摘要
The electromagnetic scattering, leaking and coupling from a cylinder with an infinite axial slit have been investigated by many authors. However, they have not obtained strict closed form solutions. Almost all of the papers only reported the method for the simplest problems. For slight complicated problems, such as the scattering, leaking or coupling from a cylinder with infinite axial slits or with arbitrary width of axial slits, the former authors have only discussed formally or even not discussed because their methods were inconvenient. In addition, the problems of the EM scattering, leaking or coupling from an elliptic cylinder with infinite axial slits, which can be used wildly in practice based on its easily variable shape, have not be solved. It is imaginable that to solve these problems is more difficult, because many authors were unfamiliar with Mathieu Functions. Meanwhile we have not had a completed Mathieu Function system as the study for Mathieu Function have been processing aiming to establish a completed system just like Bessel Function system. However, if people make use of some method and technique as well as the knowledge of Bessel Functions, the problem can be studied. In this theory, the author has studied strictly the electromagnetic problems (scattering, leaking and coupling) of an elliptic cylinder as well as a cylinder with infinite axial slits, and obtained strict closed form solutions. The train of thought is: (1) elliptic Cylinder by using separation of variables in elliptic coordinates to find the field expressions in each domain, matching them on boundary to obtain a dual series equation system, then letting the convenient auxiliary functions to change the dual series equation system to integral equations, making use of WKBJ Method to draw the singular kernel from the integral equations, we finally obtain a singular integral equations to be able to be solved by the theory of singular integral equation. (2) cylinder by using separation of variables method in cylinder coordinates to find the field expressions in each domain and matching them on the boundary, we can obtain a dual series equations system, then letting auxiliary functions to change the dual series equations to integral equations. The singular integral equation can be obtained utilizing asymptotic representation of Bessel or Hankle Function. Then the strict closed form solutions can be obtained.
The electromagnetic scattering, leaking and coupling from a cylinder with an infinite axial slit have been investigated by many authors. However, they have not obtained strict closed form solutions. Almost all of the papers only reported the method for the simplest problems. For slight complicated problems, such as the scattering, leaking or coupling from a cylinder with infinite axial slits or with arbitrary width of axial slits, the former authors have only discussed formally or even not discussed because their methods were inconvenient. In addition, the problems of the EM scattering, leaking or coupling from an elliptic cylinder with infinite axial slits, which can be used wildly in practice based on its easily variable shape, have not be solved. It is imaginable that to solve these problems is more difficult, because many authors were unfamiliar with Mathieu Functions. Meanwhile we have not had a completed Mathieu Function system as the study for Mathieu Function have been processing aiming to establish a completed system just like Bessel Function system. However, if people make use of some method and technique as well as the knowledge of Bessel Functions, the problem can be studied. In this theory, the author has studied strictly the electromagnetic problems (scattering, leaking and coupling) of an elliptic cylinder as well as a cylinder with infinite axial slits, and obtained strict closed form solutions. The train of thought is: (1) elliptic Cylinder by using separation of variables in elliptic coordinates to find the field expressions in each domain, matching them on boundary to obtain a dual series equation system, then letting the convenient auxiliary functions to change the dual series equation system to integral equations, making use of WKBJ Method to draw the singular kernel from the integral equations, we finally obtain a singular integral equations to be able to be solved by the theory of singular integral equation. (2) cylinder by using separation of variables method in cylinder coordinates to find the field expressions in each domain and matching them on the boundary, we can obtain a dual series equations system, then letting auxiliary functions to change the dual series equations to integral equations. The singular integral equation can be obtained utilizing asymptotic representation of Bessel or Hankle Function. Then the strict closed form solutions can be obtained.
