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.