【作者】 王海龙；

【导师】 吴群； 李乐伟；

【作者基本信息】 哈尔滨工业大学 ， 微电子学与固体电子学， 2008， 博士

【摘要】 多年以来,在现代电子学、计算电磁学以及计算物理学等学科中求解电磁场问题时利用积分方程方法将不可避免的存在以Sommerfeld积分形式出现的并矢格林函数,而Sommerfeld积分的求解一直是一个繁杂而困难的问题。由于直角坐标系和圆柱坐标系本身的限制,解的表达式中都存在积分的形式,无法得到精确的解。而在球坐标系下的Sommerfeld积分形式变成了双重求和的形式,因此可以讨论类似的球模型下的问题,首先对在球坐标系下出现的双重求和形式的表达式进行处理,得到适合计算的表达式,然后应用到直角坐标系中,这是解决问题的一个途径。另外,近年来,异向介质由于其异常的电磁波特性在固体物理学、材料科学、光学和应用电磁学领域内获得愈来愈多的青睐。但不可否认的是,异向介质研究作为一门新兴的前沿科学在很多方面还不完善,还有很多的基本理论问题亟待解决。其中,分层异向介质圆柱以及球模型的电磁波特性的研究是异向介质研究当中的一个重要分支。基于这一原因,作者遵循“研究球坐标系下球模型的加速算法,与已有的算法进行比较;探索分层异向介质圆柱以及球模型的电磁波特性”的研究思路撰写了本篇论文,进而实现综合发展球模型下加速算法以及研究分层异向介质球柱电磁波特性的目的。首先,本文从新的角度推导出了一种高效的计算Mie级数的新Sommerfeld-Watson变换方法,这种新Sommerfeld-Watson变换方法的物理意义更加明确,比传统的Mie级数直接求和方法需要的求和项数目更少,而本文给出的新Sommerfeld-Watson变换方法的推导过程更为简单直接。其次,本文讨论了垂直电偶极子激励导体球的电磁散射模型,在利用并矢格林函数求解的基础上给出了这个模型电场的闭合表达式解;将这个解与经典的并矢格林函数方法的直接级数解进行比较,验证了这个闭合表达式解的正确性。这种方法解决了直接级数求和表达式在k 0a较大时收敛慢的问题以及不符合物理现象的不连续性问题;最后将这种方法与Airy函数的方法进行了比较,发现当垂直电偶极子以及场点在球体表面附近并且频率较低时,两种计算方法得到的结果非常一致;而当垂直电偶极子以及场点远离球表面并且频率较高时,本章中的闭合表达式方法计算的电场逐渐出现了Airy函数的计算方法的相应结果所未出现的干涉现象,这是由于此时Airy函数的计算方法中应用到的一些近似恒等式在这种情况下不再精确造成的。第三,本文利用球坐标系下的并矢格林函数研究了水平电偶极子激励单层异向介质球的近场特性。与单层普通介质球的近场特性进行了比较。在不同的电磁参数和几何参数情况下详细的讨论了异向介质球中出现的聚焦现象。最后,本文研究了线电流源激励下异向介质覆盖理想金属和介质圆柱的近场和远场电磁波特性。详细的讨论了异向介质覆盖圆柱的聚焦特性的机理以及总结了相应的规律,从光学的角度进行了对比验证;从方向性系数以及归一化辐射阻抗的角度讨论了异向介质层覆盖圆柱的远场电磁辐射特性并总结了相应的规律。同时,将结果与普通介质层覆盖理想金属和介质圆柱模型的近场和远场的电磁波特性进行比较,总结得出分层异向介质圆柱模型特有的规律。本文发展了球坐标系下球模型加速算法,在与已有方法比较的基础上总结了相应的规律;较为深刻讨论了单层异向介质球以及分层异向介质圆柱在外源激励下的近场以及远场电磁波特性,在与相应的普通介质模型比较的基础上总结出了特有的规律。本文的研究成果在丰富计算电磁学的内容的同时,也更为深刻的向人们展示了异向介质的异常电磁波特性。不但在一些特定的方面有利于改善现有电磁仿真软件在计算相应的球模型时的计算效率以及计算精度,降低对计算机硬件的需求,而且丰富了人们对异向介质的异常电磁波特性的认知,加快了异向介质从理论向实用阶段前进的步伐,拓宽了异向介质的应用领域,对相关研究的发展具有较为重要的指导意义和实用价值。更多还原

