Advertisement

The Angular Spectrum Representation of Pulsed Electromagnetic and Optical Beam Fields in Temporally Dispersive Media

  • Kurt E. Oughstun
Chapter
  • 415 Downloads
Part of the Springer Series in Optical Sciences book series (SSOS, volume 224)

Abstract

A completely general representation of the propagation of a freely propagating electromagnetic wave field into the half-space z ≥ z0 > Z of a homogeneous, isotropic, locally linear, temporally dispersive medium is now considered. The term “freely propagating” is used here to indicate that there are no externally supplied charge or current sources for the field present in this half-space, the field source residing somewhere in the region z ≤ Z.

References

  1. 1.
    G. C. Sherman, “Application of the convolution theorem to Rayleigh’s integral formulas,” J. Opt. Soc. Am., vol. 57, pp. 546–547, 1967.CrossRefGoogle Scholar
  2. 2.
    G. C. Sherman, “Integral-transform formulation of diffraction theory,” J. Opt. Soc. Am., vol. 57, pp. 1490–1498, 1967.ADSCrossRefGoogle Scholar
  3. 3.
    J. R. Shewell and E. Wolf, “Inverse diffraction and a new reciprocity theorem,” J. Opt. Soc. Am., vol. 58, no. 12, pp. 1596–1603, 1968.ADSCrossRefGoogle Scholar
  4. 4.
    G. C. Sherman, “Diffracted wave fields expressible by plane-wave expansions containing only homogeneous waves,” Phys. Rev. Lett., vol. 21, no. 11, pp. 761–764, 1968.ADSCrossRefGoogle Scholar
  5. 5.
    G. C. Sherman and H. J. Bremermann, “Generalization of the angular spectrum of plane waves and the diffraction transform,” J. Opt. Soc. Am., vol. 59, no. 2, pp. 146–156, 1969.ADSCrossRefGoogle Scholar
  6. 6.
    G. C. Sherman, “Diffracted wave fields expressible by plane-wave expansions containing only homogeneous waves,” J. Opt. Soc. Am., vol. 59, pp. 697–711, 1969.ADSCrossRefGoogle Scholar
  7. 7.
    C. J. Bouwkamp, “Diffraction theory,” Rept. Prog. Phys., vol. 17, pp. 35–100, 1954.ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1968.Google Scholar
  9. 9.
    W. H. Carter, “Electromagnetic beam fields,” Optica Acta, vol. 21, pp. 871–892, 1974.ADSCrossRefGoogle Scholar
  10. 10.
    J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves. Bristol, UK: Adam Hilger, 1986.zbMATHGoogle Scholar
  11. 11.
    M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics. New York: Wiley-Interscience, 1991.zbMATHGoogle Scholar
  12. 12.
    A. J. Devaney, Mathematical Foundations of Imaging, Tomography and Wavefield Inversion. Cambridge: Cambridge University Press, 2012.CrossRefGoogle Scholar
  13. 13.
    M. Born and E. Wolf, Principles of Optics. Cambridge: Cambridge University Press, seventh (expanded) ed., 1999.Google Scholar
  14. 14.
    E. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am., vol. 58, pp. 1235–1237, 1968.ADSCrossRefGoogle Scholar
  15. 15.
    H. L. Royden, Real Analysis. New York: Macmillan, second ed., 1968. p. 269.Google Scholar
  16. 16.
    A. Sommerfeld, Optics, vol. IV of Lectures in Theoretical Physics. New York: Academic, 1964. paperback edition.Google Scholar
  17. 17.
    A. Nisbet and E. Wolf, “On linearly polarized electromagnetic waves of arbitrary form,” Proc. Camb. Phil. Soc., vol. 50, pp. 614–622, 1954.ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    K. E. Oughstun, “Polarization properties of the freely-propagating electromagnetic field of arbitrary spatial and temporal form,” J. Opt. Soc. Am. A, vol. 9, no. 4, pp. 578–584, 1992.ADSCrossRefGoogle Scholar
  19. 19.
    E. Wolf, “Recollections of Max Born,” in Tribute to Emil Wolf: Science and Engineering Legacy in Physical Optics (T. P. Jannson, ed.), ch. 2, pp. 29–49, Bellingham, WA, USA: SPIE Press, 2004.Google Scholar
  20. 20.
    L. Mandel and E. Wolf, Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press, 1995. Ch. 3.Google Scholar
  21. 21.
    E. Wolf, Introduction to the Theory of Coherence and Polarized Light. Cambridge: Cambridge University Press, 2007.zbMATHGoogle Scholar
  22. 22.
    M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. New York: Pergamon Press, 1 ed., 1959.Google Scholar
  23. 23.
    T. Voipio, T. Setälä, and A. T. Friberg, “Statistical similarity and complete coherence of electromagnetic fields in time and frequency domains,” J. Opt. Soc. Am. A, vol. 32, no. 5, pp. 741–750, 2015.ADSCrossRefGoogle Scholar
  24. 24.
    C. Brosseau, “What polarization of light is: The contribution of Emil Wolf,” in Tribute to Emil Wolf: Science and Engineering Legacy in Physical Optics (T. P. Jannson, ed.), pp. 51–93, Bellingham, WA, USA: SPIE Press, 2004.Google Scholar
  25. 25.
    A. Friberg, “Electromagnetic theory of optical coherence,” in Tribute to Emil Wolf: Science and Engineering Legacy in Physical Optics (T. P. Jannson, ed.), ch. 4, pp. 95–113, Bellingham, WA, USA: SPIE Press, 2004.Google Scholar
  26. 26.
    K. E. Oughstun, “The angular spectrum representation and the Sherman expansion of pulsed electromagnetic beam fields in dispersive, attenuative media,” Pure Appl. Opt., vol. 7, no. 5, pp. 1059–1078, 1998.ADSCrossRefGoogle Scholar
