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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 6, Iss. 9 — Sep. 1, 1989
  • pp: 1394–1420

Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium)

Kurt Edmund Oughstun and George C. Sherman  »View Author Affiliations


JOSA A, Vol. 6, Issue 9, pp. 1394-1420 (1989)
http://dx.doi.org/10.1364/JOSAA.6.001394


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Abstract

The uniform asymptotic description of electromagnetic pulse propagation in a single-resonance Lorentz medium is presented. The modern asymptotic theory used here relies on Olver’s saddle-point method [ Stud. Appl. Math. Rev. 12, 228 ( 1970)] together with the uniform asymptotic theory of Handelsman and Bleistein [ Arch. Ration. Mech. Anal. 35, 267 ( 1969)] when two saddle points are at infinity (for the Sommerfeld precursor), the uniform asymptotic theory of Chester et al. [ Proc. Cambridge Philos. Soc. 53, 599 ( 1957)] for two neighboring saddle points (for the Brillouin precursor), and the uniform asymptotic theory of Bleistein [ Commun. Pure Appl. Math. 19, 353 ( 1966)] for a saddle point and nearby pole singularity (for the signal arrival). Together with the recently derived approximations for the dynamical saddle-point evolution, which are accurate over the entire space–time domain of interest, the resultant asymptotic expressions provide a complete, uniformly valid description of the entire dynamic field evolution in the mature dispersion limit. Specific examples of the delta-function pulse and the unit-step-function-modulated signal are considered.

© 1989 Optical Society of America

History
Original Manuscript: January 9, 1989
Manuscript Accepted: May 19, 1989
Published: September 1, 1989

Citation
Kurt Edmund Oughstun and George 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, 1394-1420 (1989)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-6-9-1394

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