Abstract

A fast, hybrid numerical–asymptotic algorithm for the calculation of the dynamical field evolution that is due to an arbitrary input pulse in any linear dispersive, attenuative medium is presented. The algorithm combines the numerical efficiency of the fast-Fourier-transform algorithm over a finite frequency domain that encompasses all the medium resonances with the accuracy and analytical efficiency of the asymptotic description that fully accounts for the high-frequency structure above the highest resonance that is characteristic of the dispersive medium.

© 1998 Optical Society of America

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  1. O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
    [CrossRef]
  2. R. E. McIntosh, A. Malaga, “Time dispersion of electromagnetic pulses by the ionosphere,” Radio Sci. 15, 645–654 (1980).
    [CrossRef]
  3. D. B. Trizna, T. A. Weber, “Brillouin revisited: signal velocity definition for pulse propagation in a medium with resonant anomalous dispersion,” Radio Sci. 17, 1169–1180 (1982).
    [CrossRef]
  4. V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Pergamon, Oxford, 1970).
  5. K. E. Oughstun, G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, Heidelberg, 1994).
  6. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 3.
  8. A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914).
    [CrossRef]
  9. L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 203–240 (1914).
    [CrossRef]
  10. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).
  11. P. Debye, “Näherungsformeln für die zylinderfunktionen für grosse werte des arguments und unbeschränkt verander lichte werte des index,” Math. Ann. 67, 535–558 (1909).
    [CrossRef]
  12. K. E. Oughstun, G. C. Sherman, “Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. B 5, 817–849 (1988).
    [CrossRef]
  13. K. E. Oughstun, 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, 1394–1420 (1989).
    [CrossRef]
  14. G. C. Sherman, K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett. 47, 1451–1454 (1981).
    [CrossRef]
  15. G. C. Sherman, K. E. Oughstun, “Energy velocity description of pulse propagation in absorbing, dispersive dielectrics,” J. Opt. Soc. Am. B 12, 229–247 (1995).
    [CrossRef]
  16. S. Shen, K. E. Oughstun, “Dispersive pulse propagation in a double resonance Lorentz medium,” J. Opt. Soc. Am. B 6, 948–963 (1989); S. Shen, “Dispersive pulse propagation in a multiple resonance Lorentz medium,” M.S. dissertation (Department of Electrical and Computer Engineering, University of Wisconsin–Madison, 1986).
    [CrossRef]
  17. K. E. Oughstun, G. C. Sherman, “Asymptotic theory of pulse propagation in absorbing and dispersive dielectrics,” in Review of Radio Science, 1990–1992, W. Ross Stone, ed. (Oxford U. Press, Oxford, 1993), pp. 75–105.
  18. J. E. K. Laurens, K. E. Oughstun, “Electromagnetic impulse response of triply-distilled water,” in Ultra-Wideband, Short-Pulse Electromagnetics 4, C. E. Baum, ed. (Plenum, New York, to be published); J. E. K. Laurens, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” Ph.D. dissertation (Department of Electrical Engineering, University of Vermont, Burlington, Vt., 1993); J. E. K. Laurens, K. E. Oughstun, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” (University of Vermont, Burlington, Vt., 1993).
  19. T. Hosono, “Numerical inversion of Laplace transform and some applications to wave optics,” in Proceedings of the 1980 International Union of Radio Science International Symposium on Electromagnetic Waves (International Union of Radio Science, Munich, 1980), paper 112.
  20. P. Wyns, D. P. Foty, K. E. Oughstun, “Numerical analysis of the precursor fields in dispersive pulse propagation,” J. Opt. Soc. Am. A 6, 1421–1429 (1989).
    [CrossRef]
  21. C. M. Balictsis, K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E 47, 3645–3669 (1993).
    [CrossRef]
  22. C. M. Balictsis, K. E. Oughstun, “Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium,” Phys. Rev. E 55, 1910–1921 (1997).
    [CrossRef]
  23. K. E. Oughstun, “Transient field properties of ultrawideband pulse propagation in complex dispersive media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 795.
  24. S. L. Dvorak, R. W. Ziolkowski, L. B. Felsen, “Propagation of ultrawideband electromagnetic pulses in Lorentz media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 796.
  25. S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultrawideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997).
    [CrossRef]
  26. S. L. Dvorak, D. G. Dudley, R. W. Ziolkowski, “Propagation of UWB electromagnetic pulses through lossy plasmas,” in Ultra-Wideband, Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin, A. P. Stone, eds. (Plenum, New York, 1997), pp. 247–254.
  27. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 333–340.
  28. H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972), Chap. 1.
  29. K. E. Oughstun, “Dynamical structure of the precursor fields in linear dispersive pulse propagation in lossy dielectrics,” in Ultra-Wideband, Short-Pulse Electromagnetics 2, L. Carin, L. B. Felsen, eds. (Plenum, New York, 1995), pp. 257–272.
  30. K. E. Oughstun, H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium,” Phys. Rev. Lett. 78, 642–645 (1997).
    [CrossRef]
  31. L. M. Soroko, Holography and Coherent Optics (Plenum, New York, 1980), Sec. 5.5; J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Sec. 2.3.
  32. M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
    [CrossRef]
  33. R. A. Handelsman, N. Bleistein, “Uniform asymptotic expansions of integrals that arise in the analysis of precursors,” Arch. Ration. Mech. Anal. 35, 267–283 (1969).
  34. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 9.
  35. C. J. F. Böttcher, A. Bordewijk, Theory of Electric Polarization (Elsevier, Amsterdam, 1980).
  36. P. Debye, Polar Molecules (Dover, New York, 1929).
  37. J. McConnell, Rotational Brownian Motion and Dielectric Theory (Academic, London, 1980).
  38. R. Albanese, J. Penn, R. Medina, “Short rise-time microwave pulse propagation through dispersive biological media,” J. Opt. Soc. Am. A 6, 1441–1446 (1989).
    [CrossRef]