  27. 27.
    I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. New York: Academic Press, 1980.zbMATHGoogle Scholar
  28. 28.
    G. N. Watson, A Treatise on the Theory of Bessel Functions. Cambridge: Cambridge University Press, 1922.zbMATHGoogle Scholar
  29. 29.
    D. C. Bertilone, “The contribution of homogeneous and evanescent plane waves to the scalar optical field: exact diffraction formulae,” J. Modern Optics, vol. 38, no. 5, pp. 865–875, 1991.ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun., vol. 8, pp. 271–274, 1973.ADSCrossRefGoogle Scholar
  31. 31.
    W. D. Montgomery, “Algebraic formulation of diffraction applied to self imaging,” J. Opt. Soc. Am., vol. 58, no. 8, pp. 1112–1124, 1968.ADSCrossRefGoogle Scholar
  32. 32.
    E. C. Titchmarsh, The Theory of Functions. London: Oxford University Press, 1937. Section 10.5.Google Scholar
  33. 33.
    E. J. McShane, Integration. Princeton, NJ: Princeton University Press, 1944. p. 217.zbMATHGoogle Scholar
  34. 34.
    W. Kaplan, Introduction to Analytic Functions. Reading, MA: Addison-Wesley, 1966. p. 171.zbMATHGoogle Scholar
  35. 35.
    H. Bremermann, Distributions, Complex Variables, and Fourier Transforms. Reading, MA: Addison-Wesley, 1965. Ch. 8.Google Scholar
  36. 36.
    T. B. Hansen and A. D. Yaghjian, Plane-Wave Theory of Time-Domain Fields. New York: IEEE, 1999.CrossRefGoogle Scholar
  37. 37.
    I. M. Gel’fand and G. E. Shilov, Generalized Functions, vol. I. New York: Academic, 1964. Ch. 2.Google Scholar
  38. 38.
    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.ADSCrossRefGoogle Scholar
  39. 39.
    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.ADSCrossRefGoogle Scholar
  40. 40.
    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.ADSCrossRefGoogle Scholar
  41. 41.
    H. Kogelnik, “Imaging of optical modes - Resonators with internal lenses,” Bell Syst. Tech. J., vol. 44, pp. 455–494, 1965.CrossRefGoogle Scholar
  42. 42.
    H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE, vol. 54, no. 10, pp. 1312–1329, 1966.CrossRefGoogle Scholar
  43. 43.
    A. J. Devaney and E. Wolf, “Radiating and nonradiating classical current distributions and the fields they generate,” Phys. Rev. D, vol. 8, pp. 1044–1047, 1973.ADSCrossRefGoogle Scholar
  44. 44.
    N. Bleistein and J. K. Cohen, “Nonuniqueness in the inverse source problem in acoustics and electromagnetics,” J. Math. Phys., vol. 18, pp. 194–201, 1977.ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    H. E. Moses and R. T. Prosser, “Initial conditions, sources, and currents for prescribed time-dependent acoustic and electromagnetic fields in three dimensions,” IEEE Trans. Antennas Prop., vol. 24, no. 2, pp. 188–196, 1986.ADSCrossRefGoogle Scholar
  46. 46.
    H. E. Moses, “Eigenfunctions of the curl operator, rotationally invariant Helmholtz theorem, and applications to electromagnetic theory and fluid mechanics,” SIAM J. Appl. Math., vol. 21, pp. 114–144, 1971.MathSciNetCrossRefGoogle Scholar
  47. 47.
    H. E. Moses and R. T. Prosser, “A refinement of the Radon transform and its inverse,” Proc. Roy. Soc. Lond. A, vol. 422, pp. 343–349, 1989.ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    H. E. Moses and R. T. Prosser, “Exact solutions of the three-dimensional scalar wave equation and Maxwell’s equations from the approximate solutions in the wave zone through the use of the Radon transform,” Proc. Roy. Soc. Lond. A, vol. 422, pp. 351–365, 1989.ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    E. A. Marengo, A. J. Devaney, and R. W. Ziolkowski, “New aspects of the inverse source problem with far-field data,” J. Opt. Soc. Am. A, vol. 16, pp. 1612–1622, 1999.ADSCrossRefGoogle Scholar
  50. 50.
    E. Heyman and A. J. Devaney, “Time-dependent multipoles and their application for radiation from volume source distributions,” J. Math. Phys., vol. 37, pp. 682–692, 1996.ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    T. F. Jordan, Linear Operators for Quantum Mechanics. New York: John Wiley & Sons, 1969.CrossRefGoogle Scholar
  52. 52.
    M. Bertero, “Linear inverse and ill-posed problems,” in Advances in Electronics and Electron Physics (P. W. Hawkes, ed.), pp. 1–120, New York: Academic Press, 1989.Google Scholar
  53. 53.
    D. N. G. Roy, Methods of Inverse Problems in Physics. Boca Raton, Fla: CRC Press, second ed., 1991.Google Scholar
  54. 54.
    R. W. Deming and A. J. Devaney, “A filtered backpropagation algorithm for GPR,” J. Env. Eng. Geo., vol. 0, pp. 113–123, 1996.CrossRefGoogle Scholar
  55. 55.
    R. P. Porter and A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am., vol. 72, pp. 1707–1713, 1982.ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    A. J. Devaney and R. P. Porter, “Holography and the inverse source problem. Part II: inhomogeneous media,” J. Opt. Soc. Am. A, vol. 2, pp. 2006–2011, 1985.ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering and Mathematical Sciences, University of VermontBurlingtonUSA

Personalised recommendations