SPECTRAL-ANALYSIS AND SYNTHESIS OPTIONS FOR SHORT-PULSE RADIATION FROM A POINT DIPOLE IN A GROUNDED DIELECTRIC LAYER

Pulsed radiation from sources in the presence of layered dielectric media is of interest in a variety of current applications. A comprehensive three-part study has been undertaken to explore various analysis and synthesis options in the wavenumber-frequency spectral domains, with emphasis on their utility for subsequent numerical implementation, and on their respective interpretation in terms of cogent physical wave phenomena. The first part of the sequence here deals with the derivation of formal exact alternative spectral representations for the electromagnetic fields radiated from a pulsed electric current element embedded in a grounded dielectric layer. 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. Although the single-layer configuration is a special case, the spectral strategies employed here are applicable also to more general layered structures. Details of the dispersion equations for the conventional and nonconventional options, and subsequent asymptotic reductions of the formal solutions here, are treated in the companion papers, with illustrative numerical examples.