In this study, transverse magnetic electromagnetic plane wave scatterings by rectangular cylinders have been analyzed by a high frequency asymptotic method. Scattering field can be generated by the equivalent electric and magnetic currents which are obtained approximately from the geometrical optics (GO) fields. Our formulation is found to be exactly the same with the physical optics (PO) for the conducting cylinders, and it can also be applicable for dielectric cylinders. Numerical calculations are made to compare the results with those by other methods, such as the geometrical theory of diffraction (GTD) and HFSS simulation. A good agreement has been observed to confirm the validity of our method.

An algorithm is formulated for reconstructing a dielectric cylinder with the use of the T-matrix and the singular value decomposition (SVD) and is discussed through numerical examples under noisy conditions. The algorithm consists of two stages. At the first stage the measured data of scattered waves is transformed into the T-matrix. At the second stage we reconstruct the cylinder from the T-matrix. The singular value decomposition is applied in order to separate the radiating and the nonradiating currents, and the radiating current is directly obtained from the T-matrix. The nonradiating current and the object are reconstructed by decreasing a residual error of the current in the least square approximation, where linear equations are solved repeatedly. Some techniques are used in order to reduce the calculation time and to reduce the effects of noise. Numerical examples show us that the presented approach is simple and numerically feasible, and enables us to reconstruct a large object in a short time.

Frequency-domain and time-domain novel uniform asymptotic solutions for the scattered fields by an impedance cylinder and a dielectric cylinder, with a radius of curvature sufficiently larger than the wavelength, are presented in this paper. The frequency-domain novel extended UTD and the modified UTD solutions, derived by retaining the higher-order terms in the integrals for the scattered fields, may be applied in the deep shadow region in which the conventional UTD solutions produce the substantial errors. The novel time-domain uniform asymptotic solutions are derived by applying the saddle point technique in evaluating the inverse Fourier transform. We have confirmed the accuracy and validity of the uniform asymptotic solutions both in the frequency-domain and in the time-domain by comparing those solutions with the reference solutions calculated from the eigenfunction expansion (frequency-domain) and from the hybrid eigenfunction expansion and fast Fourier transform (FFT) method (time-domain).

Novel high-frequency asymptotic solutions for the scattered fields by a dielectric circular cylinder with a radius of curvature sufficiently larger than the wavelength are presented in this paper. We shall derive the modified UTD (uniform Geometrical Theory of Diffraction) solution, which is applicable in the transition regions near the geometrical boundaries produced by the incident ray on the dielectric cylinder from the tangential direction. Also derived are the uniform geometrical ray solutions applicable near the geometrical boundaries and near the caustics produced by the ray family reflected on the internal concave boundary of the dielectric cylinder. The validity and the utility of the uniform solutions are confirmed by comparing with the exact solution obtained from the eigenfuction expansion.

The applicability of a boundary matching technique is presented for reconstructing the refractive-index profile of a circularly symmetric cylinder from the measurement of the scattered wave when the cylinder is illuminated by an H-polarized plane wave. The algorithm of reconstruction is based on an iterative procedure of matching the scattered wave calculated from a certain refractive-index distribution with the measured scattered-wave. The limits of reconstruction for strongly inhomogeneous lossless and lossy cylinders are numerically shown through computer simulations under noisy environment, and are compared with those in the E-wave case.