The combination of the Lorentz-Lorenz formula with the Lorentz model of dielectric dispersion results in a decrease in the effective resonance frequency of the material when the number density of Lorentz oscillators is large. An equivalence relation is derived that equates the frequency dispersion of the Lorentz model alone with that modified by the Lorentz-Lorenz formula. Negligible differences between the computed ultrashort pulse dynamics are obtained for these equivalent models.

No abstract

The properties of ultrashort gaussian pulse propagation in a dispersive, attenuative medium are reviewed with emphasis on the pulse velocity. Of particular interest is the group velocity whose physical interpretation loses meaning in causally dispersive materials as the temporal pulse width decreases into the ultrashort pulse regime. A generalized definition of the group velocity that applies to ultrashort pulses in causally dispersive materials is provided by the centroid velocity of the pulse Poynting vector whose properties are described here. In particular, it is shown that this physical velocity measure approaches the group velocity for any value of the initial pulse carrier frequency and at any fixed value of the propagation distance in the limit as the initial pulse width increases indefinitely. This then provides a convenient measure for determining when the group velocity approximation is valid.

The description of the precursor fields in a single-resonance Lorentz model dielectric is considered in the singular and weak dispersion limits. The singular dispersion limit is obtained as the damping approaches zero and the material dispersion becomes increasingly concentrated about the resonance frequency. The algebraic peak amplitude decay of the Brillouin precursor with propagation distance z Ͼ 0 then changes from a z −1/2 to a z −1/3 behavior. The weak dispersion limit is obtained as the material density decreases to zero. The material dispersion then becomes vanishingly small everywhere and the precursors become increasingly compressed in the space-time domain immediately following the speed-of-light point ͑z , t͒ = ͑z , z / c͒. In order to circumvent the numerical difficulties introduced in this case, an approximate equivalence relation is derived that allows the propagated field evolution due to an ultrawideband signal to be calculated in an equivalent dispersive medium that is highly absorptive.

[1] We investigate a linearly polarized, plane wave electromagnetic step function modulated sine wave pulse traveling through an isotropic, homogeneous, lossy plasma with dielectric permittivity described by the Drude model. The results of this investigation extend the useful frequency domain below the plasma cutoff frequency. An asymptotic method of analysis is used to provide a closed-form approximation to the integral representation of the propagated pulse that is valid for all input carrier frequencies. This closed-form expression is the sum of its three asymptotic component fields: the Sommerfeld precursor, the Brillouin precursor and the signal contribution. These expressions reveal that, because of conductivity, each field component attenuates exponentially with distance at its own characteristic rate and that, for sufficiently large propagation distance, the Sommerfeld precursor will be the dominant contribution to the field. However, a study of the penetration capability of each field component shows that, for a large enough propagation distance with carrier frequencies below cutoff, the Brillouin precursor decays algebraically as z À2 with a minimal exponential attenuation with propagation distance while the Sommerfeld precursor decays at a rate that approaches a z À3/4 algebraic decay. Optimal signal penetration through a finite distance of a lossy plasma medium, for either radar imaging, remote sensing, or communication applications, may then be realized by using an appropriately constructed sequence of Brillouin precursor pulses.