Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Book cover Electromagnetic and Optical Pulse Propagation

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 224))

  • 859 Accesses

Abstract

The dynamical evolution of an electromagnetic pulse as it propagates through a linear, temporally dispersive medium (such as water) or system (such as a dielectric waveguide) is a classical problem in both electromagnetics and optics. With Maxwell’s unifying theory of electromagnetism and optics, Lorentz’s classical model of dielectric dispersion, and Einstein’s special theory of relativity, the stage was set for a long-standing problem of some controversy in classical physics, engineering, and applied mathematics. If the system was nondispersive, an arbitrary plane wave pulse would propagate unaltered in shape at the phase velocity of the wave field in the medium. For example, for distortionless wave propagation along the z-direction of a cartesian coordinate system, a one-dimensional wave is described by a single-valued function of the form f(z ± vt), where the argument φ = z ± vt is called the phase of the wave function. Any fixed value of this phase (for example, the value at the temporal center of the pulse) then propagates undistorted in shape along the ± z-direction with the velocity dz∕dt = ±v. The first partial derivatives of the wave function f(z ± vt) with respect to the independent variables z and t are then given by ∂f∕∂z = f′ and ∂f∕∂t = ±vf′, where f′ = df(ζ)∕dζ.

“The beginning is the most important part of the work.” Plato

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    John William Strutt, 3rd Baron Rayleigh (1842–1919).

  2. 2.

    Maxwell also played a defining role in introducing the nabla symbol ∇, so named because of its similarity with the harp, the Greek word for the Hebrew or Egyptian harp being “nabla”. This image arose in relation to a mathematical discourse between Maxwell and the Scottish mathematical physicist Peter Guthrie Tait regarding a problem on orthogonal surfaces. In his January 23, 1871 letter to Tait, Maxwell opened with “Still harping on that Nabla?”

  3. 3.

    For a more complete discussion of this early work, see E. Mach [46] as well as the well-known undergraduate optics text by Jenkins and White [47].

  4. 4.

    The role that this research played in Brillouin’s scientific career may be found in the biographical article by Mosseri [53].

  5. 5.

    The causality condition referred to as primitive causality states that the effect cannot precede the cause, where “cause” and “effect” must be appropriately defined for the particular situation considered. The causality condition known as relativistic causality states that any signal cannot propagate with a velocity greater than the speed of light c in vacuum [7].

  6. 6.

    Notice that Wait does not explicitly display the asymptotic parameter z in his analysis [103] as is done here for clarity.

  7. 7.

    The Beer–Lambert–Bouger law (more commonly referred to as “Beer’s law”) was originally discovered by Pierre Bouger, as published in his Essai d’Optique sur la Gradation de la Lumiere (Claude Jombert, Paris, 1729) and subsequently cited by Johann Heinrich Lambert in Photometri (V. E. Klett, Augsburg, 1760). The result was then extended by August Beer in Einleitung in die höhere Optik (Friedrich Viewig, Braunschweig, 1853) [see also Ann. Chem. Phys. 86, 78 (1852)] to include the concentration of solutions in the expression of the absorption coefficient for the intensity of light.

  8. 8.

    The mature dispersion regime typically includes propagation distances greater than an absorption depth at some characteristic frequency of the initial pulse.

References

  1. J. C. Maxwell, “A dynamical theory of the electromagnetic field,” Phil. Trans. Roy. Soc. (London), vol. 155, pp. 450–521, 1865.

    Google Scholar 

  2. J. C. Maxwell, A Treatise on Electricity and Magnetism. Oxford: Oxford University Press, 1873.

    MATH  Google Scholar 

  3. H. A. Lorentz, The Theory of Electrons. Leipzig: Teubner, 1906. Ch. IV.

    Google Scholar 

  4. A. Einstein, “Zur elektrodynamik bewegter körper,” Ann. Phys., vol. 17, pp. 891–921, 1905.

    Article  MATH  Google Scholar 

  5. R. B. Lindsay, Mechanical Radiation. New York: McGraw-Hill, 1960. Ch. 1.

    Google Scholar 

  6. J. S. Toll, “Causality and the dispersion relation: Logical foundations,” Phys. Rev., vol. 104, no. 6, pp. 1760–1770, 1956.

    Article  ADS  MathSciNet  Google Scholar 

  7. H. M. Nussenzveig, Causality and Dispersion Relations. New York: Academic, 1972. Ch. 1.

    Google Scholar 

  8. A. Sommerfeld, “Ein einwand gegen die relativtheorie der elektrodynamok und seine beseitigung,” Phys. Z., vol. 8, p. 841, 1907.

    MATH  Google Scholar 

  9. A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys., vol. 44, pp. 177–202, 1914.

    Article  Google Scholar 

  10. L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys., vol. 44, pp. 204–240, 1914.

    Google Scholar 

  11. L. Brillouin, Wave Propagation and Group Velocity. New York: Academic, 1960.

    MATH  Google Scholar 

  12. K. E. Oughstun, “Dynamical evolution of the precursor fields in linear dispersive pulse propagation in lossy dielectrics,” in Ultra-Wideband, Short-Pulse Electromagnetics 2 (L. Carin and L. B. Felsen, eds.), pp. 257–272, New York: Plenum, 1994.

    Google Scholar 

  13. J. A. Stratton, Electromagnetic Theory. New York: McGraw-Hill, 1941.

    MATH  Google Scholar 

  14. K. E. Oughstun, Propagation of Optical Pulses in Dispersive Media. PhD thesis, The Institute of Optics, University of Rochester, 1978.

    Google Scholar 

  15. 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, vol. 5, no. 4, pp. 817–849, 1988.

    Article  ADS  Google Scholar 

  16. S. Shen and K. E. Oughstun, “Dispersive pulse propagation in a double-resonance Lorentz medium,” J. Opt. Soc. Am. B, vol. 6, pp. 948–963, 1989.

    Article  ADS  Google Scholar 

  17. K. E. Oughstun and 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, vol. 6, no. 9, pp. 1394–1420, 1989.

    Article  ADS  MathSciNet  Google Scholar 

  18. K. E. Oughstun and G. C. Sherman, “Uniform asymptotic description of ultrashort rectangular optical pulse propagation in a linear, causally dispersive medium,” Phys. Rev. A, vol. 41, no. 11, pp. 6090–6113, 1990.

    Article  ADS  Google Scholar 

  19. C. M. Balictsis and K. E. Oughstun, “Uniform asymptotic description of ultrashort Gaussian pulse propagation in a causal, dispersive dielectric,” Phys. Rev. E, vol. 47, no. 5, pp. 3645–3669, 1993.

    Article  ADS  Google Scholar 

  20. K. E. Oughstun, “Noninstantaneous, finite rise-time effects on the precursor field formation in linear dispersive pulse propagation,” J. Opt. Soc. Am. A, vol. 12, pp. 1715–1729, 1995.

    Article  ADS  Google Scholar 

  21. J. A. Solhaug, K. E. Oughstun, J. J. Stamnes, and P. Smith, “Uniform asymptotic description of the Brillouin precursor in a single-resonance Lorentz model dielectric,” Pure Appl. Opt., vol. 7, no. 3, pp. 575–602, 1998.

    Article  ADS  Google Scholar 

  22. N. A. Cartwright and K. E. Oughstun, “Uniform asymptotics applied to ultrawideband pulse propagation,” SIAM Rev., vol. 49, no. 4, pp. 628–648, 2007.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. F. W. J. Olver, “Why steepest descents,” SIAM Rev., vol. 12, no. 2, pp. 228–247, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  24. C. Chester, B. Friedman, and F. Ursell, “An extension of the method of steepest descents,” Proc. Cambridge Phil. Soc., vol. 53, pp. 599–611, 1957.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. N. Bleistein, “Uniform asymptotic expansions of integrals with stationary point near algebraic singularity,” Com. Pure and Appl. Math., vol. XIX, no. 4, pp. 353–370, 1966.

    Article  MathSciNet  MATH  Google Scholar 

  26. N. Bleistein, “Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities,” J. Math. Mech, vol. 17, no. 6, pp. 533–559, 1967.

    MathSciNet  MATH  Google Scholar 

  27. R. A. Handelsman and N. Bleistein, “Uniform asymptotic expansions of integrals that arise in the analysis of precursors,” Arch. Rat. Mech. Anal., vol. 35, pp. 267–283, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  28. L. Felsen and N. Marcuvitz, Radiation and Scattering of Waves. Englewood Cliffs, NJ: Prentice-Hall, 1973.

    MATH  Google Scholar 

  29. N. Bleistein and R. Handelsman, Asymptotic Expansions of Integrals. New York: Dover, 1975.

    MATH  Google Scholar 

  30. K. E. Oughstun, P. Wyns, and D. P. Foty, “Numerical determination of the signal velocity in dispersive pulse propagation,” J. Opt. Soc. Am. A, vol. 6, no. 9, pp. 1430–1440, 1989.

    Article  ADS  Google Scholar 

  31. K. E. Oughstun and H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium,” Phys. Rev. Lett., vol. 78, no. 4, pp. 642–645, 1997.

    Article  ADS  Google Scholar 

  32. H. Xiao and K. E. Oughstun, “Failure of the group velocity description for ultrawideband pulse propagation in a double resonance Lorentz model dielectric,” J. Opt. Soc. Am. B, vol. 16, no. 10, pp. 1773–1785, 1999.

    Article  ADS  Google Scholar 

  33. C. M. Balictsis and K. E. Oughstun, “Uniform asymptotic description of Gaussian pulse propagation of arbitrary initial pulse width in a linear, causally dispersive medium,” in Ultra-Wideband, Short-Pulse Electromagnetics 2 (L. Carin and L. B. Felsen, eds.), pp. 273–283, New York: Plenum, 1994.

    Chapter  Google Scholar 

  34. K. E. Oughstun and C. M. Balictsis, “Gaussian pulse propagation in a dispersive, absorbing dielectric,” Phys. Rev. Lett., vol. 77, no. 11, pp. 2210–2213, 1996.

    Article  ADS  Google Scholar 

  35. 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, vol. 55, no. 2, pp. 1910–1921, 1997.

    Article  ADS  Google Scholar 

  36. G. P. Agrawal, Nonlinear Fiber Optics. Academic, 1989.

    MATH  Google Scholar 

  37. M. N. Islam, Ultrafast Fiber Switching Devices and Systems. Cambridge: Cambridge University Press, 1992.

    Google Scholar 

  38. C. Rullière, ed., Femtosecond Laser Pulses: Principles and Experiments. Berlin: Springer-Verlag, 1998.

    Google Scholar 

  39. W. R. Hamilton, “Researches respecting vibration, connected with the theory of light,” Proc. Royal Irish Academy, vol. 1, pp. 341–349, 1839.

    Google Scholar 

  40. G. G. Stokes, “Smith’s prize examination question no. 11,” in Mathematical and Physical Papers, vol. 5, Cambridge University Press, 1905. pg. 362.

    Google Scholar 

  41. L. Rayleigh, “On progressive waves,” Proc. London Math. Soc., vol. IX, pp. 21–26, 1877.

    Article  MathSciNet  MATH  Google Scholar 

  42. L. Rayleigh, “On the velocity of light,” Nature, vol. XXIV, pp. 52–55, 1881.

    Article  ADS  Google Scholar 

  43. M. Born and E. Wolf, Principles of Optics. Cambridge: Cambridge University Press, seventh (expanded) ed., 1999.

    Google Scholar 

  44. K. E. Oughstun and G. C. Sherman, Pulse Propagation in Causal Dielectrics. Berlin: Springer-Verlag, 1994.

    Book  Google Scholar 

  45. P. Drude, Lehrbuch der Optik. Leipzig: Teubner, 1900. Ch. V.

    Google Scholar 

  46. E. Mach, The Principles of Physical Optics: An Historical and Philosophical Treatment. New York: First German edition 1913. English translation 1926, reprinted by Dover, 1953. Ch. VII.

    Google Scholar 

  47. F. A. Jenkins and H. E. White, Fundamentals of Optics. New York: McGraw-Hill, third ed., 1957. Ch. 23.

    Google Scholar 

  48. W. Voigt, “Über die änderung der schwingungsform des lichtes beim fortschreiten in einem dispergirenden oder absorbirenden mittel,” Ann. Phys. und Chem. (Leipzig), vol. 68, pp. 598–603, 1899.

    Article  ADS  MATH  Google Scholar 

  49. W. Voigt, “Weiteres zur änderung der schwingungsform des lichtes beim fortschreiten in einem dispergirenden oder absorbirenden mittel,” Ann. Phys. (Leipzig), vol. 4, pp. 209–214, 1901.

    Article  ADS  MATH  Google Scholar 

  50. P. Ehrenfest, “Mißt der aberrationswinkel in fall einer dispersion des äthers die wellengeschwindigkeit?,” Ann. Phys. (Leipzig), vol. 33, p. 1571, 1910.

