Abstract

The derivation and the application of a numerical method designed to study the propagation of pulsed electromagnetic fields into dispersive dielectric materials are reported. A Fourier series based methodology, appropriate for a useful class of pulse train incident signals, is presented and utilized to study the dynamics of dispersive pulse propagation in a half-space constructed of a Debye or a Lorentz model medium. Computed solutions are presented showing precursor propagation excited by pulses obliquely incident upon a planar boundary to the medium. The results show that oblique incident pulses upon a Lorentz medium can excite different types of precursor, propagating in unique directions within the half-space.

© 1995 Optical Society of America

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  1. J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
    [CrossRef]
  2. J. Benford, J. Swegle, High Power Microwaves (Artech, Boston, Mass., 1992).
  3. R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38, 671–673 (1981).
    [CrossRef]
  4. R. L. Fork, C. V. Shank, Y. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
    [CrossRef]
  5. R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
    [CrossRef]
  6. A. Sommerfeld, Optics (Academic, New York, 1949).
  7. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).
  8. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  9. 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]
  10. S. Shen, K. E. Oughstun, “Dispersive pulse propagation in a double-resonance Lorentz medium,” J. Opt. Soc. Am. B 6, 948–963 (1989).
    [CrossRef]
  11. K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79, 1379–1390 (1991).
    [CrossRef]
  12. K. E. Oughstun, J. E. K. Laurens, “Asymptotic description of electromagnetic pulse propagation in a linear, causally dispersive medium,” Radio Sci. 26, 245–258 (1991).
    [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. K. E. Oughstun, G. C. Sherman, “Propagation of electromagnetic pulses in a dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. B 5, 817–849 (1988).
    [CrossRef]
  15. 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]
  16. K. A. Oughstun, P. Wyns, D. P. Foty, “Numerical determination of the signal velocity in dispersive pulse propagation,” J. Opt. Soc. Am. A 6, 1430–1440 (1989).
    [CrossRef]
  17. K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulse propagation in dispersive planar dielectrics,” Bioelectromagnetics 10, 35–49 (1989).
    [CrossRef] [PubMed]
  18. 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]
  19. R. Joseph, S. Hagness, A. Taflove, “Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses,” Opt. Lett. 16, 1412–1414 (1991).
    [CrossRef] [PubMed]
  20. D. H. Lam, “Finite difference methods for transient signal propagation in stratified dispersive media,” Tech. Rep. 3892-1 (Electro-science Laboratory, Ohio State University, Columbus, Ohio, 1975).
  21. R. J. Luebbers, F. Hunsberger, “FD-TD for n-th order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301 (1992).
    [CrossRef]
  22. T. Kashiwa, I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett. 3, 203–205 (1990).
    [CrossRef]
  23. J. C. Lin, C. K. Lam, “Coupling of Gaussian electromagnetic pulse into a muscle-bone model of biological structure,” J. Microwave Power 11(3), 67–75 (1976).
  24. T. M. Papazoglou, “Transmission of a transient electromagnetic plane wave into a lossy half-space,” J. Appl. Phys. 48, 3333–3341 (1975).
    [CrossRef]
  25. K. Sivaprasad, K. C. Stotz, N. N. Susungi, “Reflection of pulses at oblique incidence from stratified dispersive media,” IEEE Trans. Antennas Propag. AP-26, 95–99 (1976).
    [CrossRef]
  26. J. A. Fuller, J. R. Wait, “A pulsed dipole in the earth,” in Transient Electromagnetic Fields, L. B. Felsen, ed. (Springer-Verlag, New York, 1976).
    [CrossRef]
  27. C. J. F. Bottcher, P. Bordewijk, Dielectrics in Time-Dependent Fields, Vol. II of Theory of Electric Polarization (Elsevier, New York, 1978).
  28. J. Bolomey, C. Durix, D. Lesselier, “Time domain integral equation approach for inhomogeneous and dispersive slab problems,” IEEE Trans. Antennas Propag. AP-26, 658–667 (1978).
    [CrossRef]
  29. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
  30. P. G. Petropoulos, “Phase error control for FD-TD type methods,” in Ultra Wideband, Short Pulse Electromagnetics, H. Bertoni, ed. (Plenum, New York, 1993).
    [CrossRef]
  31. P. G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag. 42, 62–69 (1994).
    [CrossRef]
  32. A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977).
  33. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  34. R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1960).
  35. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).
  36. E. H. Grant, R. J. Sheppard, G. P. South, Dielectric Behavior of Biological Molecules in Solution (Oxford U. Press, Oxford, 1978).
  37. E. H. Grant, King’s College, London (Personal communication, 1988).
  38. H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).
  39. H. A. Lorentz, Theory of Electrons, 2nd ed. (Dover, New York, 1952).
  40. P. J. Turner, ACE/gr User’s Manual: Graphics for Exploratory Data Analysis, public domain graphics package received from Internet FTP site: amb4.ese.ogi.edu .

