Abstract

The space-frequency theory of the propagation of an ultrawideband radiation in dielectric media is presented. Characterization of the material via its susceptibility leads to a transfer function, which describes the response of the medium in the frequency domain. This description enables the consideration of broadband signals, taking into account inhomogeneous absorptive and dispersive effects of the medium. Analytical expressions are derived when a pulse-modulated signal is propagating in a general dielectric material. Conditions for apparent “superluminal” and pulse compression effects are identified. The theory is applied for a special case of transmission inside a resonant medium, revealing analytical approximations for the parameters of a Gaussian propagating pulse in terms of initial pulse width, carrier frequency, and medium parameters. Constraints of the derived analytical expressions are discussed, pointing out conditions of approximation validity. We demonstrate the approach by studying the propagation of ultrawideband signals, while transmitted in the vicinity of the 60 GHz absorption peak of the atmospheric medium at millimeter wavelengths.

© 2009 Optical Society of America

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  1. A. Sommerfeld, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 177-202 (1914).
    [CrossRef]
  2. L. Brillouin, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 203-240 (1914).
    [CrossRef]
  3. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  4. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).
  5. O. E. Delange, “Propagation studies at microwave frequencies by means of very short pulses,” Bell Syst. Tech. J. 31, 91-103 (1952).
  6. M. P. Forrer, “Analysis of millimicrosecond RF pulse transmission,” Proc. IRE 46, 1830-1835 (1958).
    [CrossRef]
  7. G. I. Terina, “On distortion of pulses in ionospheric plasma,” Radio Eng. Electron. Phys. 12, 109-113 (1967).
  8. L. E. Vogler, “Pulse distortion in resonant and nonresonant gases,” Radio Sci. 5, 1301-1305 (1970).
    [CrossRef]
  9. D. B. Trizna and 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]
  10. C. J. Gibbins, “Propagation of very short pulses through the absorptive and dispersive atmosphere,” IEE Proc., Part H: Microwaves, Antennas Propag. 137, 304-310 (1990).
    [CrossRef]
  11. A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
    [CrossRef]
  12. K. E. Oughstun and 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. C. M. Balictsis and K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian-pulse propagation in a causal, dispersive dielectrics,” Phys. Rev. E 47, 3645-3669 (1993).
    [CrossRef]
  14. K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer Series on Wave Phenomena (Springer, 1994).
  15. C. M. Balictsis and 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]
  16. H. Xiao and K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in a causally dispersive, absorptive dielectric,” J. Opt. Soc. Am B 16, 1773-1785 (1999).
    [CrossRef]
  17. N. A. Cartwright and K. E. Oughstun, “Pulse centroid velocity of the Poynting vector,” J. Opt. Soc. Am. A 21, 439-450 (2004).
    [CrossRef]
  18. Y. Pinhasi, Yu. Lurie and A. Yahalom, “Space-frequency model of ultra wide-band interactions in millimeter wave masers,” Phys. Rev. E 71, 036503 (2005).
    [CrossRef]
  19. H. A. Kramers, “Some remarks on the theory of absorption and refraction of x-rays,” Nature 117, 775-778 (1926).
  20. R. de L. Kronig, “On the theory of dispersion of x-rays,” J. Opt. Soc. Am. 12, 547-557 (1926).
    [CrossRef]
  21. P. Diament, Wave Transmission and Fiber Optics, Intl. ed. (Maxwell Macmillan, 1990).
  22. S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738-741 (1982).
    [CrossRef]
  23. A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
    [CrossRef]
  24. M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
    [CrossRef]
  25. Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
    [CrossRef]
  26. A. Yariv, Quantum Electronics (Wiley, 1988).
  27. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  28. H. J. Liebe, “MPM--An atmospheric millimeter-wave propagation model,” Int. J. Infrared Millim. Waves 10, 631-650 (1989).
    [CrossRef]
  29. H. J. Liebe, “Atmospheric EHF window transparencies near 35, 90,140 and 220 GHz,” IEEE Trans. Antennas Propag. 31, 127-135 (1983).
    [CrossRef]
  30. A. Yahalom and Y. Pinhasi, “Control of intense millimeter wave propagation by tailoring the dispersive properties of the medium,” in Quasi-Optical Control of Intense Microwave Transmission, Vol. 203 of NATO Science Series II: Mathematics, Physics and Chemistry, J.L.Hirshfield and M.I.Petelin, eds. (Springer, 2005), pp. 219-237.
    [CrossRef]