    Article  ADS  MATH  Google Scholar 

  51. A. Laue, “Die fortpflanzung der strahlung in dispergierenden und absorpierenden medien,” Ann. Phys., vol. 18, p. 523, 1905.

    Article  MATH  Google Scholar 

  52. P. Debye, “Näherungsformeln für die zylinderfunktionen für grosse werte des arguments und unbeschränkt verander liche werte des index,” Math Ann., vol. 67, pp. 535–558, 1909.

    Article  MathSciNet  MATH  Google Scholar 

  53. R. Mosseri, “Léon Brillouin: une vie à la croisée des ondes,” Sciences et Vie, vol. numero special “200 ans de sciences 1789-1989”, pp. 256–261, 1989.

    Google Scholar 

  54. W. Colby, “Signal propagation in dispersive media,” Phys. Rev., vol. 5, no. 3, pp. 253–265, 1915.

    Article  ADS  Google Scholar 

  55. T. H. Havelock, “The propagation of groups of waves in dispersive media,” Proc. Roy. Soc. A, vol. LXXXI, p. 398, 1908.

    Google Scholar 

  56. T. H. Havelock, The Propagation of Disturbances in Dispersive Media. Cambridge: Cambridge University Press, 1914.

    Google Scholar 

  57. L. Kelvin, “On the waves produced by a single impulse in water of any depth, or in a dispersive medium,” Proc. Roy. Soc., vol. XLII, p. 80, 1887.

    Google Scholar 

  58. E. T. Copson, Asymptotic Expansions. London: Cambridge University Press, 1965.

    Book  MATH  Google Scholar 

  59. P. M. Morse and H. Feshbach, Methods of Theoretical Physics. New York: McGraw-Hill, 1953. Vol. I.

    Google Scholar 

  60. H. Baerwald, “Über die fortpflanzung von signalen in disperdierenden medien,” Ann. Phys., vol. 7, pp. 731–760, 1930.

    Article  Google Scholar 

  61. N. S. Shiren, “Measurement of signal velocity in a region of resonant absorption by ultrasonic paramagnetic resonance,” Phys. Rev., vol. 128, pp. 2103–2112, 1962.

    Article  ADS  Google Scholar 

  62. T. A. Weber and D. B. Trizna, “Wave propagation in a dispersive and emissive medium,” Phys. Rev., vol. 144, pp. 277–282, 1966.

    Article  ADS  Google Scholar 

  63. P. Pleshko and I. Palócz, “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain,” Phys. Rev. Lett., vol. 22, pp. 1201–1204, 1969.

    Article  ADS  Google Scholar 

  64. O. Avenel, M. Rouff, E. Varoquaux, and G. A. Williams, “Resonant pulse propagation of sound in superfluid 3 He − B,” Phys. Rev. Lett., vol. 50, no. 20, pp. 1591–1594, 1983.

    Article  ADS  Google Scholar 

  65. E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid 3 He − B,” Phys. Rev. B, vol. 34, no. 11, pp. 7617–7640, 1986.

    Article  ADS  Google Scholar 

  66. C. Eckart, “The approximate solution of one-dimensional wave equations,” Rev. Modern Physics, vol. 20, pp. 399–417, 1948.

    Article  ADS  MathSciNet  Google Scholar 

  67. G. B. Whitham, “Group velocity and energy propagation for three-dimensional waves,” Comm. Pure Appl. Math., vol. XIV, pp. 675–691, 1961.

    Article  MathSciNet  MATH  Google Scholar 

  68. M. J. Lighthill, “Group velocity,” J. Inst. Maths. Applics., vol. 1, pp. 1–28, 1964.

    Article  MathSciNet  Google Scholar 

  69. L. J. F. Broer, “On the propagation of energy in linear conservative waves,” Appl. Sci. Res., vol. A2, pp. 329–344, 1950.

    MathSciNet  MATH  Google Scholar 

  70. C. O. Hines, “Wave packets, the Poynting vector, and energy flow: Part I – Non-dissipative (anisotropic) homogeneous media,” J. Geophysical Research, vol. 56, no. 1, pp. 63–72, 1951.

    Article  ADS  Google Scholar 

  71. M. A. Biot, “General theorems on the equivalence of group velocity and energy velocity,” Phys. Rev., vol. 105, pp. 1129–1137, 1957.

    Article  ADS  MATH  Google Scholar 

  72. C. O. Hines, “Wave packets, the Poynting vector, and energy flow: Part II – Group propagation through dissipative isotropic media,” J. Geophysical Research, vol. 56, no. 2, pp. 197–220, 1951.

    Article  ADS  Google Scholar 

  73. C. O. Hines, “Wave packets, the Poynting vector, and energy flow: Part III – Poynting and Macdonald velocities in dissipative anisotropic media (conclusions),” J. Geophysical Research, vol. 56, no. 4, pp. 535–544, 1951.

    Article  ADS  Google Scholar 

  74. R. M. Lewis, “Asymptotic theory of wave-propagation,” Archive Rational Mech. Analysis, vol. 20, pp. 191–250, 1965.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  75. R. M. Lewis, “Asymptotic theory of transients,” in Electromagnetic Wave Theory (J. Brown, ed.), pp. 845–869, New York: Pergamon, 1967.

    Chapter  Google Scholar 

  76. Y. A. Kravtsov, L. A. Ostrovsky, and N. S. Stepanov, “Geometrical optics of inhomogeneous and nonstationary dispersive media,” Proc. IEEE, vol. 62, pp. 1492–1510, 1974.

    Article  ADS  Google Scholar 

  77. D. Censor, “The group Doppler effect,” Journal Franklin Inst., vol. 299, pp. 333–338, 1975.

    Article  ADS  Google Scholar 

  78. D. Censor, “Fermat’s principle and real space-time rays in absorbing media,” J. Phys. A, vol. 10, pp. 1781–1790, 1977.

    Article  ADS  Google Scholar 

  79. D. Censor, “Wave packets and localized pulses – A dual approach,” Phys. Rev. A, vol. 24, pp. 1452–1459, 1981.

    Article  ADS  Google Scholar 

  80. V. Krejči and L. Pekárek, “Determination of dispersion curve parameters from transient wave,” Czech. J. Phys., vol. 17, 1967.

    Article  ADS  Google Scholar 

  81. L. B. Felsen, “Rays, dispersion surfaces and their uses for radiation and diffraction problems,” SIAM Rev., vol. 12, pp. 424–448, 1970.

    Article  Google Scholar 

  82. K. A. Connor and L. B. Felsen, “Complex space-time rays and their application to pulse propagation in lossy dispersive media,” Proc. IEEE, vol. 62, pp. 1586–1598, 1974.

