PROPAGATION OF ULTRA-WIDE-BAND ELECTROMAGNETIC PULSES THROUGH DISPERSIVE MEDIA

In this paper, we develop an efficient method for the analysis of ultr a-wide-band (UWB) electromagnetic pulses (e.g., double-exponential pul se) propagating through a waveguide or cold plasma (i.e., the ionosphe re), First we show that the inverse Fourier-transform representations for the electric and magnetic fields satisfy second order, nonhomogene ous, ordinary, differential equations, These differential equations ar e solved analytically, thereby yielding closed-form expressions in inv olving incomplete Lipschitz-Hankel integrals (ILHI's). The ILHI's are computed using efficient convergent and asymptotic series expansions, We demonstrate the usefulness of the ILHI expressions by comparing the m with the fast Fourier-transform technique (FFT), Because of the long tails associated with UWB pulses, a large number of sample points are required in the FFT, to avoid aliasing errors, In contrast, the ILHI expressions provide accurate and efficient numerical results, regardle ss of the number of points computed, An asymptotic series representati on for the ILHI's is also employed, to obtain a relatively simple, lat e-time approximation for the transient fields, This approximate late-t ime expression is shown to accurately model the waveform over a large portion of its time history.