AbstractThe responses of a plane‐wave pulse train irradiating a lossy dispersive dielectric half‐space are investigated. The incident pulse train is expressed as a Fourier series with summing done by the inverse fast Fourier transform. The Fourier series technique is adopted to avoid the many difficulties often encountered in finding the inverse Fourier transform when transform analyses are used. Calculations are made for propagation in pure water, and typical waveforms inside the dielectric half‐space are presented. Higher harmonics are strongly attenuated, resulting in a single continuous sinusoidal waveform at the frequency of the fundamental depth in the material. The time‐averaged specific absorption rate (SAR) for pulse‐train propagation is shown to be the sum of the time‐averaged SARs of the individual harmonic components of the pulse train. For the same average power, calculated SARs reveal that pulse trains generally penetrate deeper than carrier‐frequency continuous waves but not deeper than continuous waves at frequencies approaching the fundamental of the pulse train. The effects of rise time on the propagating pulse train in the dielectrics are shown and explained. Since most practical pulsed systems are very limited in bandwidth, no pronounced differences between their response and continuous wave (CW) response would be expected. Typical results for pulse‐train propagation in arrays of dispersive planar dielectric slabs are presented. Expressing the pulse train as a Fourier series provides a practical way of interpreting the dispersion characteristics from the spectra