1997 (3)

C. M. Balictsis, K. E. Oughstun, “Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium,” Phys. Rev. E 55, 1910–1921 (1997).
[CrossRef]

S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultrawideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997).
[CrossRef]

K. E. Oughstun, H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium,” Phys. Rev. Lett. 78, 642–645 (1997).
[CrossRef]

1995 (1)

1993 (1)

C. M. Balictsis, K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E 47, 3645–3669 (1993).
[CrossRef]

1989 (4)

1988 (1)

1983 (1)

O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
[CrossRef]

1982 (1)

D. B. Trizna, T. A. Weber, “Brillouin revisited: signal velocity definition for pulse propagation in a medium with resonant anomalous dispersion,” Radio Sci. 17, 1169–1180 (1982).
[CrossRef]

1981 (1)

G. C. Sherman, K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett. 47, 1451–1454 (1981).
[CrossRef]

1980 (1)

R. E. McIntosh, A. Malaga, “Time dispersion of electromagnetic pulses by the ionosphere,” Radio Sci. 15, 645–654 (1980).
[CrossRef]

1972 (1)

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

1969 (1)

R. A. Handelsman, N. Bleistein, “Uniform asymptotic expansions of integrals that arise in the analysis of precursors,” Arch. Ration. Mech. Anal. 35, 267–283 (1969).

1914 (2)

A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914).
[CrossRef]

L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 203–240 (1914).
[CrossRef]

1909 (1)

P. Debye, “Näherungsformeln für die zylinderfunktionen für grosse werte des arguments und unbeschränkt verander lichte werte des index,” Math. Ann. 67, 535–558 (1909).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 3.

Albanese, R.

Altarelli, M.

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Avenel, O.

O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
[CrossRef]

Balictsis, C. M.

C. M. Balictsis, K. E. Oughstun, “Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium,” Phys. Rev. E 55, 1910–1921 (1997).
[CrossRef]

C. M. Balictsis, K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E 47, 3645–3669 (1993).
[CrossRef]

Bleistein, N.

R. A. Handelsman, N. Bleistein, “Uniform asymptotic expansions of integrals that arise in the analysis of precursors,” Arch. Ration. Mech. Anal. 35, 267–283 (1969).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 9.

Bordewijk, A.

C. J. F. Böttcher, A. Bordewijk, Theory of Electric Polarization (Elsevier, Amsterdam, 1980).

Böttcher, C. J. F.

C. J. F. Böttcher, A. Bordewijk, Theory of Electric Polarization (Elsevier, Amsterdam, 1980).

Brillouin, L.

L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 203–240 (1914).
[CrossRef]

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

Debye, P.

P. Debye, “Näherungsformeln für die zylinderfunktionen für grosse werte des arguments und unbeschränkt verander lichte werte des index,” Math. Ann. 67, 535–558 (1909).
[CrossRef]

P. Debye, Polar Molecules (Dover, New York, 1929).

Dexter, D. L.

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Dudley, D. G.

S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultrawideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997).
[CrossRef]

S. L. Dvorak, D. G. Dudley, R. W. Ziolkowski, “Propagation of UWB electromagnetic pulses through lossy plasmas,” in Ultra-Wideband, Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin, A. P. Stone, eds. (Plenum, New York, 1997), pp. 247–254.

Dvorak, S. L.

S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultrawideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997).
[CrossRef]

S. L. Dvorak, D. G. Dudley, R. W. Ziolkowski, “Propagation of UWB electromagnetic pulses through lossy plasmas,” in Ultra-Wideband, Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin, A. P. Stone, eds. (Plenum, New York, 1997), pp. 247–254.

S. L. Dvorak, R. W. Ziolkowski, L. B. Felsen, “Propagation of ultrawideband electromagnetic pulses in Lorentz media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 796.

Felsen, L. B.

S. L. Dvorak, R. W. Ziolkowski, L. B. Felsen, “Propagation of ultrawideband electromagnetic pulses in Lorentz media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 796.

Foty, D. P.

Ginzburg, V. L.

V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Pergamon, Oxford, 1970).

Handelsman, R. A.

R. A. Handelsman, N. Bleistein, “Uniform asymptotic expansions of integrals that arise in the analysis of precursors,” Arch. Ration. Mech. Anal. 35, 267–283 (1969).

Hosono, T.

T. Hosono, “Numerical inversion of Laplace transform and some applications to wave optics,” in Proceedings of the 1980 International Union of Radio Science International Symposium on Electromagnetic Waves (International Union of Radio Science, Munich, 1980), paper 112.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 9.

Laurens, J. E. K.

J. E. K. Laurens, K. E. Oughstun, “Electromagnetic impulse response of triply-distilled water,” in Ultra-Wideband, Short-Pulse Electromagnetics 4, C. E. Baum, ed. (Plenum, New York, to be published); J. E. K. Laurens, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” Ph.D. dissertation (Department of Electrical Engineering, University of Vermont, Burlington, Vt., 1993); J. E. K. Laurens, K. E. Oughstun, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” (University of Vermont, Burlington, Vt., 1993).

Malaga, A.

R. E. McIntosh, A. Malaga, “Time dispersion of electromagnetic pulses by the ionosphere,” Radio Sci. 15, 645–654 (1980).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

McConnell, J.

J. McConnell, Rotational Brownian Motion and Dielectric Theory (Academic, London, 1980).

McIntosh, R. E.

R. E. McIntosh, A. Malaga, “Time dispersion of electromagnetic pulses by the ionosphere,” Radio Sci. 15, 645–654 (1980).
[CrossRef]

Medina, R.

Nussenzveig, H. M.

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972), Chap. 1.

Oughstun, K. E.