1994

P. G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag. 42, 62–69 (1994).
[CrossRef]

1992

R. J. Luebbers, F. Hunsberger, “FD-TD for n-th order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301 (1992).
[CrossRef]

1991

K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79, 1379–1390 (1991).
[CrossRef]

K. E. Oughstun, J. E. K. Laurens, “Asymptotic description of electromagnetic pulse propagation in a linear, causally dispersive medium,” Radio Sci. 26, 245–258 (1991).
[CrossRef]

R. Joseph, S. Hagness, A. Taflove, “Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses,” Opt. Lett. 16, 1412–1414 (1991).
[CrossRef] [PubMed]

1990

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]

T. Kashiwa, I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett. 3, 203–205 (1990).
[CrossRef]

1989

1988

1987

J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
[CrossRef]

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

1982

R. L. Fork, C. V. Shank, Y. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[CrossRef]

1981

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38, 671–673 (1981).
[CrossRef]

1978

J. Bolomey, C. Durix, D. Lesselier, “Time domain integral equation approach for inhomogeneous and dispersive slab problems,” IEEE Trans. Antennas Propag. AP-26, 658–667 (1978).
[CrossRef]

1976

J. C. Lin, C. K. Lam, “Coupling of Gaussian electromagnetic pulse into a muscle-bone model of biological structure,” J. Microwave Power 11(3), 67–75 (1976).

K. Sivaprasad, K. C. Stotz, N. N. Susungi, “Reflection of pulses at oblique incidence from stratified dispersive media,” IEEE Trans. Antennas Propag. AP-26, 95–99 (1976).
[CrossRef]

1975

T. M. Papazoglou, “Transmission of a transient electromagnetic plane wave into a lossy half-space,” J. Appl. Phys. 48, 3333–3341 (1975).
[CrossRef]

Adler, R. B.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1960).

Albanese, R.

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).

Benford, J.

J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
[CrossRef]

J. Benford, J. Swegle, High Power Microwaves (Artech, Boston, Mass., 1992).

Birngruber, R.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

Bolomey, J.

J. Bolomey, C. Durix, D. Lesselier, “Time domain integral equation approach for inhomogeneous and dispersive slab problems,” IEEE Trans. Antennas Propag. AP-26, 658–667 (1978).
[CrossRef]

Bordewijk, P.

C. J. F. Bottcher, P. Bordewijk, Dielectrics in Time-Dependent Fields, Vol. II of Theory of Electric Polarization (Elsevier, New York, 1978).

Bottcher, C. J. F.

C. J. F. Bottcher, P. Bordewijk, Dielectrics in Time-Dependent Fields, Vol. II of Theory of Electric Polarization (Elsevier, New York, 1978).

Brillouin, L.

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

Bromley, D.

J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
[CrossRef]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

Chu, L. J.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1960).

Durix, C.

J. Bolomey, C. Durix, D. Lesselier, “Time domain integral equation approach for inhomogeneous and dispersive slab problems,” IEEE Trans. Antennas Propag. AP-26, 658–667 (1978).
[CrossRef]

Durney, C. H.

