Propagation of ultra-wide-band electromagnetic pulses through dispersive media

We develop an efficient method for the analysis of ultra-wide-band (UWB) electromagnetic pulses (e.g., double-exponential pulse) propagating through a waveguide or cold plasma (i.e., the ionosphere). First we show that the inverse Fourier-transform representations for the electric and magnetic fields satisfy second order, nonhomogeneous, ordinary, differential equations. These differential equations are solved analytically, thereby yielding closed-form expressions involving incomplete Lipschitz-Hankel integrals (ILHIs). The ILHIs are computed using efficient convergent and asymptotic series expansions. We demonstrate the usefulness of the ILHI expressions by comparing them 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, regardless of the number of points computed. An asymptotic series representation for the ILHIs is also employed, to obtain a relatively simple, late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the waveform over a large portion of its time history