Spectral Analysis of Line Sources With Complex Longitudinal Wavenumbers in Planarly Layered Media

Spectral properties of line sources carrying electric or magnetic current placed in a planarly layered medium are analyzed. It is shown that when the current along the line varies in the longitudinal direction by an exponential function with a complex exponent, classical Sommerfeld radiation condition that ensures outgoing and decaying fields simultaneously cannot always be used. Instead, depending on the exponent and the material properties of the layered medium, outgoing and exponentially increasing or incoming and exponentially decreasing waves are generated. This property is not observed when the exponent is real where the classical Sommerfeld radiation condition is fulfilled. In this article, an in-depth analysis of layered media is first performed in spectral domain as a function of the longitudinal dependence of the line sources. Then, the fields generated by the line sources are obtained by Sommerfeld integrations using two different radiation conditions separately. The effect of the radiation condition on the fields are discussed both in the spectral and spatial domains. In addition, field patterns are compared with the results obtained by finite element method (FEM) combined with perfectly matched layers (PMLs) and several guidelines for increasing the efficiency of simulations by FEM are introduced.