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulse propagation in dispersive planar dielectrics,” Bioelectromagnetics 10, 35–49 (1989).
[CrossRef] [PubMed]

Fano, R. M.

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1960).

Fork, R. L.

R. L. Fork, C. V. Shank, Y. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[CrossRef]

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38, 671–673 (1981).
[CrossRef]

Foty, D. P.

Fujimoto, J. G.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

Fukai, I.

T. Kashiwa, I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett. 3, 203–205 (1990).
[CrossRef]

Fuller, J. A.

J. A. Fuller, J. R. Wait, “A pulsed dipole in the earth,” in Transient Electromagnetic Fields, L. B. Felsen, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

Gawande, A.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

Grant, E. H.

E. H. Grant, King’s College, London (Personal communication, 1988).

E. H. Grant, R. J. Sheppard, G. P. South, Dielectric Behavior of Biological Molecules in Solution (Oxford U. Press, Oxford, 1978).

Greene, B. I.

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38, 671–673 (1981).
[CrossRef]

Hagness, S.

Hunsberger, F.

R. J. Luebbers, F. Hunsberger, “FD-TD for n-th order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301 (1992).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Joseph, R.

Kashiwa, T.

T. Kashiwa, I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett. 3, 203–205 (1990).
[CrossRef]

Lam, C. K.

J. C. Lin, C. K. Lam, “Coupling of Gaussian electromagnetic pulse into a muscle-bone model of biological structure,” J. Microwave Power 11(3), 67–75 (1976).

Lam, D. H.

D. H. Lam, “Finite difference methods for transient signal propagation in stratified dispersive media,” Tech. Rep. 3892-1 (Electro-science Laboratory, Ohio State University, Columbus, Ohio, 1975).

Laurens, J. E. K.

K. E. Oughstun, J. E. K. Laurens, “Asymptotic description of electromagnetic pulse propagation in a linear, causally dispersive medium,” Radio Sci. 26, 245–258 (1991).
[CrossRef]

Lesselier, D.

J. Bolomey, C. Durix, D. Lesselier, “Time domain integral equation approach for inhomogeneous and dispersive slab problems,” IEEE Trans. Antennas Propag. AP-26, 658–667 (1978).
[CrossRef]

Lin, J. C.

J. C. Lin, C. K. Lam, “Coupling of Gaussian electromagnetic pulse into a muscle-bone model of biological structure,” J. Microwave Power 11(3), 67–75 (1976).

Lin, W. Z.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz, Theory of Electrons, 2nd ed. (Dover, New York, 1952).

Luebbers, R. J.

R. J. Luebbers, F. Hunsberger, “FD-TD for n-th order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301 (1992).
[CrossRef]

Medina, R.

Moten, K.

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulse propagation in dispersive planar dielectrics,” Bioelectromagnetics 10, 35–49 (1989).
[CrossRef] [PubMed]

Nussenzveig, H. M.

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

Oughstun, K. A.

Oughstun, K. E.

Papazoglou, T. M.

T. M. Papazoglou, “Transmission of a transient electromagnetic plane wave into a lossy half-space,” J. Appl. Phys. 48, 3333–3341 (1975).
[CrossRef]

Papoulis, A.

A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977).

Penn, J.

Petropoulos, P. G.

P. G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag. 42, 62–69 (1994).
[CrossRef]

P. G. Petropoulos, “Phase error control for FD-TD type methods,” in Ultra Wideband, Short Pulse Electromagnetics, H. Bertoni, ed. (Plenum, New York, 1993).
[CrossRef]

Price, D.

J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
[CrossRef]

Puliafito, C. A.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

Schoenlein, R. W.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

Shank, C. V.

R. L. Fork, C. V. Shank, Y. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[CrossRef]

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38, 671–673 (1981).
[CrossRef]

Shen, S.

Sheppard, R. J.

