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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 8 — Aug. 1, 2002
  • pp: 1701–1711

Traveling and evanescent parts of the electromagnetic Green's tensor

Henk F. Arnoldus and John T. Foley  »View Author Affiliations


JOSA A, Vol. 19, Issue 8, pp. 1701-1711 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001701


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Abstract

The angular spectrum representation of the electromagnetic Green’s tensor has a part that is a superposition of exponentially decaying waves in the +z and −z directions (evanescent part) and a part that is a superposition of traveling waves, both of which are defined by integral representations. We have derived an asymptotic expansion for the <i>z</i> dependence of the evanescent part of the Green’s tensor and obtained a closed-form solution in terms of the Lommel functions, which holds in all space. We have shown that the traveling part can be extracted from the Green’s tensor by means of a filter operation on the tensor, without regard to the angular spectrum integral representation of this part. We also show that the so-called self-field part of the tensor is properly included in the integral representation, and we were able to identify this part explicitly.

© 2002 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(240.6690) Optics at surfaces : Surface waves
(260.2110) Physical optics : Electromagnetic optics

Citation
Henk F. Arnoldus and John T. Foley, "Traveling and evanescent parts of the electromagnetic Green's tensor," J. Opt. Soc. Am. A 19, 1701-1711 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-8-1701


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References

  1. D. W. Pohl, “Scanning near-field optical microscopy,” in Advances in Optical and Electron Microscopy, T. Mulvey and C. J. R. Sheppard, eds. (Academic, San Diego, Calif., 1991), p. 243.
  2. D. W. Pohl and D. Courjon, eds., Near Field Optics, Vol. 242 of Proceedings of the NATO Advanced Research Workshop on Near Field Optics, Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1993).
  3. D. Courjon and C. Bainier, “Near-field microscopy and near-field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
  4. M. A. Paesler and P. J. Moyer, Near-Field Optics: Theory, Instrumentation, and Applications (Wiley, New York, 1996).
  5. M. Ohtsu, ed., Near-Field Nano/Atom Optics and Technology (Springer, Berlin, 1998).
  6. K. T. V. Grattan and B. T. Meggitt eds., Optical Fiber Sensor Technology: Fundamentals (Kluwer Academic, Boston, Mass., 2000).
  7. H. F. Arnoldus, “Representation of the near-field, middle-field, and far-field electromagnetic Green’s functions in reciprocal space,” J. Opt. Soc. Am. B 18, 547–555 (2001).
  8. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
  9. J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
  10. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. 67, 1607–1615 (1977).
  11. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. II. Radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am. 67, 1615–1619 (1977).
  12. H. F. Arnoldus and T. F. George, “Phase-conjugated fluorescence,” Phys. Rev. A 43, 3675–3689 (1991).
  13. A. Baños, “Dipole radiation in the presence of a conducting half-space,” International Series of Monographs in Electromagnetic Waves, Vol. 9, A. L. Cullen, V. A. Fock, and J. R. Wait, eds. (Pergamon, Oxford, UK, 1966).
  14. C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext, Scranton, Pa., 1971).
  15. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), App. III, p. 890.
  16. G. C. Sherman, J. J. Stamnes, and É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
  17. T. Setälä, M. Kaivola, and A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
  18. A. V. Shchegrov and P. S. Carney, “Far-field contribution to the electromagnetic Green’s tensor from evanescent modes,” J. Opt. Soc. Am. A 16, 2583–2584 (1999).
  19. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).
  20. V. M. Agranovich and D. L. Mills, Surface Polaritons (North-Holland, Amsterdam, 1982).
  21. R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emit-ting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974)
  22. R. R. Chance, A. H. Miller, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
  23. E. Wolf and J. T. Foley, “Do evanescent waves contribute to the far field?” Opt. Lett. 23, 16–18 (1998).
  24. M. Xiao, “Evanescent waves do contribute to the far field,” J. Mod. Opt. 46, 729–733 (1999).
  25. P. S. Carney, D. G. Fisher, J. T. Foley, A. T. Friberg, A. V. Shchegrov, T. D. Fisher, and E. Wolf, “Comment: evanescent waves do contribute to the far field,” J. Mod. Opt. 47, 757–758 (2000).
  26. A. Lakhtakia and W. S. