Advertisement

Pulse Centrovelocity: Asymptotic and FFT Results

  • Natalie A. Cartwright
  • Kurt E. Oughstun
Conference paper

Abstract

Over the past 100 years a variety of definitions have been introduced in order to describe the velocity of an electromagnetic pulse as it travels through a dispersive material. Although these velocity measures provide comparable results in those frequency regions of the material dispersion where the loss is small, they disagree wherever the material loss is large. In fact, some definitions of the pulse velocity yield nonphysical results (superluminal or negative velocities), while others apply only to certain pulse characteristics. In 1970, Smith1 addressed these issues while proposing a new definition for the velocity of an electromagnetic pulse which he called the centrovelocity. This centrovelocity is defined by the quantity
$$ \left| {\nabla \left( {\int_{ - \infty }^\infty {tE^2 (r,t)dt} /\int_{ - \infty }^\infty {E^2 (r,t)dt} } \right)} \right|^{ - 1} $$
where E(r, t) is the real electric intensity vector. Notice that the ratio of the two integrals is analogous to a center of mass calculation since it tracks the temporal center of gravity of the intensity of the pulse. Recently, Peatross, Glasgow and Ware2 introduced a variant of Smith’s centrovelocity which tracks the temporal center of gravity of the real Poynting vector S(r, t) rather than that of the intensity of the pulse, where the Poynting vector is defined (in MKS units) as
$$ S(r,t) = E(r,t) \times H(r,t). $$
(1)
In this paper, the centrovelocity of a rectangular-modulated plane-wave electromagnetic pulse traveling in the positive z -direction in a Lorentz model3 dielectric material is calculated in two independent ways: the first uses an asymptotic approximation and the second uses a numerical code based on the fast Fourier transform algorithm. The results show that, in the asymptotic limit as z → ∞, the centrovelocity approaches the speed at which the Brillouin precursor travels through the causally dispersive material

Keywords

Carrier Frequency Propagation Distance Asymptotic Approximation Electromagnetic Pulse Dispersive Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Smith, The Velocities of Light, Am. J. Phys. 38(8), 978–984 (1970).CrossRefGoogle Scholar
  2. 2.
    J. Peatross, S.A. Glasgow, M. Ware, Average energy flow of optical pulses in dispersive media, Phys. Rev. Lett. 84(11), 2370–2373 (2000).CrossRefGoogle Scholar
  3. 3.
    H.A. Lorentz, The Theory of Electrons (Leipzig, Teubner,1909), Ch. IV.Google Scholar
  4. 4.
    L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).MATHGoogle Scholar
  5. 5.
    K.E. Oughstun and G.C. Sherman, Pulse Propagation in Causal Dielectrics (Springer-Verlag, Berlin, 1994).CrossRefGoogle Scholar
  6. 6.
    K.E. Oughstun and G.C. Sherman, Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium), J. Opt. Soc. Am. B 5(4), 817–849 (1988).CrossRefGoogle Scholar
  7. 7.
    K.E. Oughstun and G.C. Sherman, Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium), J. Opt. Soc. Am. A 6(9), 1394–1420 (1989).MathSciNetCrossRefGoogle Scholar
  8. 8.
    K.E. Oughstun and G.C. Sherman, Uniform asymptotic description of ultrashort rectangular optical pulse propagation in a linear, causally dispersive medium, Phys. Rev. A 41(11), 6090–6113 (1990).CrossRefGoogle Scholar
  9. 9.
    K.E. Oughstun, Pulse Propagation in a Linear, Causally Dispersive Medium, Proc. IEEE 79(10), 1394–1420 (1991).Google Scholar
  10. 10.
    K.E. Oughstun and P.D. Smith, On the accuracy of asymptotic approximations in ultrawideband signal, short pulse, time-domain electromagnetics, Proc. 2000 IEEE Ant. & Prop. Soc. Ann. Mtg. 685–688 (2000).Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Natalie A. Cartwright
    • 1
  • Kurt E. Oughstun
    • 2
  1. 1.Department of Mathematics and StatisticsUniverisity of VermontBurlington
  2. 2.College of Engineering and MathematicsUniversity of VermontBurlington

Personalised recommendations