E. H. Grant, R. J. Sheppard, G. P. South, Dielectric Behavior of Biological Molecules in Solution (Oxford U. Press, Oxford, 1978).

Sherman, G. C.

Sivaprasad, K.

K. Sivaprasad, K. C. Stotz, N. N. Susungi, “Reflection of pulses at oblique incidence from stratified dispersive media,” IEEE Trans. Antennas Propag. AP-26, 95–99 (1976).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1949).

South, G. P.

E. H. Grant, R. J. Sheppard, G. P. South, Dielectric Behavior of Biological Molecules in Solution (Oxford U. Press, Oxford, 1978).

Stockham, T. G.

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulse propagation in dispersive planar dielectrics,” Bioelectromagnetics 10, 35–49 (1989).
[CrossRef] [PubMed]

Stotz, K. C.

K. Sivaprasad, K. C. Stotz, N. N. Susungi, “Reflection of pulses at oblique incidence from stratified dispersive media,” IEEE Trans. Antennas Propag. AP-26, 95–99 (1976).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Susungi, N. N.

K. Sivaprasad, K. C. Stotz, N. N. Susungi, “Reflection of pulses at oblique incidence from stratified dispersive media,” IEEE Trans. Antennas Propag. AP-26, 95–99 (1976).
[CrossRef]

Swegle, J.

J. Benford, J. Swegle, High Power Microwaves (Artech, Boston, Mass., 1992).

Sze, H.

J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
[CrossRef]

Taflove, A.

Turner, P. J.

P. J. Turner, ACE/gr User’s Manual: Graphics for Exploratory Data Analysis, public domain graphics package received from Internet FTP site: amb4.ese.ogi.edu .

Wait, J. R.

J. A. Fuller, J. R. Wait, “A pulsed dipole in the earth,” in Transient Electromagnetic Fields, L. B. Felsen, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

Wyns, P.

Yen, Y. T.

R. L. Fork, C. V. Shank, Y. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[CrossRef]

Appl. Phys. Lett.

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38, 671–673 (1981).
[CrossRef]

R. L. Fork, C. V. Shank, Y. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[CrossRef]

Bioelectromagnetics

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulse propagation in dispersive planar dielectrics,” Bioelectromagnetics 10, 35–49 (1989).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond laser–tissue interactions: retinal injury studies,” IEEE J. Quantum Electron. QE-23, 1836–1844 (1987).
[CrossRef]

IEEE Trans. Antennas Propag.

R. J. Luebbers, F. Hunsberger, “FD-TD for n-th order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301 (1992).
[CrossRef]

K. Sivaprasad, K. C. Stotz, N. N. Susungi, “Reflection of pulses at oblique incidence from stratified dispersive media,” IEEE Trans. Antennas Propag. AP-26, 95–99 (1976).
[CrossRef]

P. G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag. 42, 62–69 (1994).
[CrossRef]

J. Bolomey, C. Durix, D. Lesselier, “Time domain integral equation approach for inhomogeneous and dispersive slab problems,” IEEE Trans. Antennas Propag. AP-26, 658–667 (1978).
[CrossRef]

J. Appl. Phys.

T. M. Papazoglou, “Transmission of a transient electromagnetic plane wave into a lossy half-space,” J. Appl. Phys. 48, 3333–3341 (1975).
[CrossRef]

J. Benford, D. Price, H. Sze, D. Bromley, “Interaction of a vircator microwave generator with an enclosing resonant cavity,” J. Appl. Phys. 61, 2098–2100 (1987).
[CrossRef]

J. Microwave Power

J. C. Lin, C. K. Lam, “Coupling of Gaussian electromagnetic pulse into a muscle-bone model of biological structure,” J. Microwave Power 11(3), 67–75 (1976).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Microwave Opt. Technol. Lett.

T. Kashiwa, I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett. 3, 203–205 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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]

Proc. IEEE

K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79, 1379–1390 (1991).
[CrossRef]

Radio Sci.

