Elliptical Dielectric Waveguides
The guiding properties of a circular dielectric waveguide have been considered in detail in the preceding chapter. It is of interest, however, to understand how the propagation characteristics of the guided wave are affected when the circular cylinder is deformed and when the circular symmetry no longer exists. No analytic solution exists for the problem of wave propagation along a dielectric waveguide of arbitrary cross-sectional shape. Nevertheless, a deformed circular cylinder can, in general, be approximated by an elliptical cylinder. Depending upon the eccentricity of the elliptical cylinder, it can take the form of a circular cylinder or the form of a flat ribbon. The exact solution, although very involved, does exist for the elliptical dielectric waveguide problem. One notes that this solution is the only available exact solution for a noncircular dielectric waveguide of finite cross-section. Detailed theoretical as well as experimental results for the dominant modes and analytical results for higher order modes on an elliptical dielectric waveguides were given by Yeh , who provided the most thorough (analytical and theoretical) treatment for the propagation of the dominant modes on an elliptical dielectric waveguide. Lynbimov et al.  and Piefke  also derived the characteristic equations for various modes on an elliptical dielectric waveguide.
We shall first provide the fundamental theory of wave propagation along an elliptical dielectric rod. The distinct differences between the analytic solutions for a circular dielectric waveguide and for an elliptical dielectric waveguide are discussed in detail. The method developed by Yeh  to assure that the solutions of the wave equation will satisfy all the boundary conditions on the surface of the elliptical dielectric rod will be followed. The dispersion equations for all guided modes are obtained. These equations can be used to obtain the propagation characteristics of these modes. It is shown analytically that there exist two nondegenerate modes that possess no cutoff-frequency. They are called the dominant modes. We consider in detail the propagation characteristics of these modes. It is shown that all the principal modes on an elliptical dielectric rod degenerate smoothly to the well known modes on the circular dielectric guide, as the eccentricity of the elliptical rod approaches zero. In addition to providing the numerical results for the propagation characteristics of the two dominant modes, their field configurations, attenuation properties, as well as power distributions will be analyzed . Selected results for higher order modes are also given.
KeywordsHigh Order Mode Relative Dielectric Constant Dielectric Waveguide Elliptical Cylinder Dielectric Cylinder
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