Electromagnetic Characterisations Of Waves In Layered Cylinders And Spheres

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.