K. E. Oughstun, J. E. K. Laurens, “Asymptotic description of electromagnetic pulse propagation in a linear, causally dispersive medium,” Radio Sci. 26, 245–258 (1991).
[CrossRef]

Other

J. Benford, J. Swegle, High Power Microwaves (Artech, Boston, Mass., 1992).

A. Sommerfeld, Optics (Academic, New York, 1949).

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

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

D. H. Lam, “Finite difference methods for transient signal propagation in stratified dispersive media,” Tech. Rep. 3892-1 (Electro-science Laboratory, Ohio State University, Columbus, Ohio, 1975).

J. A. Fuller, J. R. Wait, “A pulsed dipole in the earth,” in Transient Electromagnetic Fields, L. B. Felsen, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

C. J. F. Bottcher, P. Bordewijk, Dielectrics in Time-Dependent Fields, Vol. II of Theory of Electric Polarization (Elsevier, New York, 1978).

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

P. G. Petropoulos, “Phase error control for FD-TD type methods,” in Ultra Wideband, Short Pulse Electromagnetics, H. Bertoni, ed. (Plenum, New York, 1993).
[CrossRef]

A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1977).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

R. B. Adler, L. J. Chu, R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, New York, 1960).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).

E. H. Grant, R. J. Sheppard, G. P. South, Dielectric Behavior of Biological Molecules in Solution (Oxford U. Press, Oxford, 1978).

E. H. Grant, King’s College, London (Personal communication, 1988).

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

H. A. Lorentz, Theory of Electrons, 2nd ed. (Dover, New York, 1952).

P. J. Turner, ACE/gr User’s Manual: Graphics for Exploratory Data Analysis, public domain graphics package received from Internet FTP site: amb4.ese.ogi.edu .

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Figures (17)

Fig. 1
Fig. 1

Geometric reference for problem development. Illustration of a single harmonic component of a pulsed, transverse electric (TE) polarized plane wave incident at oblique angle θi upon a planar interface at z = 0.

Fig. 2
Fig. 2

Time variation of the incident-wave electric field. The example shows one period of a sinusoidal pulse train with trapezoidal modulation envelope. For this example the signal parameters are carrier frequency, fc = 10 GHz; pulse rise/fall time, a = 3 cycles; pulse duration, b = 10 cycles; and pulse repetition interval, T = 20 cycles of the carrier wave.

Fig. 3
Fig. 3

Planes of constant phase and constant amplitude for a nonuniform plane wave propagating in a lossy dielectric medium. A vector in the direction defined by the angle ψt is perpendicular to the planes of constant phase and defines the direction of propagation for the transmitted wave.

Fig. 4
Fig. 4

Frequency dependence of the single relaxation Debye medium model for water used in our computations. The model parameters are = 5.5, s = 80.1, τ = 8.1 × 10−12 s, and σc = 10−5 S m−1.

Fig. 5
Fig. 5

Transmitted electric-field signal (TE case) in a Debye medium for fc = 1 GHz. Each solution is plotted as it appears along the z axis (normal to the interface) and for pulse trains incident at angles (a) θi = 0°, (b) θi = 40°, and (c) θi = 80°.

Fig. 6
Fig. 6

Same as Fig. 5 but for fc = 10 GHz.

Fig. 7
Fig. 7

Resultant transmitted magnetic-field amplitude in a Debye medium for fc = 10 GHz. This is the time-domain signal computed at position (0, 0.005) for (a) normal incidence and (b) θi = 80°, showing the differences between the TE and transverse magnetic (TM) cases introduced by the transmission coefficients.

Fig. 8
Fig. 8

Comparison of the frequency behavior of transmission coefficient magnitudes at the interface to a Debye medium: (a) |T| at normal incidence compared with |TTE| and |TTM| for θi = 80°, (b) normalized versions of |TTE| and |TTM| for θi = 80° superimposed upon the discrete spectrum of the incident pulse train.

Fig. 9
Fig. 9

Frequency dependence of the single-resonance Lorentz model used in our computations. The model parameters are = 1.0, s = 2.5, ω0 = 4 × 1016 rad/s, and δ = 0.28 × 1016 s−1.