K. E. Oughstun, H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium,” Phys. Rev. Lett. 78, 642–645 (1997).
[CrossRef]

C. M. Balictsis, K. E. Oughstun, “Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium,” Phys. Rev. E 55, 1910–1921 (1997).
[CrossRef]

G. C. Sherman, K. E. Oughstun, “Energy velocity description of pulse propagation in absorbing, dispersive dielectrics,” J. Opt. Soc. Am. B 12, 229–247 (1995).
[CrossRef]

C. M. Balictsis, K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E 47, 3645–3669 (1993).
[CrossRef]

P. Wyns, D. P. Foty, K. E. Oughstun, “Numerical analysis of the precursor fields in dispersive pulse propagation,” J. Opt. Soc. Am. A 6, 1421–1429 (1989).
[CrossRef]

S. Shen, K. E. Oughstun, “Dispersive pulse propagation in a double resonance Lorentz medium,” J. Opt. Soc. Am. B 6, 948–963 (1989); S. Shen, “Dispersive pulse propagation in a multiple resonance Lorentz medium,” M.S. dissertation (Department of Electrical and Computer Engineering, University of Wisconsin–Madison, 1986).
[CrossRef]

K. E. Oughstun, 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, 1394–1420 (1989).
[CrossRef]

K. E. Oughstun, G. C. Sherman, “Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. B 5, 817–849 (1988).
[CrossRef]

G. C. Sherman, K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett. 47, 1451–1454 (1981).
[CrossRef]

K. E. Oughstun, G. C. Sherman, “Asymptotic theory of pulse propagation in absorbing and dispersive dielectrics,” in Review of Radio Science, 1990–1992, W. Ross Stone, ed. (Oxford U. Press, Oxford, 1993), pp. 75–105.

J. E. K. Laurens, K. E. Oughstun, “Electromagnetic impulse response of triply-distilled water,” in Ultra-Wideband, Short-Pulse Electromagnetics 4, C. E. Baum, ed. (Plenum, New York, to be published); J. E. K. Laurens, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” Ph.D. dissertation (Department of Electrical Engineering, University of Vermont, Burlington, Vt., 1993); J. E. K. Laurens, K. E. Oughstun, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” (University of Vermont, Burlington, Vt., 1993).

K. E. Oughstun, G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, Heidelberg, 1994).

K. E. Oughstun, “Transient field properties of ultrawideband pulse propagation in complex dispersive media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 795.

K. E. Oughstun, “Dynamical structure of the precursor fields in linear dispersive pulse propagation in lossy dielectrics,” in Ultra-Wideband, Short-Pulse Electromagnetics 2, L. Carin, L. B. Felsen, eds. (Plenum, New York, 1995), pp. 257–272.

Penn, J.

Rouff, M.

O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
[CrossRef]

Shen, S.

Sherman, G. C.

G. C. Sherman, K. E. Oughstun, “Energy velocity description of pulse propagation in absorbing, dispersive dielectrics,” J. Opt. Soc. Am. B 12, 229–247 (1995).
[CrossRef]

K. E. Oughstun, 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, 1394–1420 (1989).
[CrossRef]

K. E. Oughstun, G. C. Sherman, “Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. B 5, 817–849 (1988).
[CrossRef]

G. C. Sherman, K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett. 47, 1451–1454 (1981).
[CrossRef]

K. E. Oughstun, G. C. Sherman, “Asymptotic theory of pulse propagation in absorbing and dispersive dielectrics,” in Review of Radio Science, 1990–1992, W. Ross Stone, ed. (Oxford U. Press, Oxford, 1993), pp. 75–105.

K. E. Oughstun, G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, Heidelberg, 1994).

Smith, D. Y.

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914).
[CrossRef]

Soroko, L. M.

L. M. Soroko, Holography and Coherent Optics (Plenum, New York, 1980), Sec. 5.5; J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Sec. 2.3.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 333–340.

Trizna, D. B.

