While measuring the effective permittivity of dispersive material it may be of interest to distinguish between conductivity losses (caused by free electrons) and dielectric losses (caused by bounded electrons) which both are included in the imaginary part. This usually turns out to be a non-trivial task unless suitable dispersion models for the dielectric and/or the conductivity properties of the material are assumed. In this paper we present a more general method based on the Kramers-Kronig transformations to separate the conductivity from the effective complex permittivity of a dispersive material. The Kramers-Kronig transforms (or KK-transforms) are unique integral relations between the real and the imaginary part of a complex quantity describing a causal system. The proposed method and the corresponding algorithm are tested by first supposing some fictitious values of the complex permittivity satisfying the KK-transforms. Then, different values of a conductivity are added leading to a change of the imaginary part of the effective permittivity while the real part remains the same. The effective permittivity (including a conductivity part) does generally not satisfy the KK-transforms. This fact will be employed to retrieve the conductivity from that effective complex permittivity. Finally the method is applied to measured values found in the literature to retrieve the conductivity from the effective permittivity of composite material.

An analytical approach is presented to analyze the diffraction of a scalar complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone. The beam is described by a spherical-multipole expansion and impinges exactly on the tip of the cone from an arbitrary direction. The numerical results include an investigation of the total field and of the convergence properties of the method.

A complex-source beam (CSB) is used to investigate the electromagnetic scattering and diffraction by the tip of a perfectly conducting semi-infinite circular cone. The boundary value problem is defined by assigning a complex-valued source coordinate in the spherical-multipole expansion of the field due to a Hertzian dipole in the presence of the PEC circular cone. Since the incident CSB field can be interpreted as a localized plane wave illuminating the tip, the classical exact tip scattering problem can be analysed by an eigenfunction expansion without having the convergence problems in case of a full plane wave incident field. The numerical evaluation includes corresponding near- and far-fields.

An analytical approach to analyze the diffraction of an arbitrarily directed complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone is presented. The beam is generated by assigning a complex-valued location to a point source; its waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by a spherical-multipole analysis. The solution requires the calculation of associated Legendre functions of the first kind for complex-valued arguments which turns out to be a non-trivial task. Beside a numerical analysis of the corresponding algorithms we present numerical results for the total near- and scattered far-fields.