Ultrawideband pulse propagation through a homogeneous, isotropic, lossy plasma

Abstract

[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.

Brillouin precursors propagation through sea water at GHz frequency

“…When an ultrawide-band pulse propagates through plasma, the attenuation factor C of the Brillouin precursor is -2. However, the other precursor (Sommerfeld precursor) can have a smaller attenuation factor of -0.75 [8]. High frequencies give rise to the Sommerfeld precursor, while low frequencies give rise to the Brillouin precursor.…”

“…Each spectral component travels through the medium with its own phase velocity and attenuation rate, so that the phase relationship and the relative amplitudes between the spectral components of the pulse change with propagation distance. Asymptotic theory can accurately describe this complex dynamic evolution of the propagation field [5]- [8].…”

Precursors of chirped pulses in dispersive media

“…We restrict our analysis to the branch on which Re[k(ω)] is negative by introducing one branch cut that extends between the branch points −iδ + 1 −δ 2 and − iδ + 1 +ω 2 p −δ 2 (6) in the right half plane and another branch cut symmetrically located across the imaginary axis.…”

“…It wasn't until the late 1970's that the results of Oughstun and Sherman [3] clearly showed that the peak amplitude point of the Brillouin precursor occurs at the space-time point ct/z = (0) and that the field at this spacetime point decays algebraically with propagation distance, whereas the remainder of the field decays exponentially. Since then, asymptotic methods have been used successfully to describe the propagation of step-modulated sinusoids of fixed central frequency through single-resonance Lorentz material [4], Rocard-Powles-Debye material [5] and lossy plasma [6], as well as propagation of a Gaussianmodulated cosine wave of fixed central frequency through a single-resonance Lorentz dielectric [7,8].…”

Exact analytical calculation and numerical modelling by finite-difference time-domain method of the transient transmission of electromagnetic waves through cold plasmas

“…The asymptotic description with the integral representation of the propagated plane-wave pulse was used in the study. The same technique was used to study the propagation of the step sinusoidal wave (Cartwright & Oughstun 2009). Although the obtained result was valid for all input carrier frequencies, special attention was paid to the carrier frequency below the plasma frequency.…”