| Waveguides are structures that are typically designed to transmit energy along aspecified trajectory with minimal attenuation and signal distortion.Various avenues canbe pursued when attempting to improve on a waveguides' capabilities,includingmodifying the shap of structure,or constitutive effective material parameters of theguide.Elliptical waveguides have found wide applications in a variety of microwavecomponents:waveguide filters,radiators,resonators,and wide-band transmission lines,etc.Comparing other shapes,there are still a lot of questions remained in the ellipticalshape structure.It's nessesary to study the electromagnetics characteristcs with twoapproaches:combining different structures and filling with new materials.Finned and ridged waveguides offer the advantages of low cutoff frequency,widebandwidth,and low impedance.Circular and rectangular ridged waveguide have beenstudies extensively for many years.Elliptical ridged waveguide is still a new domainwhich needs to be explored.The problem of electromagnetic scattering by dielectric elliptical cylindersprovides a useful model to study electromagnetic scattering by the fuselage of aircraft.The scattering by lossy dielectric ellipitic cylinders involves caculating of complexMathieu functions which are ignored by many researchers.The modes in isotropic nonchiral media with elliptical shape are classifiedaccording to their even and odd symmetries with respect to the x axis and/ory axis.Thefield solutions are split into even and odd components in terms of even and odd Mathieufunctions respectively.In bianisotropic and bi-isotropic media,the longitudinalcomponents of electric and magnetic fields are coupled.And no even or odd modesexist individually in such elliptical cylinder.The detailed analysis of ellipticalwaveguide filled by chiroferrite material is presented in this dissertaion.The range of available electromagnetic material properties has been broadened byrecent developments in structured media,notably photonic band gap materials andmetamaterials.Wave propagation in waveguide of nanometer size has unique properties.The unique properties of the elliptical nano-waveguide made from extremelyanisotropic metamaterials have been revealed for in chapter 5 and 6. The structure of this dissertation is presented as follow:Chapter 1 is introduction.The background of research and the obstacles ofpresent research will be firstly explained.Then,the significance and the researchingscope of this dissertation will be presented.In chapter 2,the elliptical waveguide with double infinite thin ridges has beenformulated using mode-matching method.Exact closed-form expressions for eigenvlueproblem of all TE and TM modes are presented.With the Rayleigh-Ritz method andpolynomial representation,the wave propagation characteristics in the ridged ellipticalwaveguide are analyzed.The bandwidth with variation of physical dimensions has beenstudied.In chapter 3,the method for the computation of Mathieu functions with complexparameter q was presented.Electromagnetic scattering by a conducting circular cylindercoated by an elliptic lossy dielectric is derived rigorously by using the mode-matchingtechnique.The effects of dielectric loss and eccentricity on scattering cross section arepresented by numerical techniques.In chapter 4,the propagation characteristics of an elliptical chiroferrite waveguidehave been studied.We have presented correct boundary conditions for ideally conductorwall applicable with coupled wave equations,and obtained the complete solution ofcharacteristics equation.Some field patterns are presented here and have been used toillustrate the complex nature of the fields within the ellipitcal chiral waveguide.Thedispersion characteristics of the ellipitcal chiroferrite waveguide can be freely controlledby varying different medium and structure parameters.In chapter 5,Electromagnetic wave propagation propeties in elliptical cylindermade of metamaterial with permittivity and permeability tensors.The electromagneticwaves are classified according to the parameters of tensors.The formulas for all themodes on the elliptic anisotropic cylinders were derived and discussed.In chapter 6,we propose the realization of elliptical nano-waveguide made ofextremely anisotropic metamaterials,which is confirmed in CST MWS simulations.Theunique properties of this kind of structured material were highlighted.The chapter 7 is conclusion.
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