【Abstract】 For many years, the dyadic Green’s function, which is expressed as the Sommerfeld integral, unavoidable exists in the modern electronics, computational electromagnetic and computational physics when the electromagnetic field is solved by the approach of integral equation. While solving the Sommerfeld integral is always a complex and difficult problem. As the limit of the rectangular coordinate and cylindrical coordinate, the integrals exist in the expressions of the solution, so the exact solutions of the Sommerfeld integrals could not be obtained. While in the spherical coordinate, the Sommerfeld integrals are changed to twofold summation. So the similar problems in the spherical model could be discussed, the expression which is expressed in twofold summation in the spherical coordinate could be solved firstly, then the expression which is adapt to compute could be applied into the rectangular coordinate. It is an approach of solving the problems. Furthermore, in the recent years, metamaterial has gets more and more attentions because of its abnormal electromagnetic characterisations of waves in the fields of solid-state physics, material science, optics and applied electromagnetics. However, the detail research on the metamaterial is just at its beginning stage, and it is still incomplete in many research aspects such as many fundamental researches. The research on the electromagnetic characteristics of the layered metamaterial cylinder and sphere model is an important branch of the metamaterial. In this paper, the author investigates on the acceleration algorithms of the sphere model in the spherical coordinate and compared with the former algorithms; the electromagnetic characterisations of waves in the layered metamaterial cylinder and sphere model are also explored.Firstly, from a new point of view, the new Sommerfeld-Watson transformation method, which is utilized to compute the Mie series efficiently, is deduced. The newly derived Sommerfeld-Watson transformation method has much more clear physical meaning and needs fewer summation items than the traditional Mie series. This approach makes the new Sommerfeld-Watson transformation possible for directness and simplification. Secondly, the vertical electric dipole radiating in the presence of the conductor sphere is discussed. The closed solution of the model is given based on the Green’s function method. After comparing with the direct series solution of the classical Green’s function, the correctness of the closed solution is proven. The problems of the slow convergence property with relative big k 0a and discontinuity which is not consistent with the physical phenomenon are solved in the closed solution. In the end, the closed solution is compared with the Airy function method. It is obtained that when the location of the vertical electric dipole and the observation point are near the surface and the frequency is low, the results of the two methods are consistent; While on the other hand, the interference phenomenon, which does not exist in the result of the Airy function method, appear in the result of the closed solution.Thirdly, the near field property of the horizontal electric dipole radiating in the presence of the single metamaterial sphere is investigated based on the Green’s function in the spherical coordinate and compared with the near field property of the single conventional material sphere. The focus phenomenon which exists in the metamaterial sphere is discussed under different electromagnetic and geometrical parameters.Finally, the near field and far field properties of the electric line source illuminating of an infinite long metamaterial covered conductor or material cylinder are investigated. The principle of the focus characteristic is discussed and its law is concluded and proven in the views of the optics. The far field properties of the models are discussed and concluded based on the directivities and the normalized radiation resistance. The results are always compared with the near field and far field properties of an infinite long conventional material covered conductor or material cylinder. Some special laws of the layered metamaterial cylinder model are concluded.In this paper, the acceleration algorithm of the sphere model in the spherical coordinate is developed and the relative law is concluded base on the comparison with the former methods. The near field and far field properties of the single metamaterial sphere and layered metamaterial cylinder which are excited by the external source are concluded. The special laws are also obtained based on the comparison with the relative conventional material model. This research results not only increases the contents of the computational electromagnetics, but also shows the abnormal electromagnetic characterisations of waves of the metamaterial widely. The new methods increase the efficiency of computing the sphere model and decrease the hardware requirements. The laws enrich the content of the abnormal electromagnetic characterisations of waves of the metamaterial, accelerate the application of the metamaterial and enlarge the application scope of the metamaterial. The important research results are very useful for the development of computational electromagnetics and metamaterial applications.更多还原