In this paper, the scattering far-field from a circular electric conducting cylinder has been analyzed by physical optics (PO) approximation for both H and E polarizations. The evaluation of radiation integrations due to the PO current is conducted numerically and analytically. While non-uniform and uniform asymptotic solutions have been derived by the saddle point method, a separate approximation has been made for forward scattering direction. Comparisons among our approximation, direct numerical integration and exact solution results yield a good agreement for electrically large cylinders.

Asymptotic expansions of the amplitudes of the direct and scattered waves in a waveguide system with an imperfection core are derived for large core number and the partial cancellation of the direct wave by the scattered wave is shown in detail. The total power of light in the cross section of a waveguide system is analytically derived and it is shown that the total power of the sum of the direct and scattered waves decreases from that of the direct wave because of the cancellation, the difference of the total power transfers to the localized wave and the total power of light is conserved.

An asymptotic expansion of the amplitude of the scattered wave by an imperfection core in a waveguide system is derived and it is shown that the scattered wave is partially canceled by the direct wave at large distance and a shadow takes place. For z→ ∞ where z is the distance along the waveguide axis the amplitudes of the direct and scattered waves decrease in proportion to z- and in the shadow region the amplitude of the sum of both waves decreases in proportion to z-. To supplement the analytical results some numerical examples are shown.

This paper describes a method for the fast evaluation of the Sommerfeld integrals for modeling a vertical dipole antenna array in a borehole. When we analyze the antenna inside a medium modeled by multiple cylindrical layers with the Method of Moment (MoM), we need a Green's function including the scattered field from the cylindrical boundaries. We focus on the calculation of Green's functions under the condition that both the detector and the source are situated in the innermost layer, since the Green's functions are used to form the impedance matrix of the antenna. Considering bounds on the location of singularities on a complex wave number plane, a fast convergent integration path where pole tracking is unnecessary is considered for numerical integration. Furthermore, as an approximation of the Sommerfeld integral, we describe an asymptotic expansion of the integrals along the branch cuts. The pole contribution of TM01 and HE11 modes are considered in the asymptotic expansion. To obtain numerical results, we use a fast convergent integration path that always proves to be accurate and efficient. The asymptotic expansion works well under specific conditions. The Sommerfeld integral values calculated with the fast evaluation method is used to model the array antenna in a borehole with the MoM. We compare the MoM data with experimental data, and we show the validity of the fast evaluation method.

Hankel's asymptotic expansions are frequently used for numerical calculation of cylindrical functions of complex order. We beforehand need to estimate the precisions of the cylindrical functions calculated with Hankel's asymptotic expansions in order to use these expansions. This letter presents comparatively simple expressions for rough estimations of the errors of the cylindrical functions calculated with the asymptotic expansions, and features of the errors are discussed.