    Article  ADS  Google Scholar 

  83. J. Arnaud, “A theory of Gaussian pulse propagation,” Opt. Quantum Electron., vol. 16, pp. 125–130, 1984.

    Article  Google Scholar 

  84. L. B. Felsen, “Transients in dispersive media-I. Theory,” IEEE Trans. Antennas Prop., vol. 17, pp. 191–200, 1969.

    Article  ADS  Google Scholar 

  85. G. M. Whitham and L. B. Felsen, “Transients in dispersive media-Part II: Excitation of space waves in a bounded cold magnetoplasma,” IEEE Trans. Antennas Prop., vol. 17, pp. 200–208, 1969.

    Article  ADS  Google Scholar 

  86. L. B. Felsen, “Asymptotic theory of pulse compression in dispersive media,” IEEE Trans. Antennas Prop., vol. 19, pp. 424–432, 1971.

    Article  ADS  Google Scholar 

  87. E. Heyman, “Complex source pulsed beam expansion of transient radiation,” Wave Motion, vol. 11, pp. 337–349, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  88. E. Heyman and L. B. Felsen, “Weakly dispersive spectral theory of transients (SST). Part I: Formulation and interpretation,” IEEE Trans. Antennas Prop., vol. 35, pp. 80–86, 1987.

    Article  ADS  MATH  Google Scholar 

  89. E. Heyman and L. B. Felsen, “Weakly dispersive spectral theory of transients (SST). Part II: Evaluation of the spectral integral,” IEEE Trans. Antennas Prop., vol. 35, pp. 574–580, 1987.

    Article  ADS  MATH  Google Scholar 

  90. E. Heyman and L. B. Felsen, “Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A, vol. 18, pp. 1588–1611, 2001.

    Article  ADS  Google Scholar 

  91. T. Melamed, E. Heyman, and L. B. Felsen, “Local spectral analysis of short-pule-excited scattering from weakly inhomogeneous media. Part I: Forward scattering,” IEEE Trans. Antennas Prop., vol. 47, pp. 1208–1217, 1999.

    Article  ADS  MATH  Google Scholar 

  92. T. Melamed, E. Heyman, and L. B. Felsen, “Local spectral analysis of short-pule-excited scattering from weakly inhomogeneous media. Part I: Inverse scattering,” IEEE Trans. Antennas Prop., vol. 47, pp. 1218–1227, 1999.

    Article  ADS  MATH  Google Scholar 

  93. T. Melamed and L. B. Felsen, “Pulsed-beam propagation in lossless dispersive media. I. A numerical example,” J. Opt. Soc. Am. A, vol. 15, pp. 1277–1284, 1998.

    Article  ADS  Google Scholar 

  94. T. Melamed and L. B. Felsen, “Pulsed-beam propagation in lossless dispersive media. II. Theory,” J. Opt. Soc. Am. A, vol. 15, pp. 1268–1276, 1998.

    Article  ADS  Google Scholar 

  95. J. D. Jackson, Classical Electrodynamics. New York: John Wiley & Sons, third ed., 1999.

    MATH  Google Scholar 

  96. R. S. Elliott, “Pulse waveform degradation due to dispersion in waveguide,” IRE Trans. Microwave Theory Tech., vol. 5, pp. 254–257, 1957.

    Article  ADS  Google Scholar 

  97. M. P. Forrer, “Analysis of millimicrosecond RF pulse transmission,” Proc. IRE, vol. 46, pp. 1830–1835, 1958.

    Article  Google Scholar 

  98. R. D. Wanselow, “Rectangular pulse distortion due to a nonlinear complex transmission propagation constant,” J. Franklin Inst., vol. 274, pp. 178–184, 1962.

    Article  Google Scholar 

  99. C. M. Knop and G. I. Cohn, “Comments on pulse waveform degradation due to dispersion in waveguide,” IEEE Trans. Microwave Theory Tech., vol. 11, pp. 445–447, 1963.

    Article  ADS  Google Scholar 

  100. C. M. Knop, “Pulsed electromagnetic wave propagation in dispersive media,” IEEE Trans. Antennas Prop., vol. 12, pp. 494–496, 1964.

    Article  ADS  Google Scholar 

  101. C. T. Case and R. E. Haskell, “On pulsed electromagnetic wave propagation in dispersive media,” IEEE Trans. Antennas Prop., vol. 14, p. 401, 1966.

    Article  ADS  Google Scholar 

  102. L. E. Vogler, “An exact solution for wave-form distortion of arbitrary signals in ideal wave guides,” Radio Sci., vol. 5, pp. 1469–1474, 1970.

    Article  ADS  Google Scholar 

  103. J. R. Wait, “Propagation of pulses in dispersive media,” Radio Sci., vol. 69D, pp. 1387–1401, 1965.

    Google Scholar 

  104. R. E. Haskell and C. T. Case, “Transient signal propagation in lossless, isotropic plasmas,” IEEE Trans. Antennas Prop., vol. 15, no. 3, pp. 458–464, 1967.

    Article  ADS  Google Scholar 

  105. R. E. Haskell and C. T. Case, “Transient signal propagation in lossless, isotropic plasmas: Volume I,” Tech. Rep. No. 212, Physical Sciences Research Papers, Microwave Physics Laboratory, Air Force Cambridge Research Laboratories, 1966.

    Google Scholar 

  106. R. E. Haskell and C. T. Case, “Transient signal propagation in lossless, isotropic plasmas: Volume II,” Tech. Rep. No. 241, Physical Sciences Research Papers, Microwave Physics Laboratory, Air Force Cambridge Research Laboratories, 1966.

    Google Scholar 

  107. D. Ludwig, “Uniform asymptotic expansions for wave propagation and diffraction problems,” SIAM Rev., vol. 12, pp. 325–331, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  108. M. D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A, vol. 1, no. 6, pp. 1604–1611, 1970.

    Article  ADS  Google Scholar 

  109. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett., vol. 18, no. 21, pp. 908–912, 1967.

    Article  ADS  Google Scholar 

  110. B. R. Horowitz and T. Tamir, “Unified theory of total reflection phenomena at a dielectric interface,” Applied Phys., vol. 1, pp. 31–38, 1973.

    Article  ADS  Google Scholar 

  111. C. C. Chan and T. Tamir, “Beam phenomena at and near critical incidence upon a dielectric interface,” J. Opt. Soc. Am. A, vol. 4, pp. 655–663, 1987.

    Article  ADS  Google Scholar 

  112. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik, vol. 6, no. 1, pp. 333–345, 1947.

