双光纤共球耦合场能量分布研究
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摘要
双光纤共球耦合结构适于在深入狭小的半封闭空间和易燃易爆环境下进行精密测量。基于双光纤共球耦合原理的内尺寸测量传感器,具有高分辨力,高精度的特点,可以精密测量用传统测量方法和技术难以进行的微深腔体及沟槽等结构。研究双光纤耦合过程中光能量场的分布规律,分析耦合效率的影响因素,将为双光纤耦合原理在提高内尺寸测量传感器的综合性能方面打下理论基础。
针对现有光线模型的不足,本文首先依据电磁问题的解析方法研究并分析单光纤在柱坐标系下和单球体在球坐标系下矢量波与标量波及其关系;研究矢量波加法并获得柱矢量波的坐标变换关系;通过柱标量波的球标量波分解式得到光纤内标量驻波在耦合球内的球矢量波展开式。研究Debye级数与Mie系数之间的关系,进而获得球行波的反射和透射系数及球体远场分布。结合双光纤共球耦合结构的尺寸特点及相关电磁分析方法,本文推导出双光纤共球耦合结构的近似数学模型。在近似模型中,耦合球结构的场分布通过将耦合球划分为不同区域并分别求得散射系数的方法求得。光纤模式系数则是通过球模场的正交性及定域积分等获得。分析并给出数学模型中散射系数的数值算法。由双光纤共球耦合结构对称特点,采用有限时域差分法分析双光纤共球耦合结构在传光平面上的场分布。
结合现有微球,微柱电磁散射的远场测量方案,与耦合球结构的空间特性,提出耦合球结构的远场光强分布测量方案。由测量方案中成像关系得到耦合球定位方法及远场光强分布测量的主要影响因素。最后通过实验,证明了双光纤共球耦合结构的近似数学模型的正确性。
Double optical fiber ball coupling structure can be worked in a semi-enclosed space or a flammable and explosive enviromnet. Comparing with traditional methods and techniques, the inner dimension measuring sensor based on the princple of double optical fiber ball coupling canbe uesed in the micro-cavity and the deep trench to complete a high-resolution, high-precision measuring. By analyzing the impact of coupling efficiency factor and energy distribution of double optical fiber ball coupling field, which lay the foudation for the next research on the improving of comprehensive performance of the inner dimension measuring sensor.
For the disadvantage of ray-tracing model, this paper firstly analyze the field in a single optical fiber and a single sphere, and get the relation between the vector wave and scarlar wave. In this paper, the theory of vecto addtion and the expansion of the cylinder wave is studied and applied in ball coupler. By researching on the Mie-Debye series, the reflection and transmission coefficients of spherical wave is computed. According the feature of the Double optical fiber ball coupling structure, the inner and outer field of ball coupler is given by dividing the ball coupler into different zones. With the outer and inner field of ball coupler, the far field can be directly acchieved. The optical fiber mode coeffecent can be obtained by the boundary condition (the surface of the ball coupler and the transerve surface of the optical fiber)and the Lorentz reciprocity .By the study of FDTD, this paper give a experiment for the whole structrure.With the result, the disadvantage of the FDTD is give and the model is approved basiclly.
According the existing far field measuring system of microspherr and micro cylinder and the feature of the ball coupler, we propose a new measuring system for the ball coupler. By a real structure experiment, the model is supported and testified.