Fig. 10
Fig. 10

Transmitted electric-field signal (TE case) in a Lorentz medium for fc = 8 × 1014 Hz, below the material absorption band. Each response corresponds to a pulse train incident at θi = 80°. The solutions are plotted as a function of position along projection directions of (a) 0°, (b) 40°, and (c) 80° measured counterclockwise with respect to the +z axis.

Fig. 11
Fig. 11

Transmitted electric-field signal (TE case) in a Lorentz medium for fc = 8 × 1016 Hz, above the material absorption band. Each response corresponds to a pulse train incident at θi = 80°. The solutions are plotted as a function of position along projection directions of (a) 0°, (b) 40°, and (c) 80° measured counterclockwise with respect to the +z axis.

Fig. 12
Fig. 12

Computed results for the same conditions used to produce Fig. 11. The solutions are observed farther from the interface and show the surviving Sommerfeld precursor signals. The solutions are plotted along projection directions of (a) 0°, (b) 40°, and (c) 80°.

Fig. 13
Fig. 13

Transmitted electric-field signal (TE case) in a Lorentz medium for fc = 8 × 1015 Hz, within the material absorption band. Each response corresponds to a pulse train incident at θi = 80°. The solutions are plotted as a function of position along projection directions of (a) 0°, (b) 40°, and (c) 80° measured counterclockwise with respect to the +z axis. Both Brillouin and Sommerfeld precursor signals are evident in the solutions and have different propagation directions within the medium.

Fig. 14
Fig. 14

Material frequency response functions for (a) Debye and (b) Lorentz medium models. The curves show the frequency behavior of |TE|, expressed as 20 log(|TE|), for various depths. The response of the Debye medium is plotted at depths of 0.001, 0.01, 0.1 and 1 m. The Lorentz material response is shown for depths of 1, 10, and 100 μm.

Fig. 15
Fig. 15

Transmitted electric-field signal (TE case) in a Lorentz medium for fc = 8 × 1015 Hz, within the material absorption band. Each response corresponds to a pulse train incident at θi = 0° (normal incidence). The solutions are plotted as a function of position along the projection directions of (a) 0°, (b) 40°, and (c) 80°. Both the Brillouin and Sommerfeld precursor signals are refracted by the interface at an angle of ψt = 0°.

Fig. 16
Fig. 16

Frequency dependence of the angle of transmission, ψt, at the interface to the Lorentz medium for θi = 80° (dashed curve). Superimposed upon the plot is the discrete line spectrum, expressed as 20 log(|ck|), for the transmitted signal constructed at a depth of 10 μm in the material. The harmonic components below the absorption band are refracted at approximately 40°, and the components above the absorption band are refracted at approximately 80°. On the logarithmic scale the line spacing becomes very dense for the high frequency components. The highest-frequency component retained in the Fourier series was 4 × 1017 Hz, representing 2000 spectral components.

Fig. 17
Fig. 17

Geometry reference used to develop Eq. (42). The vectors r1, along direction α, and r2, along direction β, are used to estimate ψt, the wave-front propagation direction. The distances along each projection direction are d1 = |r1| and d2 = |r2|.

Tables (1)

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Table 1 Estimates of Propagation Direction ψt for Precursors in a Lorentz Medium

Equations (45)

