Investigation On The Propagation Characteristics Of The Cylindrical Waveguide Filled With Multilayered Media

The investigations on the propagation characteristics of waveguides are an important major in electromagnetic theory. Though many investigations have taken to the regular cylinderical metal waveguides or coaxial lines, these investigations mainly focused on the waveguides or coaxial lines filled with single layer medium or two layers of media. No investigations are related to the regular cylinderical metal waveguides or coaxil lines filled with multilayered media. These propagation characteristics will be given in this thesis.We know that their constitutive relations of the materials represent the respondences of the materials to the electromagnetic wave. The constitutive relations of the media describe the relationships between electric and magnetic fields. Since there are many types of constitutive relations of chiral media in the scientific literatures, some mistakes are easily made when we use them.Firstly, in this thesis, we will summarize the types of the chiral constitutive relations and introduce four elementary types of constitutive relations for the reciprocal and non-reciprocal chiral medium. The forms will be changed as different time conventions are used in the electromagnetic theory. In addition, some other constitutive relations for chiral medium are given.Secondly, the methods to solve the homogeneous scalar Helmholtz equation in the elliptical-cylindrical coordinate system and the angular and the radial Mathieu functions are introduced. Mathieu functions are the solutions of the angular and radial Mathieu equations. These functions are used in many physical and astronomical problems, and were inroduced by French mathematician Emile Leonard Mathieu in 1868, as the result of investigating the vibrating modes in an elliptic membrane. These functions are also used to solve the problems of the electromagnetic waves scattered by an elliptical cylinder and of electromagnetic wave propagation in the elliptical waveguide or elliptical coaxial line. Actually, Mathieu equations are two transversal equations derived from the homogeneous scalar Helmholtz equation by using the method of separation of variables in the elliptical-cylindrical coordinate system. These two equations are called angular Mathieu and radial Mathieu equations, respectively, and their solutions are called angular Mathieu and radial Mathieu functions. They can be divided into integral...