针对现有光线模型的不足,本文首先依据电磁问题的解析方法研究并分析单光纤在柱坐标系下和单球体在球坐标系下矢量波与标量波及其关系;研究矢量波加法并获得柱矢量波的坐标变换关系;通过柱标量波的球标量波分解式得到光纤内标量驻波在耦合球内的球矢量波展开式。研究Debye级数与Mie系数之间的关系,进而获得球行波的反射和透射系数及球体远场分布。结合双光纤共球耦合结构的尺寸特点及相关电磁分析方法,本文推导出双光纤共球耦合结构的近似数学模型。在近似模型中,耦合球结构的场分布通过将耦合球划分为不同区域并分别求得散射系数的方法求得。光纤模式系数则是通过球模场的正交性及定域积分等获得。分析并给出数学模型中散射系数的数值算法。由双光纤共球耦合结构对称特点,采用有限时域差分法分析双光纤共球耦合结构在传光平面上的场分布。
结合现有微球,微柱电磁散射的远场测量方案,与耦合球结构的空间特性,提出耦合球结构的远场光强分布测量方案。由测量方案中成像关系得到耦合球定位方法及远场光强分布测量的主要影响因素。最后通过实验,证明了双光纤共球耦合结构的近似数学模型的正确性。
Double optical fiber ball coupling structure can be worked in a semi-enclosed space or a flammable and explosive enviromnet. Comparing with traditional methods and techniques, the inner dimension measuring sensor based on the princple of double optical fiber ball coupling canbe uesed in the micro-cavity and the deep trench to complete a high-resolution, high-precision measuring. By analyzing the impact of coupling efficiency factor and energy distribution of double optical fiber ball coupling field, which lay the foudation for the next research on the improving of comprehensive performance of the inner dimension measuring sensor.
For the disadvantage of ray-tracing model, this paper firstly analyze the field in a single optical fiber and a single sphere, and get the relation between the vector wave and scarlar wave. In this paper, the theory of vecto addtion and the expansion of the cylinder wave is studied and applied in ball coupler. By researching on the Mie-Debye series, the reflection and transmission coefficients of spherical wave is computed. According the feature of the Double optical fiber ball coupling structure, the inner and outer field of ball coupler is given by dividing the ball coupler into different zones. With the outer and inner field of ball coupler, the far field can be directly acchieved. The optical fiber mode coeffecent can be obtained by the boundary condition (the surface of the ball coupler and the transerve surface of the optical fiber)and the Lorentz reciprocity .By the study of FDTD, this paper give a experiment for the whole structrure.With the result, the disadvantage of the FDTD is give and the model is approved basiclly.
According the existing far field measuring system of microspherr and micro cylinder and the feature of the ball coupler, we propose a new measuring system for the ball coupler. By a real structure experiment, the model is supported and testified.
引文
1杨春曦,胡中功,戴克中.光纤传感器的应用及发展.武汉化工学院学报. 2004, 26 (2): 63–66
2奥诚喜,雷松鹤,徐云兵,王永仓,陈长乐.光纤真空压力传感器的实验研究.传感器技术. 2004, 23 (10):27-32
3吉贵军, S. H Trapet,罗霞.发动机喷油嘴微小喷油孔尺寸和形状测量系统.内燃机学报. 1998, 16 (4):475-479
4崔继文,谭久彬,刘洋.基于双光纤耦合的微深孔测量方法.红外与激光工程. 2009, 38(1):106-109
5 T. A.Eftimov, W. J. Bock. A Simple Multifunctional Fiber Optic Level/Moisture/Vapor Sensor Using Large-Core Quartz Polymer Fiber Pairs. IEEE Transactions On Instrumebtation And Measurement. 2006, 55(6):2080-2087
6 T. A. Eftimov, W. J. Bock. An All-Fibre Optic Multifunctional Sensor Based on Large-Core Quartz-Polymer Microlens-Ended Fiber Pairs. Instrumentation and Measurement Technology Conference, Ottawa, 2005:1182-1184
7滕爱萍,李英俊.反射式光纤探头结构的理论研究.烟台大学学报. 1995, 4:9-12
8耿立升.触点式光纤液位传感器的数学模拟及其污染研究,大连理工大学硕士学位论文. 2004:20-22
9张福根,荣跃龙,程路.用激光散射法测量大颗粒时使用衍射理论的误差.粉体技术. 1996, 2(1):7-14