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2 ( ω ) = 2 ( ω ) - i 2 ( ω ) ,             n 2 ( ω ) = 2 ( ω ) ,
E 1 + ( r , t ) = E 1 + ( r , t ) y ^ ,
E 1 ( r , t ) = [ E 1 + ( r , t ) + E 1 - ( r , t ) ] y ^ .
l ^ 1 + = ( sin θ i ) x ^ + ( cos θ i ) z ^ ,             l ^ 1 - = ( sin θ r ) x ^ - ( cos θ r ) z ^ .
E 2 ( r , t ) = E 2 + ( r , t ) y ^ .
E 1 + ( r , t ) = E 1 + ( r , t + T ) ,
E 0 + ( t ) = f ( t ) sin ( ω c t )
E 1 + ( t ) = δ ¯ ( t ) * E 0 + ( t ) ,
δ ¯ ( t ) = m = - δ ( t + m T ) ,
f ( t ) = { ( 1 / a ) t 0 < t < a 1 a < t < ( b - a ) 1 - ( 1 / a ) [ t - ( b - a ) ] ( b - a ) < t < b 0 b < t < T ,
E 1 + ( t ) = m = - z m exp ( i m ω 0 t ) ,
E ˜ 1 + ( m ) = c m exp ( i ϕ m ) ,
c m = 2 z m = A m 2 + B m 2 ,             ϕ m = - tan - 1 ( B m A m ) ,
E 1 + ( r , m ) = E ˜ 1 + ( m ) exp [ - i k 1 + ( m ) · r ] y ^ ,
k 1 + ( m ) = k 1 ( m ) ( sin θ i ) x ^ + k 1 ( m ) ( cos θ i ) z ^ ,
H 1 + ( r , m ) = - cos θ i η 1 E ˜ 1 + ( m ) exp [ - i k 1 + ( m ) · r ] x ^ + sin θ i η 1 E ˜ 1 + ( m ) exp [ - i k 1 + ( m ) · r ] z ^ ,
H 1 + ( r , m ) = E ˜ 1 + ( m ) η 1 exp [ - i k 1 + ( m ) · r ] y ^ ,
E 1 + ( r , m ) = ( cos θ i ) E ˜ 1 + ( m ) exp [ - i k 1 + ( m ) · r ] x ^ - ( sin θ i ) E ˜ 1 + ( m ) exp [ - i k 1 + ( m ) · r ] z ^ .
E 2 ( r , m ) = T ˜ TE ( θ i , m ) E ˜ 1 + ( m ) exp [ - i k 2 + ( m ) · r ] y ^ ,
T ˜ TE ( θ i , m ) = 2 μ 2 / 2 ( m ) cos θ i μ 2 / 2 ( m ) cos θ i + μ 1 / 1 cos [ θ t ( m ) ] ,
k 2 + ( m ) = k 2 ( m ) sin [ θ t ( m ) ] x ^ + k 2 ( m ) cos [ θ t ( m ) ] z ^ ,
sin [ θ t ( m ) ] = n 1 n 2 ( m ) sin θ i ,
cos [ θ t ( m ) ] = { 1 - [ n 1 n 2 ( m ) sin θ i ] 2 } 1 / 2 ,
l ^ 2 + ( m ) = sin [ ψ t ( m ) ] x ^ + cos [ ψ t ( m ) ] z ^ ,
tan [ ψ t ( m ) ] = k 1 ( m ) sin θ i q ( m ) ,
q ( m ) = γ [ α 2 ( m ) sin ξ + β 2 ( m ) cos ξ ] ,
γ exp ( i ξ ) = cos [ θ t ( m ) ] ,
H 2 + ( r , m ) = - cos [ θ t ( m ) ] η 2 ( m ) T ˜ TE ( θ i , m ) E ˜ 1 + ( m ) × exp [ - i k 2 + ( m ) · r ] x ^ + sin [ θ t ( m ) ] η 2 ( m ) T ˜ TE ( θ i , m ) E ˜ 1 + ( m ) × exp [ - i k 2 + ( m ) · r ] z ^ ,
H 2 + ( r , m ) = T ˜ TM ( θ i , m ) E ˜ 1 + ( m ) η 2 ( m ) exp [ - i k 2 + ( m ) · r ] y ^ ,