D. B. Trizna, T. A. Weber, “Brillouin revisited: signal velocity definition for pulse propagation in a medium with resonant anomalous dispersion,” Radio Sci. 17, 1169–1180 (1982).
[CrossRef]

Varoquaux, E.

O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
[CrossRef]

Weber, T. A.

D. B. Trizna, T. A. Weber, “Brillouin revisited: signal velocity definition for pulse propagation in a medium with resonant anomalous dispersion,” Radio Sci. 17, 1169–1180 (1982).
[CrossRef]

Williams, G. A.

O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
[CrossRef]

Wyns, P.

Xiao, H.

K. E. Oughstun, H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium,” Phys. Rev. Lett. 78, 642–645 (1997).
[CrossRef]

Ziolkowski, R. W.

S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultrawideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997).
[CrossRef]

S. L. Dvorak, R. W. Ziolkowski, L. B. Felsen, “Propagation of ultrawideband electromagnetic pulses in Lorentz media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 796.

S. L. Dvorak, D. G. Dudley, R. W. Ziolkowski, “Propagation of UWB electromagnetic pulses through lossy plasmas,” in Ultra-Wideband, Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin, A. P. Stone, eds. (Plenum, New York, 1997), pp. 247–254.

Ann. Phys. (Leipzig) (2)

A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914).
[CrossRef]

L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 44, 203–240 (1914).
[CrossRef]

Arch. Ration. Mech. Anal. (1)

R. A. Handelsman, N. Bleistein, “Uniform asymptotic expansions of integrals that arise in the analysis of precursors,” Arch. Ration. Mech. Anal. 35, 267–283 (1969).

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (3)

Math. Ann. (1)

P. Debye, “Näherungsformeln für die zylinderfunktionen für grosse werte des arguments und unbeschränkt verander lichte werte des index,” Math. Ann. 67, 535–558 (1909).
[CrossRef]

Phys. Rev. B (1)

M. Altarelli, D. L. Dexter, H. M. Nussenzveig, D. Y. Smith, “Superconvergence and sum rules for the optical constants,” Phys. Rev. B 6, 4502–4509 (1972).
[CrossRef]

Phys. Rev. E (2)

C. M. Balictsis, K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E 47, 3645–3669 (1993).
[CrossRef]

C. M. Balictsis, K. E. Oughstun, “Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium,” Phys. Rev. E 55, 1910–1921 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

O. Avenel, M. Rouff, E. Varoquaux, G. A. Williams, “Resonant pulse propagation of sound in superfluid He-3,” Phys. Rev. Lett. 50, 1591–1594 (1983).
[CrossRef]

G. C. Sherman, K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett. 47, 1451–1454 (1981).
[CrossRef]

K. E. Oughstun, H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium,” Phys. Rev. Lett. 78, 642–645 (1997).
[CrossRef]

Radio Sci. (3)

S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultrawideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997).
[CrossRef]

R. E. McIntosh, A. Malaga, “Time dispersion of electromagnetic pulses by the ionosphere,” Radio Sci. 15, 645–654 (1980).
[CrossRef]

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K. E. Oughstun, G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, Heidelberg, 1994).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 3.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

K. E. Oughstun, “Transient field properties of ultrawideband pulse propagation in complex dispersive media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 795.

S. L. Dvorak, R. W. Ziolkowski, L. B. Felsen, “Propagation of ultrawideband electromagnetic pulses in Lorentz media,” in Proceedings of the Progress in Electromagnetics Research Symposium (PIERS’97, Cambridge, Mass., 1997), p. 796.

K. E. Oughstun, G. C. Sherman, “Asymptotic theory of pulse propagation in absorbing and dispersive dielectrics,” in Review of Radio Science, 1990–1992, W. Ross Stone, ed. (Oxford U. Press, Oxford, 1993), pp. 75–105.