10 M. J. Humphrey, E. Dale, A. T. Rosenberger, et al. Calculation of Optimal Fiber Radius And Whispering-gallery Mode Spectra For A Fiber-coupled Microsphere. Optics Communications. 2007, 271:124-131
11王志良.电磁散射理论.四川科学技术出版社, 1994: 56-111
12杨儒贵.高等电磁理论.高等教育出版社, 2008:36-104
13 R. K. Mongia, R. K. Arora. Equivalent of an Aperture Coupled Open Resonator Cavity. IEEE Transaction on Microwave Theory and Technology. 1993,41(8):1245-1250
14 L. W. Li, M. S. Leong, P. S. Kooi. Radiation of Aperture Antenna Covered by a Spherical-Shell Chiral Radome and Fed by a circular waveguide. IEEETranaction on Antenna and Propagation. 1998, 46(5):664-671
15 R. W. Ziolkowski, D. P. Marsland,L. F. Libelo, et al. Scattering from an Open Sphercial Shell Having a Circular Aperture and Enclosing a Concentric Dielectric Sphere. IEEE Transaction on Antenna and propagation. 1988, 36(7):985-991
16 T. D. Visser, S. H. Wiersma. Spherical Aberration and the Electromagnetic Field in High-Aperture Systems. Optical Society of America. 1991, 8(9):1404-1410
17 S. Blume, L. Klinkenbusch. Scattering of a Plane Eletromagnetic Wave by Spherical Shell with an Ellipitcal Aperutre. IEEE Transaction on Electromagnetic Compatibility. 1992, 34(3):308-312
18 E. Ubeda, J. M. Rius. Novel Monopolar MFIE MOM- discretization for the Scattering Analysis of Small object. IEEE Transaction on Antennas and Propagation. 2006, 54(1):50-57
19 P. Y. Oijala, M. Taskinen. Well Conditoned Muller Formulation for ElEctromagnetic Scattering by Dielectric Object. IEEE Transaction on Antennas and Propagation. 2005, 53(10): 3316-3323
20 S. Adams, J. Payne, R. Boppana. Finite Difference Time Domain Simulation Using Graphics. DoD High Performance Computing Modernization Program Users Group Conference, Pittsburgh, 2007:334-475
21 S. Oqurtsov, S. V. Geoqakopoulos. Fdtd Schemes with Minimal Numerical Dispersion. IEEE Transactions on Advanced Packaging. 2009, 32(1):199-204
22 A. K. Mills, W. J. Chappell. On the Use of Commercial Fem Electromagnetic Software in an Undergraduate Curriculum. IEEE Transaction on Antennas and Propagation. 2004, 3:3365-3368
23 V. W. Leung, G. W. Roberts. Effects of Transistor Nonidealities on High-Order Log-Domain Ladder Filter Frequency Responses. IEEE Transaction on Circuits and Systems. 2000, 47(5):373-378
24 W. P. Ding. Fem/Po-Ptd for Evaluatin of Scattering by Complex objects. Antennas and Propagation Society International Sympostium.2004.IEEE. 2004, 1:363-366
25 P. J.Debye. Das elektromagnetische Feld um einen Zylinder und die Theorie des Tegenbogens. Physik zeitung.1908,9:775
26吴鹏,韩一平,刘德芳.大粒子对高斯波束散射的数值模拟.物理学报.2005, 54(6):2676-2679
27鞠涛,杨小丽.作图法求解光学微球腔的本征模.光电子激光. 2006, 17(6):775-777
28韩一平.一种求解任意入射波束的波束因子的方法.物理学报. 2005, 54(11):5139-5140
29周学松,林康云.常用矢量波函数的坐标变换关系.电子科学学刊. 1989, 11(3):308-311
30 L.V. Lorenz. Upon the Light Reflected and Refracted by a Transparent Sphere,Vidensk, Selsk, Shritfer6, InDanish, 1890:1-60
31 G. Mie. Beitrage zur Optik turber Medien speziell kolloidaler Metallosungen,Ann.Phys. 1908, 25:377-455
32 O. B. Toon, T. Packerman,Algorithms for the Calculation of Scattering by Stratifield Sphere. Apply of Optics. 1981, 20:3657-3660
33 C. F. Bohren, D. R. Htlffillan. Absorption and Scattering of Light by Small Particle. Wiley一Interscience.1983:120-134
34 Z. S. Wang, X. P. Wang Electromagnetic Scattering for a Multilayered sphere Recursive Algorithms. Radio Science. 1991,26(6):1393一1401.
