Radiation of open-ended waveguides through a multi-layer superstrate - Tan, Weihua (2009)
In this thesis, the radiation of open-ended waveguides radiating into a half free space through a layered superstrate is analyzed. Firstly, surface waves propagating in a multilayer medium backed by a conductive ground plane are studied. The fields' expressions for $TM$ and $TE$ modes are formulated in a recursive form, respectively. Transcendental equations are built up to find the propagation constant $k_y$ so that the fields in all layers can be obtained. Numerical results are provided to illustrate the surface wave propagating in one-layer and two-layer media, respectively. Parametric studies are carried out to show the relationship between the layered dielectric medium's parameters and the surface wave's propagation constant. Radiation from infinitely flanged open-ended waveguides is then studied to verify the efficiency of a numerical method. Firstly, the formulation for a general open-ended waveguide is provided to obtain the reflection coefficient matrix at the opening. The field equation containing double surface integrations on the aperture is obtained. These surface integrals are then converted to one integral in the spectral domain through the Sommerfeld identity. Secondly, an efficient method for calculating the reflection coefficient matrix of open-ended coaxial lines is proposed. The generalized pencil of functions method (GPOF) is employed to fit the Sommerfeld integrands with exponential series so that the integrals can be analytically solved in closed form. Thirdly, the accelerating technique is applied to calculate the reflection coefficient matrix of open-ended rectangular waveguides. In addition to the GPOF method, Gaussian quadrature is also employed to accelerate the computation. Numerical results for the reflection coefficient of an open-ended WR-90 waveguide are provided. It is shown that the proposed method is very efficient in calculating the reflection coefficient matrix of open-ended waveguides.