2005 (1)

Y. Pinhasi, Yu. Lurie and A. Yahalom, “Space-frequency model of ultra wide-band interactions in millimeter wave masers,” Phys. Rev. E 71, 036503 (2005).
[CrossRef]

2004 (2)

N. A. Cartwright and K. E. Oughstun, “Pulse centroid velocity of the Poynting vector,” J. Opt. Soc. Am. A 21, 439-450 (2004).
[CrossRef]

Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
[CrossRef]

2000 (1)

M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
[CrossRef]

1999 (1)

H. Xiao and K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in a causally dispersive, absorptive dielectric,” J. Opt. Soc. Am B 16, 1773-1785 (1999).
[CrossRef]

1997 (1)

C. M. Balictsis and 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]

1993 (2)

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

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

1990 (1)

C. J. Gibbins, “Propagation of very short pulses through the absorptive and dispersive atmosphere,” IEE Proc., Part H: Microwaves, Antennas Propag. 137, 304-310 (1990).
[CrossRef]

1989 (1)

H. J. Liebe, “MPM--An atmospheric millimeter-wave propagation model,” Int. J. Infrared Millim. Waves 10, 631-650 (1989).
[CrossRef]

1988 (1)

1983 (1)

H. J. Liebe, “Atmospheric EHF window transparencies near 35, 90,140 and 220 GHz,” IEEE Trans. Antennas Propag. 31, 127-135 (1983).
[CrossRef]

1982 (3)

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
[CrossRef]

D. B. Trizna and 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]

1970 (1)

L. E. Vogler, “Pulse distortion in resonant and nonresonant gases,” Radio Sci. 5, 1301-1305 (1970).
[CrossRef]

1967 (1)

G. I. Terina, “On distortion of pulses in ionospheric plasma,” Radio Eng. Electron. Phys. 12, 109-113 (1967).

1958 (1)

M. P. Forrer, “Analysis of millimicrosecond RF pulse transmission,” Proc. IRE 46, 1830-1835 (1958).
[CrossRef]

1952 (1)

O. E. Delange, “Propagation studies at microwave frequencies by means of very short pulses,” Bell Syst. Tech. J. 31, 91-103 (1952).

1926 (2)

H. A. Kramers, “Some remarks on the theory of absorption and refraction of x-rays,” Nature 117, 775-778 (1926).

R. de L. Kronig, “On the theory of dispersion of x-rays,” J. Opt. Soc. Am. 12, 547-557 (1926).
[CrossRef]

1914 (2)

A. Sommerfeld, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 177-202 (1914).
[CrossRef]

L. Brillouin, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 203-240 (1914).
[CrossRef]

Alfano, R.

A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
[CrossRef]

Balictsis, C. M.

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

Bhattacharyya, S.

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

Brillouin, L.

L. Brillouin, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 203-240 (1914).
[CrossRef]

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

Cartwright, N. A.

Chu, S.

A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
[CrossRef]

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

Dan, M.

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

Delange, O. E.

O. E. Delange, “Propagation studies at microwave frequencies by means of very short pulses,” Bell Syst. Tech. J. 31, 91-103 (1952).

Diament, P.

P. Diament, Wave Transmission and Fiber Optics, Intl. ed. (Maxwell Macmillan, 1990).

Forrer, M. P.

M. P. Forrer, “Analysis of millimicrosecond RF pulse transmission,” Proc. IRE 46, 1830-1835 (1958).
[CrossRef]

Gibbins, C. J.

C. J. Gibbins, “Propagation of very short pulses through the absorptive and dispersive atmosphere,” IEE Proc., Part H: Microwaves, Antennas Propag. 137, 304-310 (1990).
[CrossRef]

Harpaz, O.

Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
[CrossRef]

Hegeler, F.

M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Katz, A.

A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
[CrossRef]

Kramers, H. A.

H. A. Kramers, “Some remarks on the theory of absorption and refraction of x-rays,” Nature 117, 775-778 (1926).

Kronig, R. de L.

Liebe, H. J.

H. J. Liebe, “MPM--An atmospheric millimeter-wave propagation model,” Int. J. Infrared Millim. Waves 10, 631-650 (1989).
[CrossRef]

H. J. Liebe, “Atmospheric EHF window transparencies near 35, 90,140 and 220 GHz,” IEEE Trans. Antennas Propag. 31, 127-135 (1983).
[CrossRef]

Lurie, Yu.

Y. Pinhasi, Yu. Lurie and A. Yahalom, “Space-frequency model of ultra wide-band interactions in millimeter wave masers,” Phys. Rev. E 71, 036503 (2005).
[CrossRef]

Maitra, A.

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

Malloy, K. J.

M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
[CrossRef]

Mojahedi, M.

M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
[CrossRef]

Oughstun, K. E.

N. A. Cartwright and K. E. Oughstun, “Pulse centroid velocity of the Poynting vector,” J. Opt. Soc. Am. A 21, 439-450 (2004).
[CrossRef]

H. Xiao and K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in a causally dispersive, absorptive dielectric,” J. Opt. Soc. Am B 16, 1773-1785 (1999).
[CrossRef]

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

K. E. Oughstun and 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]

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer Series on Wave Phenomena (Springer, 1994).

Pinhasi, Y.

Y. Pinhasi, Yu. Lurie and A. Yahalom, “Space-frequency model of ultra wide-band interactions in millimeter wave masers,” Phys. Rev. E 71, 036503 (2005).
[CrossRef]

Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
[CrossRef]

A. Yahalom and Y. Pinhasi, “Control of intense millimeter wave propagation by tailoring the dispersive properties of the medium,” in Quasi-Optical Control of Intense Microwave Transmission, Vol. 203 of NATO Science Series II: Mathematics, Physics and Chemistry, J.L.Hirshfield and M.I.Petelin, eds. (Springer, 2005), pp. 219-237.
[CrossRef]

Sarkar, C. K.

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

Schamiloglu, E.

M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
[CrossRef]

Sen, A. K.

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

Sherman, G. C.

K. E. Oughstun and 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]

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer Series on Wave Phenomena (Springer, 1994).

Sommerfeld, A.

A. Sommerfeld, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 177-202 (1914).
[CrossRef]

Terina, G. I.

G. I. Terina, “On distortion of pulses in ionospheric plasma,” Radio Eng. Electron. Phys. 12, 109-113 (1967).

Trizna, D. B.

D. B. Trizna and 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]

Vilner, G.

Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
[CrossRef]

Vogler, L. E.

L. E. Vogler, “Pulse distortion in resonant and nonresonant gases,” Radio Sci. 5, 1301-1305 (1970).
[CrossRef]

Weber, T. A.

D. B. Trizna and 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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

Wong, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
[CrossRef]

Xiao, H.

H. Xiao and K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in a causally dispersive, absorptive dielectric,” J. Opt. Soc. Am B 16, 1773-1785 (1999).
[CrossRef]

Yahalom, A.

Y. Pinhasi, Yu. Lurie and A. Yahalom, “Space-frequency model of ultra wide-band interactions in millimeter wave masers,” Phys. Rev. E 71, 036503 (2005).
[CrossRef]

Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
[CrossRef]

A. Yahalom and Y. Pinhasi, “Control of intense millimeter wave propagation by tailoring the dispersive properties of the medium,” in Quasi-Optical Control of Intense Microwave Transmission, Vol. 203 of NATO Science Series II: Mathematics, Physics and Chemistry, J.L.Hirshfield and M.I.Petelin, eds. (Springer, 2005), pp. 219-237.
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1988).

Ann. Phys. (Leipzig) (2)

A. Sommerfeld, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 177-202 (1914).
[CrossRef]

L. Brillouin, “Über die Fortpflanzung des Lichtes in disperdierenden Medien,” Ann. Phys. (Leipzig) 349, 203-240 (1914).
[CrossRef]

Bell Syst. Tech. J. (1)

O. E. Delange, “Propagation studies at microwave frequencies by means of very short pulses,” Bell Syst. Tech. J. 31, 91-103 (1952).

IEE Proc., Part H: Microwaves, Antennas Propag. (1)

C. J. Gibbins, “Propagation of very short pulses through the absorptive and dispersive atmosphere,” IEE Proc., Part H: Microwaves, Antennas Propag. 137, 304-310 (1990).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

Y. Pinhasi, A. Yahalom, O. Harpaz, and G. Vilner, “Study of ultra wideband transmission in the extremely high frequency (EHF) band,” IEEE Trans. Antennas Propag. 52, 2833-2842 (2004).
[CrossRef]

H. J. Liebe, “Atmospheric EHF window transparencies near 35, 90,140 and 220 GHz,” IEEE Trans. Antennas Propag. 31, 127-135 (1983).
[CrossRef]

Int. J. Infrared Millim. Waves (2)

H. J. Liebe, “MPM--An atmospheric millimeter-wave propagation model,” Int. J. Infrared Millim. Waves 10, 631-650 (1989).
[CrossRef]

A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, and C. K. Sarkar, “Propagation of very short pulses at millimeter wavelengths through rain filled medium,” Int. J. Infrared Millim. Waves 14, 703-713 (1993).
[CrossRef]

J. Opt. Soc. Am B (1)

H. Xiao and K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in a causally dispersive, absorptive dielectric,” J. Opt. Soc. Am B 16, 1773-1785 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nature (1)

H. A. Kramers, “Some remarks on the theory of absorption and refraction of x-rays,” Nature 117, 775-778 (1926).

Phys. Rev. E (4)

C. M. Balictsis and 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]

Y. Pinhasi, Yu. Lurie and A. Yahalom, “Space-frequency model of ultra wide-band interactions in millimeter wave masers,” Phys. Rev. E 71, 036503 (2005).
[CrossRef]

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

M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758-5766 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

A. Katz, R. Alfano, S. Chu, and S. Wong, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292-1292 (1982).
[CrossRef]

Proc. IRE (1)

M. P. Forrer, “Analysis of millimicrosecond RF pulse transmission,” Proc. IRE 46, 1830-1835 (1958).
[CrossRef]

Radio Eng. Electron. Phys. (1)

G. I. Terina, “On distortion of pulses in ionospheric plasma,” Radio Eng. Electron. Phys. 12, 109-113 (1967).

Radio Sci. (2)

L. E. Vogler, “Pulse distortion in resonant and nonresonant gases,” Radio Sci. 5, 1301-1305 (1970).
[CrossRef]

D. B. Trizna and 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]

Other (7)

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

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer Series on Wave Phenomena (Springer, 1994).

P. Diament, Wave Transmission and Fiber Optics, Intl. ed. (Maxwell Macmillan, 1990).

A. Yariv, Quantum Electronics (Wiley, 1988).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

A. Yahalom and Y. Pinhasi, “Control of intense millimeter wave propagation by tailoring the dispersive properties of the medium,” in Quasi-Optical Control of Intense Microwave Transmission, Vol. 203 of NATO Science Series II: Mathematics, Physics and Chemistry, J.L.Hirshfield and M.I.Petelin, eds. (Springer, 2005), pp. 219-237.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Propagation of electromagnetic waves in a homogeneous dielectric medium.

Fig. 2
Fig. 2

Gaussian line shape in the frequency domain for σ i n = 1 .

Fig. 3
Fig. 3

Magnitude | χ e ( f ) | , real part χ e ( f ) , and imaginary part χ e ( f ) of susceptibility for χ DC = 0.001 and Q = 10 .

Fig. 4
Fig. 4

(a) Attenuation coefficient α ( f ) / β 0 and (b) Wavenumber increment Δ β ( f ) / β 0 = β ( f ) / β 0 1 for χ DC = 0.001 and Q = 10 .

Fig. 5
Fig. 5

Normalized (a) attenuation coefficient α ( f ) / β 0 and (b) wavenumber β ( f ) / β 0 and their derivatives for χ DC = 0.001 and Q = 10 .