    Article  ADS  Google Scholar 

  113. E. G. Skrotskaya, A. N. Makhlin, V. A. Kashin, and G. V. Skrotskiĭ, “Formation of a forerunner in the passage of the front of a light pulse through a vacuum-medium interface,” Zh. Eksp. Teor. Fiz., vol. 56, no. 1, pp. 220–226, 1969. [English translation: Sov. Phys. JETP vol. 29, 123–125 (1969].

    Google Scholar 

  114. E. Gitterman and M. Gitterman, “Transient processes for incidence of a light signal on a vacuum-medium interface,” Phys. Rev. A, vol. 13, pp. 763–776, 1976.

    Article  ADS  Google Scholar 

  115. J. G. Blaschak and J. Franzen, “Precursor propagation in dispersive media from short-rise-time pulses at oblique incidence,” J. Opt. Soc. Am. A, vol. 12, no. 7, pp. 1501–1512, 1995.

    Article  ADS  Google Scholar 

  116. N. A. Cartwright, “Electromagnetic plane-wave pulse transmission into a Lorentz half-space,” J. Opt. Soc. Am. A, vol. 28, no. 12, pp. 2647–2654, 2011.

    Article  ADS  Google Scholar 

  117. J. A. Marozas and K. E. Oughstun, “Electromagnetic pulse propagation across a planar interface separating two lossy, dispersive dielectrics,” in Ultra-Wideband, Short-Pulse Electromagnetics 3 (C. Baum, L. Carin, and A. P. Stone, eds.), pp. 217–230, New York: Plenum, 1996.

    Chapter  Google Scholar 

  118. J. M. Stone, Radiation and Optics, An Introduction to the Classical Theory. New York: McGraw-Hill, 1963.

    Google Scholar 

  119. C. L. Palombini and K. E. Oughstun, “Reflection and transmission of pulsed electromagnetic fields through multilayered biological media,” in Proc. 2011 International Conference on Electromagnetics in Advanced Applications, 2011. paper #216.

    Google Scholar 

  120. J. R. Wait, “Electromagnetic-pulse propagation in a simple dispersive medium,” Elect. Lett., vol. 7, pp. 285–286, 1971.

    Article  Google Scholar 

  121. P. Debye, Polar Molecules. New York: Dover, 1929.

    MATH  Google Scholar 

  122. J. R. Wait, “Electromagnetic fields of a pulsed dipole in dissipative and dispersive media,” Radio Sci., vol. 5, pp. 733–735, 1970.

    Article  ADS  Google Scholar 

  123. J. Jones, “On the propagation of a pulse through a dispersive medium,” Am. J. Physics, vol. 42, pp. 43–46, 1974.

    Article  ADS  Google Scholar 

  124. D. G. Anderson and J. I. H. Askne, “Wave packets in strongly dispersive media,” Proc. IEEE, vol. 62, pp. 1518–1523, 1974.

    Article  ADS  Google Scholar 

  125. D. Anderson, J. Askne, and M. Lisak, “Wave packets in an absorptive and strongly dispersive medium,” Phys. Rev. A, vol. 12, pp. 1546–1552, 1975.

    Article  ADS  Google Scholar 

  126. L. A. Vainshtein, “Propagation of pulses,” Usp. Fiz. Nauk., vol. 118, pp. 339–367, 1976. [English translation: Sov. Phys.-Usp. vol.19, 189–205, (1976)].

    Article  ADS  Google Scholar 

  127. S. A. Akhmanov, V. A. Yysloukh, and A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Usp. Fiz. Nauk., vol. 149, pp. 449–509, 1986. [English translation: Sov. Phys.-Usp. vol.29, 642–677 (1986)].

    Google Scholar 

  128. S. A. Akhamanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses. New York: American Institute of Physics, 1992.

    Google Scholar 

  129. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics. Cambridge: Cambridge University Press, 1990.

    Book  Google Scholar 

  130. N. D. Hoc, I. M. Besieris, and M. E. Sockell, “Phase-space asymptotic analysis of wave propagation in homogeneous dispersive and dissipative media,” IEEE Trans. Antennas Prop., vol. 33, no. 11, pp. 1237–1248, 1985.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  131. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev., vol. 40, pp. 749–759, 1932.

    Article  ADS  MATH  Google Scholar 

  132. K. E. Oughstun, “Computational methods in ultrafast time-domain optics,” Computing in Science & Engineering, vol. 5, no. 6, pp. 22–32, 2003.

    Article  Google Scholar 

  133. R. L. Veghte and C. A. Balanis, “Dispersion of transient signals in microstrip transmission lines,” IEEE Trans. Antennas Prop., vol. 34, no. 12, pp. 1427–1436, 1986.

    Google Scholar 

  134. K. Moten, C. H. Durney, and T. G. Stockham, “Electromagnetic pulse propagation in dispersive planar dielectrics,” Bioelectromagnetics, vol. 10, pp. 35–49, 1989.

    Article  Google Scholar 

  135. R. Albanese, J. Penn, and R. Medina, “Short-rise-time microwave pulse propagation through dispersive biological media,” J. Opt. Soc. Am. A, vol. 6, pp. 1441–1446, 1989.

    Article  ADS  Google Scholar 

  136. R. Albanese, J. Blaschak, R. Medina, and J. Penn, “Ultrashort electromagnetic signals: Biophysical questions, safety issues, and medical opportunities,” Aviation. Space and Environmental Medicine, vol. 65, no. 5, pp. 116–120, 1994.

    Google Scholar 

  137. T. Hosono, “Numerical inversion of Laplace transform,” Trans. IEE of Japan, vol. 99, no. 10, pp. 44–50, 1979.

    Google Scholar 

  138. T. Hosono, “Numerical inversion of Laplace transform and some applications to wave optics,” in Proceedings of the URSI Symposium on Electromagnetic Wave Theory, (München), pp. C1–C4, 1980.

    Google Scholar 

  139. T. Hosono, “Numerical inversion of Laplace transform and some applications to wave optics,” Radio Science, vol. 16, no. 6, pp. 1015–1019, 1981.

    Article  ADS  Google Scholar 

  140. P. Wyns, D. P. Foty, and K. E. Oughstun, “Numerical analysis of the precursor fields in dispersive pulse propagation,” J. Opt. Soc. Am. A, vol. 6, no. 9, pp. 1421–1429, 1989.

    Article  ADS  Google Scholar 

  141. H. Xiao and K. E. Oughstun, “Hybrid numerical-asymptotic code for dispersive pulse propagation calculations,” J. Opt. Soc. Am. A, vol. 15, no. 5, pp. 1256–1267, 1998.

