Electromagnetic transient analysis of radiation by canonical sources in planarly layered media using leaky modes

The transient radiation from line and point sources embedded in planarly layered media is investigated in connection with the leaky modes. The proposed method involves the evaluation of the spatial-wavenumber inversion integral using complex-plane analysis, which results in the frequency-domain eld represented by a discrete series of residues and a continuous branch-cut in- tegral. By properly deforming integration paths in both the complex frequency plane and complex wavenumber plane it is shown that the branch-cut integral contribution vanishes. The method leads to an e±cient computation of the transient ¯elds due to line and point sources in a layered medium and is applicable to multi-layered lossy dielectric media and planarly layered media with negative frequency-dependent permittivity and permeabil- ity.