Analytical Solution Of EM Scattering From A Bianisotropic Sphere

The properties of electromagnetic scattering of a plane-wave are very important to theapplications of new antenna, space remode sensing, radar detection. In fact, scattering by complexspheres has attracted continued interests of engineering communities. Various numerical andanalytical methods have been reported to study this problem.The solution to a plane wave scattering by a sphere of bianisotropic media is obtained in termsof spherical vector wave functions. Analytical solution of the electromagnetic scattering from ananisotropic sphere is studied, constitutive relations that contains three tensors inside the sphere istaken into consideration then. Finally, numerical results for radar cross sections (RCSs) are given.The thesis work involves the following aspects:First, from the source-free Maxwell equations, and the constitutive relations of anisotropicmedium, the differential equation of the magnetic flux density vector BIinside the sphere ofanisotropic media can be derived. All terms in the equation related to BIare expanded in terms ofthe spherical vector wave functions (SVWFs) in isotropic media. To take advantage of SVWFs, amatrix can be yielded. The eigenvalues and eigenvectors of the matrix will be obtained. Applyingthe continue boundary conditions, the scattering matrix can be derived.Second, add a new tensor to the constitutive relations of anisotropic medium, make the electriccurrent displacement vector relate to electric field and magnetic field. As the same, the differentialequation of the magnetic flux density vector is derived from the Maxell equations and theconstitutive relations of complex medium. All terms in the equation related to BIare expanded interms of the SVWFs. To take advantage of SVWFs, a matrix equation that contains parameter canbe yielded. The parameter is obtained as the existence of nonzero solutions for the matrix equation.Then nonzero solutions for the matrix equation are obtained with the parameter solved. The incidentand scattered fields are expanded in terms of the SVWFs in isotropic medium. Applying thecontinue boundary conditions on the surface between isotropic medium and the sphere of complexmedia, the unknown expansion coefficients of fields in the sphere of complex media are obtainedand then solved for the solution to the scattering problem.