Trapezoidal envelope pulse dynamics in debye-model dielectrics

The dynamical evolution of a trapezoidal envelope microwave pulse as it penetrates into a Debye-type dielectric is described using both asymptotic methods and numerical simulations. When the initial pulse rise/fall- time exceeds a critical value independent of the material relaxation time, the pulse evolution is dominated by a pair of Brillouin precursors whose peak values decay as (Δz)^−1/2 with propagation distance Δz → ∞. The pulse then penetrates much farther into the material than that described by Beer´s law, carrying a significant fraction of the initial pulse energy.