35施丽娟.非均匀球粒子对高斯波束散射的Debye技术展开.西安电子科技大学硕士论文. 2006:30-43
36沈明浩.球面镜的散射理论.物理学报. 1978, 27(5):534-540
37 N. K. Uzunoglu. Scattering from Inhomogeneities Inside a Fiber Waveguide. Optical Society of America. 1981, 71(3):259-270
38 N. Morita, N. Kumagai. Scattering and Mode Conversion of Guided Modes by a Spherical Object in an Optial Fiber. IEEE Transaction on Microwave Theory and Technology. 1980, 28(2):137-139
39王志良,胡力.介质波导中非均匀性散射的T矩阵方法.电子科技大学学报. 1993, 22(6):584-589
40付裕.环绕定点的全景图生成技术研究.沈阳工业大学硕士学位论文. 2007:35-45
41姜丽凤.全景图拼接关键技术研究.山东理工大学硕士学位论文. 2008:42-50
2奥诚喜,雷松鹤,徐云兵,王永仓,陈长乐.光纤真空压力传感器的实验研究.传感器技术. 2004, 23 (10):27-32
3吉贵军, S. H Trapet,罗霞.发动机喷油嘴微小喷油孔尺寸和形状测量系统.内燃机学报. 1998, 16 (4):475-479
4崔继文,谭久彬,刘洋.基于双光纤耦合的微深孔测量方法.红外与激光工程. 2009, 38(1):106-109
5 T. A.Eftimov, W. J. Bock. A Simple Multifunctional Fiber Optic Level/Moisture/Vapor Sensor Using Large-Core Quartz Polymer Fiber Pairs. IEEE Transactions On Instrumebtation And Measurement. 2006, 55(6):2080-2087
6 T. A. Eftimov, W. J. Bock. An All-Fibre Optic Multifunctional Sensor Based on Large-Core Quartz-Polymer Microlens-Ended Fiber Pairs. Instrumentation and Measurement Technology Conference, Ottawa, 2005:1182-1184
7滕爱萍,李英俊.反射式光纤探头结构的理论研究.烟台大学学报. 1995, 4:9-12
8耿立升.触点式光纤液位传感器的数学模拟及其污染研究,大连理工大学硕士学位论文. 2004:20-22
9张福根,荣跃龙,程路.用激光散射法测量大颗粒时使用衍射理论的误差.粉体技术. 1996, 2(1):7-14
10 M. J. Humphrey, E. Dale, A. T. Rosenberger, et al. Calculation of Optimal Fiber Radius And Whispering-gallery Mode Spectra For A Fiber-coupled Microsphere. Optics Communications. 2007, 271:124-131
11王志良.电磁散射理论.四川科学技术出版社, 1994: 56-111
12杨儒贵.高等电磁理论.高等教育出版社, 2008:36-104
13 R. K. Mongia, R. K. Arora. Equivalent of an Aperture Coupled Open Resonator Cavity. IEEE Transaction on Microwave Theory and Technology. 1993,41(8):1245-1250
14 L. W. Li, M. S. Leong, P. S. Kooi. Radiation of Aperture Antenna Covered by a Spherical-Shell Chiral Radome and Fed by a circular waveguide. IEEETranaction on Antenna and Propagation. 1998, 46(5):664-671
15 R. W. Ziolkowski, D. P. Marsland,L. F. Libelo, et al. Scattering from an Open Sphercial Shell Having a Circular Aperture and Enclosing a Concentric Dielectric Sphere. IEEE Transaction on Antenna and propagation. 1988, 36(7):985-991
16 T. D. Visser, S. H. Wiersma. Spherical Aberration and the Electromagnetic Field in High-Aperture Systems. Optical Society of America. 1991, 8(9):1404-1410
17 S. Blume, L. Klinkenbusch. Scattering of a Plane Eletromagnetic Wave by Spherical Shell with an Ellipitcal Aperutre. IEEE Transaction on Electromagnetic Compatibility. 1992, 34(3):308-312
18 E. Ubeda, J. M. Rius. Novel Monopolar MFIE MOM- discretization for the Scattering Analysis of Small object. IEEE Transaction on Antennas and Propagation. 2006, 54(1):50-57