    Article  ADS  Google Scholar 

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

    Chapter  Google Scholar 

  143. H. Dubner and J. Abate, “Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform,” J. Assoc. Comput. Mach., vol. 15, pp. 115–123, 1968.

    Article  MathSciNet  MATH  Google Scholar 

  144. R. Barakat, “Ultrashort optical pulse propagation in a dispersive medium,” J. Opt. Soc. Am. B, vol. 3, no. 11, pp. 1602–1604, 1986.

    Article  ADS  Google Scholar 

  145. T. Kashiwa and I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett., vol. 3, pp. 203–205, 1990.

    Article  Google Scholar 

  146. R. Joseph, S. Hagness, and 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., vol. 16, pp. 1412–1414, 1991.

    Article  ADS  Google Scholar 

  147. R. J. Luebbers and F. Hunsberger, “FD-TD for n-th order dispersive media,” IEEE Trans. Antennas Propag., vol. 40, pp. 1297–1301, 1992.

    Article  ADS  Google Scholar 

  148. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. Piscataway, NJ: IEEE Press, 1998.

    MATH  Google Scholar 

  149. L. A. Trefethen, “Group velocity in finite difference schemes,” SIAM Review, vol. 24, no. 2, pp. 113–136, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  150. D. Gabor, “Theory of communication,” J. Inst. Electrical Eng., vol. 93, no. 26, pp. 429–457, 1946.

    Google Scholar 

  151. E. T. Whittaker, “On the functions which are represented by the expansions of the interpolation theory,” Proc. Roy. Soc. Edinburgh, Sect. A, vol. 35, p. 181, 1915.

    Article  MATH  Google Scholar 

  152. C. E. Shannon, “Communication in the presence of noise,” Proc. IRE, vol. 37, p. 10, 1949.

    Article  MathSciNet  Google Scholar 

  153. L. M. Soroko, Holography and Coherent Optics. New York: Plenum, 1980. Ch. 5.

    Google Scholar 

  154. G. Kaiser, A Friendly Guide to Wavelets. Boston: Birkhäuser, 1994.

    MATH  Google Scholar 

  155. R. S. Beezley and R. J. Krueger, “An electromagnetic inverse problem for dispersive media,” J. Math. Phys., vol. 26, no. 2, pp. 317–325, 1985.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  156. G. Kristensson and R. J. Krueger, “Direct and inverse scattering in the time domain for a dissipative wave equation. I. Scattering operators,” J. Math. Phys., vol. 27, no. 6, pp. 1667–1682, 1986.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  157. G. Kristensson and R. J. Krueger, “Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles,” J. Math. Phys., vol. 27, no. 6, pp. 1683–1693, 1986.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  158. R. J. Krueger and R. L. Ochs, “A Green’s function approach to the determination of internal fields,” Wave Motion, vol. 11, pp. 525–543, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  159. J. P. Corones, M. E. Davison, and R. J. Krueger, “Direct and inverse scattering in the time domain via invariant embedding equations,” J. Acoustic Soc. Am., vol. 74, pp. 1535–1541, 1983.

    Article  ADS  MATH  Google Scholar 

  160. G. Kristensson and R. J. Krueger, “Direct and inverse scattering in the time domain for a dissipative wave equation. Part I. Scattering operators,” J. Math. Phys., vol. 27, pp. 1683–1693, 1986.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  161. G. Kristensson and R. J. Krueger, “Direct and inverse scattering in the time domain for a dissipative wave equation. Part II. Simultaneous reconstruction of dissipation and phase velocity profiles,” J. Math. Phys., vol. 27, pp. 1667–1682, 1986.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  162. G. Kristensson and R. J. Krueger, “Direct and inverse scattering in the time domain for a dissipative wave equation. Part III. Scattering operators in the presence of a phase velocity mismatch,” J. Math. Phys., vol. 28, pp. 360–370, 1987.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  163. E. Ammicht, J. P. Corones, and R. J. Krueger, “Direct and inverse scattering for viscoelestic media,” J. Acoustic Soc. Am., vol. 81, pp. 827–834, 1987.

    Article  ADS  Google Scholar 

  164. A. Karlsson, H. Otterheim, and R. Stewart, “Transient wave propagation in composite media: Green’s function approach,” J. Opt. Soc. Am. A, vol. 10, no. 5, pp. 886–895, 1993.

    Article  ADS  Google Scholar 

  165. L. Brillouin, “Propagation of electromagnetic waves in material media,” in Congrès International d’Electricité, vol. 2, pp. 739–788, Paris: Gauthier-Villars, 1933.

    Google Scholar 

  166. E. O. Schulz-DuBois, “Energy transport velocity of electromagnetic propagation in dispersive media,” Proc. IEEE, vol. 57, pp. 1748–1757, 1969.

    Article  Google Scholar 

  167. J. Askne and B. Lind, “Energy of electromagnetic waves in the presence of absorption and dispersion,” Phys. Rev. A, vol. 2, no. 6, pp. 2335–2340, 1970.

    Article  ADS  Google Scholar 

  168. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” Phys. A, vol. 3, pp. 233–245, 1970.

    Article  ADS  Google Scholar 

  169. D. Anderson and J. Askne, “Energy relations for waves in strongly dispersive media,” Proc. IEEE Lett., vol. 60, pp. 901–902, 1972.

    Article  Google Scholar 

  170. D. Censor and J. J. Brandstatter, “Conservation and balance equations for waves in dissipative media,” Appl. Sci. Res., vol. 30, pp. 291–303, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  171. K. E. Oughstun and S. Shen, “Velocity of energy transport for a time-harmonic field in a multiple-resonance Lorentz medium,” J. Opt. Soc. Am. B, vol. 5, no. 11, pp. 2395–2398, 1988.

    Article  ADS  Google Scholar 

  172. Y. S. Barash and V. L. Ginzburg, “Expressions for the energy density and evolved heat in the electrodynamics of a dispersive and absorptive medium,” Usp. Fiz. Nauk., vol. 118, pp. 523–530, 1976. [English translation: Sov. Phys.-Usp. vol. 19, 163–270 (1976)].

    Google Scholar 

  173. C. Broadbent, G. Hovhannisyan, M. Clayton, J. Peatross, and S. A. Glasgow, “Reversible and irreversible processes in dispersive/dissipative optical media: Electro-magnetic free energy and heat production,” in Ultra-Wideband, Short-Pulse Electromagnetics 6 (E. L. Mokole, M. Kragalott, and K. R. Gerlach, eds.), pp. 131–142, New York: Kluwer Academic, 2003.

