Short-rise-time microwave pulse propagation through dispersive biological media

Numerical research is reported on the propagation of short microwave pulses into living, biological materials. These materials are dispersive, and data on the dielectric constant and conductivity for these materials follow a Debye model. A Fourier-series calculation is presented that predicts the occurrence of Brillouin precursors when the incident pulses have sufficiently short rise times. These transients are attenuated with increasing propagation distance but are attenuated more slowly than the carrier frequency of the pulse, which is attenuated exponentially with distance. An analysis of the numerical error resulting from truncation of the Fourier series is given. Upper-bound estimates of truncation error show good series convergence.