Analysis of direct and inverse problems related to circular waveguides loaded with inhomogeneous lossy dielectric objects

An integral-equation-based analysis for direct and inverse problems related to circular waveguides loaded with inhomogeneous and arbitrarily shaped lossy dielectric material is introduced. The problem is formulated as a system of integral equations composed of the well-known data and object equations, which contain the dyadic Green's function (DGF) of the empty circular waveguide. Both the direct and inverse algorithms are based on this 3-D system of equations. In the direct problem, the scattering parameters are calculated using the scattered electric fields caused by the inhomogeneous lossy dielectric objects located in circular waveguide, while in the inverse algorithm, the scattered fields are assumed to be known and used for the determination of the complex permittivity variation of the object loaded in the waveguide through a Newton-type iterative approach. In both algorithms, the integral equations are solved via a method-of-moments-based discretization, where the accurate integration of the DGF at each discrete 3-D cell is achieved by a special integration technique. The validity region and the reliability of the direct and inverse algorithms are examined analytically and numerically through elaborative examples.