    Google Scholar 

  174. S. Glasgow and M. Ware, “Real-time dissipation of optical pulses in passive dielectrics,” Phys. Rev. A, vol. 80, pp. 043817–043827, 2009.

    Article  ADS  Google Scholar 

  175. S. Glasgow, J. Corson, and C. Verhaaren, “Dispersive dielectrics and time reversal: Free energies, orthogonal spectra, and parity in dissipative media,” Phys. Rev. E, vol. 82, p. 011115, 2010.

    Article  ADS  MathSciNet  Google Scholar 

  176. R. L. Smith, “The velocities of light,” Am. J. Phys., vol. 38, no. 8, pp. 978–984, 1970.

    Article  ADS  Google Scholar 

  177. D. B. Trizna and T. A. Weber, “Time delays of electromagnetic pulses due to molecular resonances in the atmosphere and the interstellar medium,” Astrophysical J., vol. 159, no. 1, pp. 309–317, 1970.

    Article  ADS  Google Scholar 

  178. D. B. Trizna and T. A. Weber, “Brillouin revisited: Signal velocity definition for pulse propagation in a medium with resonant anomalous dispersion,” Radio Science, vol. 17, no. 5, pp. 1169–1180, 1982.

    Article  ADS  Google Scholar 

  179. S. C. Bloch, “Eighth velocity of light,” Am. J. Phys., vol. 45, no. 6, pp. 538–549, 1977.

    Article  ADS  Google Scholar 

  180. N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Propagation velocity of an intense light pulse in a medium with inverted population,” Doklady Akademii Nauk SSSR, vol. 165, pp. 58–60, 1965. [English translation: Sov. Phys.-Doklady vol. 10, 1039–1040 (1966)].

    Google Scholar 

  181. F. R. Faxvog, C. N. Y. Chow, T. Bieber, and J. A. Carruthers, “Measured pulse velocity greater than c in a neon absorption cell,” Appl. Phys. Lett., vol. 17, pp. 192–193, 1970.

    Article  ADS  Google Scholar 

  182. S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett., vol. 48, pp. 738–741, 1982.

    Article  ADS  Google Scholar 

  183. A. Katz and R. R. Alfano, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett., vol. 49, p. 1292, 1982.

    Article  ADS  Google Scholar 

  184. C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A, vol. 1, pp. 305–313, 1970.

    Article  ADS  Google Scholar 

  185. M. Tanaka, M. Fujiwara, and H. Ikegami, “Propagation of a Gaussian wave packet in an absorbing medium,” Phys. Rev. A, vol. 34, pp. 4851–4858, 1986.

    Article  ADS  Google Scholar 

  186. G. C. Sherman and 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., vol. 47, pp. 1451–1454, 1981.

    Article  ADS  Google Scholar 

  187. G. C. Sherman and K. E. Oughstun, “Energy velocity description of pulse propagation in absorbing, dispersive dielectrics,” J. Opt. Soc. Am. B, vol. 12, pp. 229–247, 1995.

    Article  ADS  Google Scholar 

  188. R. Safian, C. D. Sarris, and M. Mojahedi, “Joint time-frequency and finite-difference time-domain analysis of precursor fields in dispersive media,” Phys. Rev. E, vol. 73, pp. 066602–1–9, 2006.

    Google Scholar 

  189. R. Uitham and B. J. Hoenders, “The electromagnetic Brillouin precursor in one-dimensional photonic crystals,” Opt. Comm., vol. 281, pp. 5910–5918, 2008.

    Article  ADS  Google Scholar 

  190. V. A. Vasilev, M. Y. Kelbert, I. A. Sazonov, and I. A. Chaban, “Propagation of ultrashort light pulses in a resonant absorbing medium,” Opt. Spektrosk., vol. 64, no. 4, pp. 862–868, 1988.

    Google Scholar 

  191. N. A. Cartwright and K. E. Oughstun, “Precursors and dispersive pulse dynamics, a century after the Sommerfeld-Brillouin theory: the original theory,” in Progress in Optics (E. Wolf, ed.), vol. 59, pp. 209–265, Amsterdam, The Netherlands: Elsevier, 2014.

    Google Scholar 

  192. N. A. Cartwright and K. E. Oughstun, “Precursors and dispersive pulse dynamics, a century after the Sommerfeld-Brillouin theory: the modern asymptotic theory,” in Progress in Optics (E. Wolf, ed.), vol. 60, pp. 263–344, Amsterdam, The Netherlands: Elsevier, 2015.

    Google Scholar 

  193. R. Safian, M. Mojahedi, and C. D. Sarris, “Asymptotic description of wave propagation in an active Lorentzian medium,” Phys. Rev. E, vol. 75, pp. 066611–1–8, 2007.

    Google Scholar 

  194. S. Dvorak and D. Dudley, “Propagation of ultra-wide-band electromagnetic pulses through dispersive media,” IEEE Trans. Elec. Comp., vol. 37, no. 2, pp. 192–200, 1995.

    Google Scholar 

  195. L. Gagnon, “Similarity properties and nonlinear effects on optical precursors,” Phys. Lett. A, vol. 148, no. 8, pp. 452–456, 1990.

    Article  ADS  MathSciNet  Google Scholar 

  196. J. L. Birman and M. J. Frankel, “Predicted new electromagnetic precursors and altered signal velocity in dispersive media,” Opt. Comm., vol. 13, no. 3, pp. 303–306, 1975.

    Article  ADS  Google Scholar 

  197. M. J. Frankel and J. L. Birman, “Transient optical response of a spatially dispersive medium,” Phys. Rev. A, vol. 15, no. 5, pp. 2000–2008, 1977.

    Article  ADS  Google Scholar 

  198. E. M. Belenov and A. V. Nazarkin, “Transient diffraction and precursorlike effects in vacuum,” J. Opt. Soc. Am. A, vol. 11, no. 1, pp. 168–172, 1994.

    Article  ADS  Google Scholar 

  199. J. A. Solhaug, J. J. Stamnes, and K. E. Oughstun, “Diffraction of electromagnetic pulses in a single-resonance Lorentz model dielectric,” Pure Appl. Opt., vol. 7, no. 5, pp. 1079–1101, 1998.

    Article  ADS  Google Scholar 

  200. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press, 1995. Ch. 3.

    Google Scholar 

  201. K. E. Oughstun, N. A. Cartwright, D. J. Gauthier, and H. Jeong, “Optical precursors in the singular and weak dispersion limits,” J. Opt. Soc. Am. B, vol. 27, no. 8, pp. 1664–1670, 2010.

    Article  ADS  Google Scholar 

  202. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett., vol. 78, no. 17, pp. 3282–3285, 1997.

    Article  ADS  Google Scholar 

  203. A. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett., vol. 71, no. 5, pp. 708–711, 1993.

    Article  ADS  Google Scholar 

  204. R. Landauer, “Light faster than light,” Nature, vol. 365, pp. 692–693, 1993.

    Article  ADS  Google Scholar 

  205. G. Diener, “Superluminal group velocities and information transfer,” Phys. Lett. A, vol. 223, pp. 327–331, 1996.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  206. P. W. Milonni, K. Furuya, and R. Y. Chiao, “Quantum theory of superluminal pulse propagation,” Optics Express, vol. 8, no. 2, pp. 59–65, 2001.

    Article  ADS  Google Scholar 

  207. A. Dogariu, A. Kuzmich, H. Cao, and L. J. Wang, “Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium,” Optics Express, vol. 8, no. 6, pp. 344–350, 2001.

    Article  ADS  Google Scholar 

  208. A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett., vol. 86, no. 18, pp. 3925–3929, 2001.

    Article  ADS  Google Scholar 

  209. G. Nimtz and A. Haibel, “Basics of superluminal signals,” Ann. Phys. (Leipzig), vol. 11, no. 2, pp. 163–171, 2002.

    Article  ADS  Google Scholar 

  210. H. Winful, “Nature of “superluminal” barrier tunneling,” Phys. Rev. Lett., vol. 90, no. 2, pp. 239011–239014, 2003.

    Article  Google Scholar 

  211. K. E. Oughstun, “Asymptotic description of pulse ultrawideband electromagnetic beam field propagation in dispersive, attenuative media,” J. Opt. Soc. Am. A, vol. 18, no. 7, pp. 1704–1713, 2001.

    Article  ADS  Google Scholar 

  212. K. E. Oughstun, “Asymptotic description of ultrawideband, ultrashort pulsed electromagnetic beam field propagation in a dispersive, attenuative medium,” in Ultra-Wideband, Short-Pulse Electromagnetics 5 (P. D. Smith and S. R. Cloude, eds.), pp. 687–696, New York: Kluwer Academic, 2002.

    Google Scholar 

  213. D. Anderson, J. Askne, and M. Lisak, “The velocity of wave packets in dispersive and slightly absorptive media,” Proc. IEEE Lett., vol. 63, no. 4, pp. 715–717, 1975.

    Article  ADS  Google Scholar 

  214. M. Lisak, “Energy expressions and energy velocity for wave packets in an absorptive and dispersive medium,” J. Phys. A: Math. Gen., vol. 9, pp. 1145–1158, 1976.

    Article  ADS  Google Scholar 

  215. J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett., vol. 84, no. 11, pp. 2370–2373, 2000.

    Article  ADS  Google Scholar 

  216. M. Ware, S. A. Glasgow, and J. Peatross, “Role of group velocity in tracking field energy in linear dielectrics,” Opt. Exp., vol. 9, no. 10, pp. 506–518, 2001.

    Article  ADS  Google Scholar 

  217. K. E. Oughstun and N. A. Cartwright, “Dispersive pulse dynamics and associated pulse velocity measures,” Pure Appl. Opt., vol. 4, no. 5, pp. S125–S134, 2002.

    Article  Google Scholar 

  218. N. A. Cartwright and K. E. Oughstun, “Pulse centroid velocity of the Poynting vector,” J. Opt. Soc. Am. A, vol. 21, no. 3, pp. 439–450, 2004.

    Article  ADS  MathSciNet  Google Scholar 

  219. J. Aaviksoo, J. Lippmaa, and J. Kuhl, “Observability of optical precursors,” J. Opt. Soc. Am. B, vol. 5, no. 8, pp. 1631–1635, 1988.

    Article  ADS  Google Scholar 

  220. J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A, vol. 44, no. 9, pp. 5353–5356, 1991.

    Article  ADS  Google Scholar 

  221. S.-H. Choi and U. Österberg, “Observation of optical precursors in water,” Phys. Rev. Lett., vol. 92, no. 19, pp. 1939031–1939033, 2004.

    Article  Google Scholar 

  222. H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett., vol. 96, no. 14, p. 143901, 2006.

    Google Scholar 

  223. S. Du, C. Belthangady, P. Kolchin, G. Yin, and S. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett., vol. 33, no. 18, pp. 2149–2151, 2008.

    Article  ADS  Google Scholar 

  224. M. Pieraccini, A. Bicci, D. Mecatti, G. Macaluso, and C. Atzeni, “Propagation of large bandwidth microwave signals in water,” IEEE Trans. Ant. Prop., vol. 57, no. 11, pp. 3612–3618, 2009.

    Article  ADS  Google Scholar 

  225. A. V. Alejos, M. Dawood, and L. Medina, “Experimental dynamical evolution of the Brillouin precursor for broadband wireless communication through vegetation,” in Progress in Electromagnetics Research (J. A. Kong, ed.), vol. 111, pp. 291–309, Cambridge, MA: EMW Publishing, 2011.

    Article  Google Scholar 

  226. H. Mohammed, M. Dawood, and A. V. Alejos, “Experimental detection and characterization of Brillouin precursor through loamy soil at microwave frequencies,” IEEE Trans. Geoscience and Remote Sensing, vol. 50, no. 2, pp. 436–445, 2012.

    Article  ADS  Google Scholar 

  227. D. C. Stoudt, F. E. Peterkin, and B. J. Hankla, “Transient RF and microwave pulse propagation in a Debye medium (water),” Interaction Note 622, Dahlgren Division, Naval Surface Warfare Center, Directed Technology Office, Electromagnetic and Solid State Technologies Division, Code B20/Bldg 1470, Dahlgren, VA, 4 July 2011.

    Google Scholar 

  228. K. E. Oughstun, “Dynamical evolution of the Brillouin precursor in Rocard-Powles-Debye model dielectrics,” IEEE Trans. Ant. Prop., vol. 53, no. 5, pp. 1582–1590, 2005.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  229. D. D. Stancil, “Magnetostatic wave precursors in thin ferrite films,” J. Appl. Phys., vol. 53, no. 3, pp. 2658–2660, 1982.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Engineering and Mathematical Sciences, University of Vermont, Burlington, VT, USA

    Kurt E. Oughstun

Authors
  1. Kurt E. Oughstun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Oughstun, K.E. (2019). Introduction. In: Electromagnetic and Optical Pulse Propagation . Springer Series in Optical Sciences, vol 224. Springer, Cham. https://doi.org/10.1007/978-3-030-20835-6_1

Download citation

Publish with us

Policies and ethics

Search

Navigation