J. E. K. Laurens, K. E. Oughstun, “Electromagnetic impulse response of triply-distilled water,” in Ultra-Wideband, Short-Pulse Electromagnetics 4, C. E. Baum, ed. (Plenum, New York, to be published); J. E. K. Laurens, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” Ph.D. dissertation (Department of Electrical Engineering, University of Vermont, Burlington, Vt., 1993); J. E. K. Laurens, K. E. Oughstun, “Plane wave pulse propagation in a linear, causally dispersive polar medium,” (University of Vermont, Burlington, Vt., 1993).

T. Hosono, “Numerical inversion of Laplace transform and some applications to wave optics,” in Proceedings of the 1980 International Union of Radio Science International Symposium on Electromagnetic Waves (International Union of Radio Science, Munich, 1980), paper 112.

S. L. Dvorak, D. G. Dudley, R. W. Ziolkowski, “Propagation of UWB electromagnetic pulses through lossy plasmas,” in Ultra-Wideband, Short-Pulse Electromagnetics 3, C. E. Baum, L. Carin, A. P. Stone, eds. (Plenum, New York, 1997), pp. 247–254.

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Figures (10)

Fig. 1
Fig. 1

Contour of integration in the complex ω plane for a dispersive medium with m resonance frequencies ω0, ω2, , ω2m. The hatched areas indicate the local regions about the distant saddle points SPd±(θ) that have larger exponential decay in the complex phase function ϕ(ω, θ)=iω[n(ω)-θ] than that at the saddle point.

Fig. 2
Fig. 2

Frequency dispersion of the real and the imaginary parts of the complex index of refraction of a double-resonance Lorentz-model dielectric with undamped resonance frequencies ω0 and ω2, where ω1=ω02+b02 and ω3=ω22+b22. The regions of anomalous dispersion extend approximately over the angular frequency intervals [ω0, ω1] and [ω2, ω3]. The selected values of the signal frequency ωc for the examples considered in this paper are indicated at the bottom of the figure.

Fig. 3
Fig. 3

Dynamical evolution of the propagated field in the double-resonance Lorentz-model dielectric for the below-resonance carrier frequency case ωc=1.2×1014 s-1 as a function of the dimensionless time parameter θ=ct/z at fixed propagation distances (a) z=3zd, (b) z=5zd, (c) z=7zd, (d) z=10zd.

Fig. 4
Fig. 4

Dynamical evolution of the propagated field in the double-resonance Lorentz-model dielectric for input carrier frequency ωc=3.0×1014 s-1, which is near the lower end of the medium passband, as a function of the dimensionless time parameter θ=ct/z at fixed propagation distances (a) z=zd, (b) z=3zd, (c) z=5zd, (d) z=7zd, (e) z=10zd.

Fig. 5
Fig. 5

Dynamical evolution of the propagated field in the double-resonance Lorentz-model dielectric for input carrier frequency ωc=ωmin=1.615×1015 s-1, which is at the minimum dispersion point of the medium passband, as a function of the dimensionless time parameter θ=ct/z at fixed propagation distances (a) z=zd, (b) z=3zd, (c) z=5zd, (d) z=7zd, (e) z=10zd.

Fig. 6
Fig. 6

Dynamical evolution of the propagated field in the double-resonance Lorentz-model dielectric for the input carrier frequency ωc=7.0×1015 s-1, which is near the upper end of the medium passband, as a function of the dimensionless time parameter θ=ct/z at fixed propagation distances (a) z=5zd, (b) z=7zd, (c) z=10zd.

Fig. 7
Fig. 7

Dynamical structure of the Sommerfeld precursor field in the double-resonance Lorentz-model dielectric at propagation distance z=3zd=3α-1(ωc) for an input unit step-function-modulated signal with carrier frequency (a) ωc=1.2×1014 s-1, (b) ωc=3.0×1014 s-1, (c) ωc=ωmin=1.615×1015 s-1, (d) ωc=7.0×1015 s-1.

