Back scattering at high frequencies from a conducting cylinder with dielectric sleeve

The computational difficulties connected with the problem of high-frequency back scattering from a conducting cylinder with dielectric sleeve arise from the slow convergence of the conventional Fourier representation of the field and are compounded by the involved nature of its Fourier coefficients. In addition, the numerical results give no physical insight into the complicated structure of the back-scattering functions. An alternative representation of the diffracted amplitude as a series of radial eigenfunctions has the advantage of rapid convergence at high frequencies but presents difficulties of its own since one must find not only the complex coefficients of the expansion but also the complex indices for which the coefficients are to be evaluated. Some of these difficulties can be avoided by transforming the radial representation into a sum of terms, one of which is a well-known form of the diffracted amplitude from a conducting cylinder whose radius is the same as the outer radius of the dielectric sleeve. The second term, which contains the effect of the sleeve, turns out conveniently to be an infinite integral over a real variable. An expansion of its integrand leads to a series of terms which are analogous to optical rays. When the over-all cylinder radius is large, each of these terms has a stationary phase approximant over a certain range of dielectric thickness and relative dielectric constant. Only over this range does the corresponding ray contribute to the back-scattered amplitude. The detailed evaluation of three of these integrals gives results which account for some of the features of the back-scattering functions.