Spectral analysis and synthesis options for short pulse radiation from a point dipole in a grounded dielectric layer

Formal exact alternative spectral representations for the electromagnetic fields radiation from a pulsed electric current element embedded in a grounded dielectric layer are derived. Starting from the standard spectral decomposition into the real frequency domain and the real spatial wavenumber domains corresponding to the transverse coordinates perpendicular to the direction of stratification, alternative treatments of the spectral integrands in the various complex spectral planes lead to exact steepest descent path representations which are well suited for subsequent asymptotic reduction into the time domain (TD). Of special interest is the nonconventional synthesis strategy, which performs frequency inversion before spatial wavenumber inversion, thereby utilizing in one of the options TD leaky modes with complex frequency and real spatial wavenumbers, and also TD trapped modes, as basis fields. This is contrasted with the conventional approach built around time-harmonic real-frequency leaky modes with complex spatial spectra. The spectral strategies employed here are applicable also to layered structures