Fig. 8
Fig. 8

Frequency dispersion of the real and the imaginary parts of the complex index of refraction of the simple composite Rocard–Powles–Lorentz model of triply distilled H2O with a single relaxation time with associated frequency in the microwave region and resonance lines in the infrared and ultraviolet regions. The selected values of the signal frequency ωc for the examples considered in this paper are indicated at the bottom of the figure.

Fig. 9
Fig. 9

Dynamical evolution of the propagated field in the simple composite Rocard–Powles–Lorentz model of triply distilled water for input carrier frequency ωc=1.0×1012 s-1 as a function of the dimensionless time parameter θ=ct/z at fixed propagation distances (a) z=zd, (b) z=3zd, (c) z=5zd, (d) z=10zd.

Fig. 10
Fig. 10

Dynamical evolution of the propagated field in the simple composite Rocard–Powles–Lorentz model of triply distilled water for input carrier frequency ωc=1.0×1015 s-1 as a function of the dimensionless time parameter θ=ct/z at fixed propagation distances (a) z=zd, (b) z=3zd, (c) z=5zd, (d) z=10zd.

Equations (68)

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A(z, t)=12πC f˜(ω)exp{i[k˜(ω)z-ωt]}dω
=12πC f˜(ω)expzcϕ(ω, θ)dω,
f˜(ω)=- f(t)exp(iωt)dt.
[2+k˜2(ω)]A˜(z, ω)=0.
k˜(ω)=ωn(ω)/c,
ϕ(ω, θ)=i cz[k˜(ω)z-ωt]=iω[n(ω)-θ],
θ=ct/z
f(t)=u(t)sin(ωct+ψ),
A(z, t)=12πRie exp(-iψ)Cu˜(ω-ωc)×exp{i[k(ω)z-ωt]}dω
=12πRie exp(-iψ)Cu˜(ω-ωc)×expzcϕ(ω, θ)dω
εr(ω)=1+1π- εi(ζ)ζ-ωdζ:
εi(ω)=-1π- εr(ζ)-1ζ-ωdζ,
εi(0)=-1π- εr(ζ)-1ζdζ=0.
0ωmin<ωmax.
A(z, t)=12πC- f˜(ω)expzcϕ(ω, θ)dω+12πC+ f˜(ω)expzcϕ(ω, θ)dω+12π-ωmaxωmax f˜(ω)exp[ik˜(ω)z]exp(-iωt)dω
A(z, t)=AP(z, t)+12π-ωmaxωmax f˜(ω)exp[ik˜(ω)z]exp(-iωt)dω,
AP(z, t)=12πP- f˜(ω)expzcϕ(ω, θ)dω
+12πP+ f˜(ω)expzcϕ(ω, θ)dω
AP(z, t)=1πRP+ f˜(ω)expzcϕ(ω, θ)dω,
zd=α-1(ωc)=ωccni(ωc)-1
Aωmax(z, t)=12π-[rectωmax(ω)]{f˜(ω)exp[ik˜(ω)z]}×exp(-iωt)dω,