19 P. Y. Oijala, M. Taskinen. Well Conditoned Muller Formulation for ElEctromagnetic Scattering by Dielectric Object. IEEE Transaction on Antennas and Propagation. 2005, 53(10): 3316-3323
20 S. Adams, J. Payne, R. Boppana. Finite Difference Time Domain Simulation Using Graphics. DoD High Performance Computing Modernization Program Users Group Conference, Pittsburgh, 2007:334-475
21 S. Oqurtsov, S. V. Geoqakopoulos. Fdtd Schemes with Minimal Numerical Dispersion. IEEE Transactions on Advanced Packaging. 2009, 32(1):199-204
22 A. K. Mills, W. J. Chappell. On the Use of Commercial Fem Electromagnetic Software in an Undergraduate Curriculum. IEEE Transaction on Antennas and Propagation. 2004, 3:3365-3368
23 V. W. Leung, G. W. Roberts. Effects of Transistor Nonidealities on High-Order Log-Domain Ladder Filter Frequency Responses. IEEE Transaction on Circuits and Systems. 2000, 47(5):373-378
24 W. P. Ding. Fem/Po-Ptd for Evaluatin of Scattering by Complex objects. Antennas and Propagation Society International Sympostium.2004.IEEE. 2004, 1:363-366
25 P. J.Debye. Das elektromagnetische Feld um einen Zylinder und die Theorie des Tegenbogens. Physik zeitung.1908,9:775
26吴鹏,韩一平,刘德芳.大粒子对高斯波束散射的数值模拟.物理学报.2005, 54(6):2676-2679
27鞠涛,杨小丽.作图法求解光学微球腔的本征模.光电子激光. 2006, 17(6):775-777
28韩一平.一种求解任意入射波束的波束因子的方法.物理学报. 2005, 54(11):5139-5140
29周学松,林康云.常用矢量波函数的坐标变换关系.电子科学学刊. 1989, 11(3):308-311
30 L.V. Lorenz. Upon the Light Reflected and Refracted by a Transparent Sphere,Vidensk, Selsk, Shritfer6, InDanish, 1890:1-60
31 G. Mie. Beitrage zur Optik turber Medien speziell kolloidaler Metallosungen,Ann.Phys. 1908, 25:377-455
32 O. B. Toon, T. Packerman,Algorithms for the Calculation of Scattering by Stratifield Sphere. Apply of Optics. 1981, 20:3657-3660
33 C. F. Bohren, D. R. Htlffillan. Absorption and Scattering of Light by Small Particle. Wiley一Interscience.1983:120-134
34 Z. S. Wang, X. P. Wang Electromagnetic Scattering for a Multilayered sphere Recursive Algorithms. Radio Science. 1991,26(6):1393一1401.
35施丽娟.非均匀球粒子对高斯波束散射的Debye技术展开.西安电子科技大学硕士论文. 2006:30-43
36沈明浩.球面镜的散射理论.物理学报. 1978, 27(5):534-540
37 N. K. Uzunoglu. Scattering from Inhomogeneities Inside a Fiber Waveguide. Optical Society of America. 1981, 71(3):259-270
38 N. Morita, N. Kumagai. Scattering and Mode Conversion of Guided Modes by a Spherical Object in an Optial Fiber. IEEE Transaction on Microwave Theory and Technology. 1980, 28(2):137-139
39王志良,胡力.介质波导中非均匀性散射的T矩阵方法.电子科技大学学报. 1993, 22(6):584-589
40付裕.环绕定点的全景图生成技术研究.沈阳工业大学硕士学位论文. 2007:35-45
41姜丽凤.全景图拼接关键技术研究.山东理工大学硕士学位论文. 2008:42-50