Propagation analysis of ultrashort pulses in resonant dielectric media

The space-frequency theory of the propagation of an ultrawideband radiation in dielectric media is presented. Characterization of the material via its susceptibility leads to a transfer function, which describes the response of the medium in the frequency domain. This description enables the consideration of broadband signals, taking into account inhomogeneous absorptive and dispersive effects of the medium. Analytical expressions are derived when a pulse-modulated signal is propagating in a general dielectric material. Conditions for apparent "superluminal" and pulse compression effects are identified. The theory is applied for a special case of transmission inside a resonant medium, revealing analytical approximations for the parameters of a Gaussian propagating pulse in terms of initial pulse width, carrier frequency, and medium parameters. Constraints of the derived analytical expressions are discussed, pointing out conditions of approximation validity. We demonstrate the approach by studying the propagation of ultrawideband signals, while transmitted in the vicinity of the 60 GHz absorption peak of the atmospheric medium at millimeter wavelengths.