Fig. 6
Fig. 6

(a) Delay time [ t d ( d / c ) ] / ( d / c ) , (b) pulse width σ o u t / σ i n , and (c) attenuation as functions of carrier frequency f c for χ DC = 0.001 and Q = 10 and several σ i n f 0 .

Fig. 7
Fig. 7

Graphs of (a) group delay, (b) standard deviation, and (c) amplitude as functions of initial pulse duration for χ DC = 0.001 and Q = 10 .

Fig. 8
Fig. 8

Normalized input A i n ( f ) and the integrand | A i n ( f ) H i n ( f + f 0 ) | for α 0 d = 1 , α d = 1.53 , α d = 3 , and ( 2 π σ i n ) 2 = 9.0 .

Fig. 9
Fig. 9

Normalized input A i n ( f ) and the integrand | A i n ( f ) H i n ( f + f 0 ) | for the case α 0 d = 1 , α d = 1.53 , α d = 3 , and ( 2 π σ i n ) 2 = 3.5 .

Fig. 10
Fig. 10

Millimeter wave (a) attenuation coefficient 20   log ( e ) α ( f ) in (dB/K m) and (b) wavenumber increment Δ β ( f ) in (deg/K m) for various values of relative humidity (RH).

Fig. 11
Fig. 11

Graphs of (a) group delay and (b) standard deviation versus frequency after a pulse propagation distance of d = 1   km .

Tables (1)

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Table 1 Attenuation Coefficient and Wavenumber and Their Derivatives

Equations (63)

