Evolution of the Signal

  • Kurt E. Oughstun
Part of the Springer Series in Optical Sciences book series (SSOS, volume 144)


The contribution A c (z, t) to the asymptotic behavior of the propagated plane wavefield A(z, t) that is due to the presence of any simple pole singularities of the spectral function \tilde{u}(ω − ω c ), where \(A(0,t) = u(t)\sin ({\omega }_{c}t + \psi )\) with fixed angular carrier frequency ω c ≥ 0, is now condidered in some detail, with primary attention given to the oscillatory case when ω c > 0. As discussed in Sect. 12.4, the field component A c (z, t) is associated with any long-term signal that is being propagated through the dispersive material. The velocity of propagation of the signal and the transition from the total precursor field to the signal field are determined by the relative asymptotic dominance of the component fields A s (z, t), A b (z, t), A m (z, t), and A c (z, t). Consequently, discussion of these topics is deferred to Chap. 15 where the asymptotic description of the dynamical evolution of the total propagated wavefield A(z, t) is considered by combining the results of this chapter with those of Chap. 13.


Saddle Point Pole Contribution Pole Singularity Complementary Error Function Steep Descent Path 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering & Mathematical Sciences School of EngineeringUniversity of VermontBurlingtonUSA

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