E 2 + ( r , m ) = cos [ θ t ( m ) ] T ˜ TM ( θ i , m ) E ˜ 1 + ( m ) exp [ - i k 2 + ( m ) · r ] x ^ - sin [ θ t ( m ) ] T ˜ TM ( θ i , m ) E ˜ 1 + ( m ) × exp [ - i k 2 + ( m ) · r ] z ^ .
T ˜ TM ( θ i , m ) = 2 μ 2 / 2 ( m ) cos θ i μ 1 / 1 cos θ i + μ 2 / 2 ( m ) cos [ θ t ( m ) ] .
E 2 ( r , t ) = Re ( m = 1 M T ˜ TE ( θ i , m ) E ˜ 1 + ( m ) × exp { i [ m ω 0 t - k 2 + ( m ) · r ] } ) y ^ ,
2 ( ω ) = + s - 1 + ω 2 τ 2 ,
2 ( ω ) = ( s - ) ω τ 1 + ω 2 τ 2 + σ c ω 0 ,
= 5.5 , s = 80.1 , τ = 8.1 × 10 - 12 s , σ c = 10 - 5 S m - 1 .
2 ( ω ) = - ω L 2 ( s - ) ω 2 - 2 i ω δ - ω L 2 ,
= 1.0 , s = 2.5 , ω L = 4 × 10 16 rad / s , δ = 0.28 × 10 16 s - 1 ,
ω L 2 - δ 2 < ω < ω 1 2 - δ 2 ,
ω 1 = ω L 2 + d 2 ,             d 2 = ω L 2 ( s - ) .
H TE ( r , θ i , m ) = T ˜ TE ( θ i , m ) exp [ - i k 2 + ( m ) · r ] .
r 1 = d 1 sin ( α ) x ^ + d 1 cos ( α ) z ^ , r 2 = d 2 sin ( β ) x ^ + d 2 cos ( β ) z ^ , h = h sin ( ψ t ) x ^ + h cos ( ψ t ) z ^
h = r 1 · h h = r 2 · h h .
ψ ^ t = tan - 1 ( d 1 cos α - d 2 cos β d 2 sin β - d 1 sin α ) .
A m = 2 T 0 a t a sin ( ω c t ) cos ( m ω 0 t ) d t + 2 T a b - a sin ( ω c t ) cos ( m ω 0 t ) d t + 2 T b - a b { 1 - ( 1 a ) [ t - ( b - a ) ] } × sin ( ω c t ) cos ( m ω 0 t ) d t , B m = 2 T 0 a t a sin ( ω c t ) sin ( m ω 0 t ) d t + 2 T a b - a sin ( ω c t ) sin ( m ω 0 t ) d t + 2 T b - a b { 1 - ( 1 a ) [ t - ( b - a ) ] } × sin ( ω c t ) sin ( m ω 0 t ) d t ,
A 0 = 0 , A m = 1 a T { sin [ a ( ω c - m ω 0 ) ] ( ω c - m ω 0 ) 2 - sin [ b ( ω c - m ω 0 ) ] ( ω c - m ω 0 ) 2 + sin [ ( b - a ) ( ω c - m ω 0 ) ] ( ω c - m ω 0 ) 2 } + 1 a T { sin [ a ( ω c + m ω 0 ) ] ( ω c + m ω 0 ) 2 - sin [ b ( ω c + m ω 0 ) ] ( ω c + m ω 0 ) 2 + sin [ ( b - a ) ( ω c + m ω 0 ) ] ( ω c + m ω 0 ) 2 } , B m = 1 a T { cos [ a ( ω c - m ω 0 ) ] ( ω c - m ω 0 ) 2 - cos [ b ( ω c - m ω 0 ) ] ( ω c - m ω 0 ) 2 + cos [ ( b - a ) ( ω c - m ω 0 ) ] ( ω c - m ω 0 ) 2 - 1 ( ω c - m ω 0 ) 2 } - 1 a T { cos [ a ( ω c + m ω 0 ) ] ( ω c + m ω 0 ) 2 - cos [ b ( ω c + m ω 0 ) ] ( ω c + m ω 0 ) 2 + cos [ ( b - a ) ( ω c + m ω 0 ) ] ( ω c + m ω 0 ) 2 - 1 ( ω c - m ω 0 ) 2 }

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