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E ( r , f ) = + E ( r , t ) e j 2 π f t d t ,
E ̃ ( r , t ) = E ( r , t ) + j E ̂ ( r , t ) ,
E ̂ ( r , t ) = 1 π + E ( r , t ) t t d t
E ̃ ( r , f ) = + E ̃ ( r , t ) e j 2 π f t d t .
E ̃ ( r , f ) = { 2 E ( r , f ) , f > 0 0 , f < 0 } .
E ( r , f ) = 1 2 E ̃ ( r , f ) + 1 2 E ̃ ( r , f ) .
E ( r , t ) = + E ( r , f ) e + j 2 π f t d f = Re 0 E ̃ ( r , f ) e j 2 π f t d f .
E ̃ o u t ( f ) = E ̃ i n ( f ) e j k z ( f ) d ,
ε r ( f ) = ε ( f ) j ε ( f ) ,
t g [ δ ( f ) ] = ε ( f ) ε ( f ) = χ e ( f ) 1 + χ e ( f ) .
k z ( f ) = 2 π f c ε r ( f ) = j α ( f ) + β ( f ) ,
α ( f ) = 2 π f c ε ( f ) 2 { 1 + t g 2 [ δ ( f ) ] 1 } ,
β ( f ) = 2 π f c ε ( f ) 2 { 1 + t g 2 [ δ ( f ) ] + 1 } .
E i n ( t ) = Re { A i n ( t ) e j 2 π f c t } .
E i n ( f ) = 1 2 A i n ( f f c ) + 1 2 A i n [ ( f + f c ) ] ,
E ̃ o u t ( f ) = A i n ( f f c ) e j k z ( f ) d .
E o u t ( t ) = Re { A o u t ( t ) e j 2 π f c t } ,
A o u t ( t ) = + A i n ( f ) e j k z ( f + f c ) d d f .
A i n ( t ) = e t 2 / 2 σ i n 2 ,
A i n ( f ) = 2 π σ i n e ( 1 / 2 ) ( 2 π σ i n f ) 2 ,
k z ( f ) k c + k ( f f c ) + 1 2 k ( f f c ) 2 ,
k c k z ( f c ) ,
k | d k z d f | f c ,
k | d 2 k z d f 2 | f c .
n = 0 2 1 n ! k z ( n ) σ i n n n = 3 1 n ! k z ( n ) σ i n n ,
A o u t ( t ) = σ i n σ e [ t ( k d / 2 π ) ] 2 / 2 σ 2 e j k c d ,
σ 2 = σ i n 2 + j k ( 2 π ) 2 d = σ i n 2 + 1 ( 2 π ) 2 ( α + j β ) d .
Re { σ 2 } = σ i n 2 + α d / ( 2 π ) 2 > 0 .
| A o u t ( t ) | = σ i n | σ | exp [ α c d + 1 2 ( α d ) 2 ( 2 π σ i n ) 2 + α d ] e ( t t d ) 2 / 2 σ o u t 2 ,
t d = 1 2 π [ β α β d ( 2 π σ i n ) 2 + α d ] d ,
σ o u t 2 = σ i n 2 + α d ( 2 π ) 2 + [ β d ( 2 π ) 2 ] 2 σ i n 2 + α d ( 2 π ) 2 .
Attenuation = σ i n 2 | σ | 2 exp { 2 [ α c d + 1 2 ( α d ) 2 ( 2 π σ i n ) 2 + α d ] } ,
| σ | 2 = | σ 2 | = [ σ i n 2 + α d ( 2 π ) 2 ] 2 + [ β d ( 2 π ) 2 ] 2 .
σ i n 2 = ( | β | α ) d / ( 2 π ) 2 ,
σ o u t min 2 = 2 | β | d / ( 2 π ) 2 .
χ e ( f ) = χ DC 1 ( f f 0 ) 2 + j 1 Q f f 0 ,
χ e ( f ) = f 0 f Q χ DC 1 + Q 2 ( f f 0 f 0 f ) 2 ,
χ e ( f ) = Q ( f f 0 f 0 f ) χ e ( f ) .
χ e ( f ) f Δ f χ DC 1 + ( f f 0 Δ f / 2 ) 2 ,
χ e ( f ) ( f f 0 Δ f / 2 ) χ e ( f ) ,
k ( f ) = 2 π f c 1 + χ e ( f ) 2 π f c [ 1 + 1 2 χ e ( f ) ] .
β ( f ) β 0 f f 0 [ 1 + 1 2 χ e ( f ) ] ,
α ( f ) β 0 2 f f 0 χ e ( f ) ,
α ( f ) α 0 1 + Q 2 ( f f 0 f 0 f ) 2 ,
Δ β ( f ) β ( f ) 2 π f c Q ( f f 0 f 0 f ) α ( f ) ,
2 π σ i n f 0 Q = Δ f σ f > 8 α 0 d .
t d = 1 2 π β d = ( 1 Q 2 χ DC ) d c = ( 1 2 Q α 0 β 0 ) d c ,
σ o u t 2 = [ σ i n 2 2 ( Q π f 0 ) 2 α 0 d ] { 1 + [ 2 α 0 d Q ( 2 π σ i n f 0 Q ) 2 8 α 0 d ] 2 } ,
Attenuation = σ i n 2 [ σ i n 2 8 ( Q 2 π f 0 ) 2 α 0 d ] 2 + [ 2 Q ( 2 π f 0 ) 2 α 0 d ] 2 e 2 α 0 d ,
| A i n ( f ) H ( f + f 0 ) | = Am   e ( f f c ) 2 / 2 σ c 2 ,
Am = 2 π σ i n   exp [ α 0 d + 1 2 ( α d ) 2 ( 2 π σ i n ) 2 + α d ] ,
σ c 2 = 1 ( 2 π σ i n ) 2 + α d ,
f c = α d ( 2 π σ i n ) 2 + α d = α d σ c 2 .
Δ 1 = | α | d ( 2 π σ i n ) 2 = | α | d σ f 2 1 ,
σ f 2 = Δ 1 | α | d ,
σ c 2 = 1 ( 2 π σ i n ) 2 ( 1 Δ 1 ) σ f 2 ( 1 + Δ 1 ) ,
σ c σ f ( 1 + 1 2 Δ 1 ) ,
σ c σ f = 1 2 Δ 1 σ f .
| f c | < 2 | σ f σ c | Δ 1 σ f ,
| α | d σ c 2 < Δ 1 σ f ,
| α | d < Δ 1 σ f σ c 2 Δ 1 σ f .
| α | 2 d | α | < Δ 1 .
t n ¯ = + t n | A o u t ( t ) | d t + | A o u t ( t ) | d t .

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