Aωmax(z, t)=ωmaxπ-A(z, t)sinc[ωmax(t-t)]dt,
Aωmax(z, t)=l=-A(z, lπ/ωmax)sinc(ωmaxt-lπ),
A(z, lπ/ωmax)=12π-ωmaxωmax{f˜(ω)exp[ik˜(ω)z]}×exp(ilπω/ωmax)dω.
AP(z, t)=AE(z, t)+AS(z, t),
AE(z, t)-cπzRf˜(ωmax)ϕ(1)(ωmax, θ)expzcϕ(ω, θ)
n(ω)+ω dn(ω)dω=θ.
εr(ω)=1-1π- εi(ζ)ω1-ζω-1dζ1-j=0 1ωj+11π-εi(ζ)ζjdζ.
εr(ω)1-j=1 a2jω2j,
a2j1π-εi(ζ)ζ2j-1dζ.
a21π-εi(ζ)ζdζ>0.
εi(ω)=-ω 2π0 εr(ζ)-1ζ2-ω2dζ
εi(ω)j=0 bjω2j+1,
bj2π0[εr(ζ)-1]ζ2jdζ.
b0=2π0[εr(ζ)-1]dζ.
ε(ω)1+i b0ω-a2ω2,
n(ω)1+i b02ω-12a2-b024 1ω2,
θ-1-12a2-b024 1ω2=0.
ωSPd±(θ)±i κ(θ-1)1/2,
0[εr(ζ)-1]dζ=0
ε(ω)1-a2ω2+i b2ω31-a2ω(ω+ib2/a2),
n(ω)1-a22ω(ω+ib2/a2),
1-θ+a22ω(ω+ib2/a2)2=0.
ωSPd±(θ)±a22(θ-1)-b224a221/2-i b22a2.
ϕ(ωSPd±, θ)-b2a2(θ-1)i[2a2(θ-1)]1/2×1+b22a23(θ-1).
AS(z, t)R[2α(θ)exp(-iπ/2)]ν exp[-i(z/c)β(θ)]×γ0Jνzcα(θ)+2α(θ)exp(-iπ/2)×γ1Jν+1zcα(θ)
f˜(ω)=ω-(1+ν)q˜(ω)
lim|ω|[q˜(ω)]0.
α(θ)=i2[ϕ(ωSPd+, θ)-ϕ(ωSPd-, θ)]=-I[ϕ(ωSPd+, θ)],
β(θ)=i2[ϕ(ωSPd+, θ)+ϕ(ωSPd-, θ)]=iR[ϕ(ωSPd+, θ)],
γ0(θ)=-i2f˜(ωSPd+)[2α(θ)]-(1+ν)4α3(θ)iϕ(2)(ωSPd+, θ)1/2+f˜(ωSPd-)[-2α(θ)]-(1+ν)-4α3(θ)iϕ(2)(ωSPd-, θ)1/2,
γ1(θ)=-i4α(θ)f˜(ωSPd+)[2α(θ)]-(1+ν)4α3(θ)iϕ(2)(ωSPd+, θ)1/2-f˜(ωSPd-)[-2α(θ)]-(1+ν)-4α3(θ)iϕ(2)(ωSPd-, θ)1/2.
f˜[ωSPd±(θ)]=-{f(t)exp[η(θ)t]}exp[±iξ(θ)t]dt,
n(ω)=1-b02ω2-ω02+2iδ0ω+b22ω2-ω22+2iδ2ω1/2,
ω0=1.7412×1014 s-1,b0=1.2155×1014 s-1,
δ0=4.955×1013 s-1,ω1=2.1235×1014 s-1
ω2=9.1448×1015 s-1,b2=6.7198×1015 s-1,
δ2=1.434×1015 s-1,ω3=1.1348×1016 s-1
f(t)=h(t)sin(ωct),
n(ω)=1+a(1-iωτ)(1-iωτf)-b02ω2-ω02+2iδ0ω-b22ω2-ω22+2iδ2ω1/2.
a=77.4,τ=8.44×10-12s,
τf=4.93×10-14s
b0=1.26×1014s-1,ω0=6.28×1014s-1,
δ0=1.76×1013s-1,ω1=6.41×1014s-1
b2=2.01×1016s-1,ω2=2.33×1016s-1,
δ2=5.03×1015s-1,ω3=3.07×1016s-1
ε(ω)=1+a(1-iωτ)(1-iωτf)-b02ω2-ω02+2iδ0ω-b22ω2-ω22+2iδ2ω1-b02+b22+aττf 1ω2+i2(δ0b02+δ2b22)+aττf2 1ω3,
ε(ω)=1+a1-iωτ-b02ω2-ω02+2iδ0ω-b22ω2-ω22+2iδ2ω1+i aτω-b02+b22-aτ2 1ω2,

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