤中传输的特性研究[D].秦皇岛:燕山大学测试计量技术及仪器专业,2007
[3]杨懿.二阶光纤孤子传输特性研究[D].五邑:五邑大学信息与信号处理专业,2008
[4]王建东.空间光孤子[D].合肥:中国科学技术大学光学专业博士论文,2006.
[5]陈武喝.一维光学格子中带隙光孤子的研究[D].广州:中山大学光学专业博士论文, 2007.
[6]何影记.空间孤子传输的研究[D].广州:中山大学光学工程专业博士论文, 2007.
[7]石顺祥,陈国夫,赵卫,等.非线性光学[M].西安:西安电子科技大学出版社,2003,417-448.
[8]李均,黄德修,张新亮.光纤传输模型的数值计算研究[J].光电子技术与信息,2003,16(2):9-12
[9]王志斌,李志全,刘洋.高阶孤子在光纤中传输的数值研究[J].光子学报,2007,36(9):1641-1644.
[10]雷超.基于MATLAB的非线性薛定谔方程的数值算法研究.中国科技论文在线(http://www.paper.edu.cn). 2008年11月28日.
[11]施娟.基于对称分步傅立叶算法的光孤子仿真[J].电子元器件应用,2008,10(1):73-75.
[12]曹文华,刘颂豪.负三阶色散光纤中的孤子效应脉冲压缩[J].量子电子学报,1999,16(1):9-15.
[13]黄天水,曹文华,尹新付,等.高阶色散效应对光纤中高斯光脉冲的影响[J].半导体光电,2007,28(4):564-567.
[14]吕理想,张晓萍.不同形式非线性薛定谔方程及其傅里叶法求解[J].计算物理,2007,24(3):373-377.
[15]张晓光,杨伯君,俞重远.非线性薛定谔方程数值解法中傅立叶正逆变换选取的讨论[J]计算物理,2003,20(3):267—272.
[16]李志全,王志斌,刘洋.高阶色散对光孤子传输的影响[J].光学仪器,2008,30(2):66-69
[17]方云团,范俊.二阶孤子的传输和相互作用[J].应用光学,2008,29(2):317-320.
[18] S mith D. R. , Dalichaouch R, K roll N, et al,"Photonic band structure and defects in one and twodimensions,"J .Opt.Soc.A m.B ,1993,10:314-321.
[19] Fedele F, Yang J. K. , and Chen Z.G. ,“Properties of Defect Modes in One-Dimensional Optically Induced Photonic Lattices,”Stud.Appl.Math. 115:277-299.
[20] Alexander T. J. , Desyatnikov A. S. , and Kivshar Y. S. ,“Multivortex solitons in triangular photonic lattices”Opt. Lett. 32, 1293-1295 (2007).
[21] Wang J. D and Yang J. K. , Chen Z. G. ,“Two-dimensional defect modes in optically induced photonic lattices,”Phys. Rev. A 76 013828 (2007)
[22] Yang J. K. , and Chen Z. G. ,“Defect solitons in photonic lattices,”Phys. Rev. E 73 026609 (2006)
[23] Yang J. K. and Lakoba T. I. ,“Universally-Convergent Squared-Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations,”Stud. Appl. Math. 118, 153-197 (2007).
[24] Yang J. K. ,“Newton-conjugate gradient methods for solitary wave computations,”J. Comp. Phys. 228, 7007-7024 (2009).
[25] Fleischer J. W. , Segev M, Efremidis N. K, et al,“Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,”Nature 422, 147-150 (2003).
[26] Ablowitz M. J. , Ilan B, Schonbrun E. , et al,“Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,”Phys. Rev. E 74, 035601 (2006).
[27] Chen W. , He Y. , and Wang H. ,“Defect superlattice solitons,”Opt. Express 15, 14498–14503 (2007).
[28] Wang J. D. and Yang J. K. ,“Families of vortex solitons in periodic media,”Phys. Rev. A 77, 033834 (2008).
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