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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. 15, Iss. 5 — May. 1, 1998
  • pp: 1241–1255

Hybrid analytical–numerical approach for modeling transient wave propagation in Lorentz media

S. L. Dvorak, R. W. Ziolkowski, and L. B. Felsen  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1241-1255 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001241


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Abstract

The advent of ultrawideband, short-pulse sources has recently generated renewed interest in the problem of pulse propagation in dispersive media. When one is trying to numerically simulate transient plane-wave propagation through a dispersive medium, the main difficulties are encountered in trying to transform from the frequency domain to the time domain. We develop an asymptotic-extraction technique wherein asymptotic methods are used in conjunction with a fast Fourier transform (FFT) to overcome the limitations of each method. The basic idea behind the asymptotic-extraction technique is to extract and analytically invert as much of the signal as possible. The remainder of the signal is then transformed by use of a numerical FFT. We demonstrate that it is possible to construct functions that possess analytical inverse transforms and also asymptotically model the low- and high-frequency behavior of a field propagating in a single-resonance Lorentz medium. Extraction of the low- and high-frequency responses from the spectral representation for the waveform in essence preconditions the waveform for application of a FFT, thereby significantly reducing the number of sample points required by the FFT. It is also demonstrated that these two extracted functions, whose inverse Fourier transforms are evaluated analytically in terms of known special functions, provide a good approximation for the transient signal for the case of a square-wave-pulse-modulated source, provided that the carrier frequency resides far enough from the absorption band.

© 1998 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.2030) Physical optics : Dispersion
(320.5550) Ultrafast optics : Pulses

History
Original Manuscript: August 14, 1997
Revised Manuscript: December 22, 1997
Manuscript Accepted: January 20, 1998
Published: May 1, 1998

Citation
S. L. Dvorak, R. W. Ziolkowski, and L. B. Felsen, "Hybrid analytical–numerical approach for modeling transient wave propagation in Lorentz media," J. Opt. Soc. Am. A 15, 1241-1255 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1241


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References

  1. A. Sommerfeld, “Über die Fortpflanzung des Lichtes in dispergierenden Medien,” Ann. Phys. (Leipzig) 44, 177–202 (1914). [CrossRef]
  2. L. Brillouin, “Über die Fortpflanzung des Lichtes in dispergierenden Medien,” Ann. Phys. (Leipzig) 44, 203–240 (1914). [CrossRef]
  3. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  4. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973).
  5. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE Press, Piscataway, N.J., 1991).
  6. A. G. Lieberman, “Transient analysis of electromagnetic reflection from dispersive materials,” (U.S. GPO, Washington, D.C., 1985).
  7. 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]
  8. S. Shen, K. E. Oughstun, “Dispersive pulse propagation in a double-resonance Lorentz medium,” J. Opt. Soc. Am. B 6, 948–963 (1989). [CrossRef]
  9. 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, 1395–1420 (1989). [CrossRef]
  10. P. Wyns, D. P. Foty, K. E. Oughstun, “Numerical analysis of the precursor fields in linear dispersive pulse propagation,” J. Opt. Soc. Am. A 6, 1421–1429 (1989). [CrossRef]
  11. K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79, 1379–1390 (1991). [CrossRef]
  12. 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]
  13. C. D. Hechtman, C. Hsue, “Transient analysis of a step wave propagating in a lossy dielectric,” J. Appl. Phys. 65, 3335–3339 (1989). [CrossRef]
  14. J. J. A. Klaasen, “Time-domain analysis of one-dimensional electromagnetic scattering by lossy media,” (Electromagnetic Pulse Group, Physics and Electronics Laboratory, Netherlands Organization for Applied Scientific Research, The Hague, 1990).
  15. H. L. Bertoni, L. Carin, L. B. Felsen, S. U. Pillai, eds., Ultra-Wideband Short-Pulse Electromagnetics (Plenum, New York, 1993).
  16. K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).
  17. A. Taflove, Computational Electrodynamics. The Finite-Difference Time-Domain Method (Artech, Norwood, Mass., 1995).
  18. P. G. Petropoulos, “The wave hierarchy for propagation in relaxing dielectrics,” Wave Motion 21, 253–262 (1995). [CrossRef]
  19. J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995). [CrossRef]
  20. S. L. Dvorak, “Exact, closed-form expressions for transient fields in homogeneously filled waveguides,” IEEE Trans. Microwave Theory Tech. 42, 2164–2170 (1994). [CrossRef]
  21. S. L. Dvorak, D. G. Dudley, “Propagation of ultra-wideband electromagnetic pulses through dispersive media,” IEEE Trans. Electromagn. Compat. 37, 192–200 (1995). [CrossRef]
  22. S. L. Dvorak, D. G. Dudley, “A comment on propagation of ultra-wideband electromagnetic pulses through dispersive media—author’s reply,” IEEE Trans. Electromagn. Compat. 38, 203–205 (1996).
  23. H.-Y. Pao, S. L. Dvorak, D. G. Dudley, “An accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space (TE case),” IEEE Trans. Antennas Propag. 44, 918–924 (1996). [CrossRef]
  24. H.-Y. Pao, S. L. Dvorak, D. G. Dudley, “An accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space (TM case),” IEEE Trans. Antennas Propag. 44, 925–932 (1996). [CrossRef]
  25. S. L. Dvorak, R. W. Ziolkowski, D. G. Dudley, “Propagation of ultra-wideband electromagnetic pulses through lossy plasmas,” Radio Sci. 32, 239–250 (1997). [CrossRef]
  26. L. P. Huelsman, Active and Passive Analog Filter Design: An Introduction (McGraw-Hill, New York, 1993).
  27. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).
  28. S. L. Dvorak, E. F. Kuester, “Numerical computation of the incomplete Lipschitz–Hankel integral Je0(a, z),” J. Comput. Phys. 87, 301–327 (1990). [CrossRef]
  29. M. M. Mechaik, S. L. Dvorak, “Series expansions for the incomplete Lipschitz–Hankel integral Je0(a, z),” Radio Sci. 30, 1393–1404 (1995). [CrossRef]
  30. K. E. Oughstun, G. C. Sherman, “Uniform asymptotic description of ultrashort rectangular optical pulse propagation in a linear, causally dispersive medium,” Phys. Rev. A 41, 6090–6113 (1990). [CrossRef] [PubMed]
  31. K. E. Oughstun, G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, Berlin, 1994).

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