Dynamical Structure of the Precursor Fields in Linear Dispersive Pulse Propagation in Lossy Dielectrics

Abstract

The dynamical evolution of an electromagnetic pulse as it propagates through a homogeneous, isotropic, locally linear, temporally dispersive medium is a classical problem of electromagnetism. If the medium was nondispersive, an arbitrary plane wave pulse would propagate unaltered at the phase velocity of the wave field in the medium. In a dispersive medium, however, the pulse is modified as it propagates due to two interrelated effects. First of all, each spectral component of the initial pulse propagates through the dispersive medium with its own phase velocity v_p = ω /ß(ω) so that the phasal relationship between the various spectral components of the pulse changes as it propagates. For a narrowband pulse whose bandwidth satisfies the inequality Δω/ω_c < <1, the pulse envelope propagates with the group velocity v_g = (dß(ω))/dω))^-1 at the carrier frequency ω_c, provided that the frequency dispersion of the loss over the bandwidth of the pulse is negligible. Here ω n_r(ω)/c is the real-valued wavenumber of the electromagnetic plane wave field in the dispersive medium with real-valued index of refraction n_r(ω)). Secondly, each spectral component is absorbed at its own rate so that the amplitudinal relationship between the spectral components of the pulse changes as it propagates. Although this effect may be negligible for narrowband pulses whose bandwidth is removed from the material absorption bands, it is not negligible otherwise. Taken together, these two simple effects result in a complicated change in the dynamical structure of the propagated field due to an input broadband pulse.