Numerical-analytical methods for the analysis of forward and inverse scattering by dielectric bodies in waveguides

We present statement and a review of the proofs of uniqueness and solution techniques for forward and inverse problems of the electromagnetic wave scattering from a dielectric inclusion in a 3D waveguide. The inverse problem consists in reconstructing the permittivity from the transmission characteristics. The approach employs a volume singular integral equation (VSIE). The unique solvability of VSIE is established. The inverse problem is solved by the method of iterations applied to VSIE; the convergence of the method is proved. Particularly, the determination of permittivity of an inhomogeneous dielectric body in a rectangular waveguide is considered; a method of iterations for the numerical solution is proposed; and convergence of the method is proved. Numerical results for the determination of permittivity of parallelepiped-shaped dielectric bodies are presented.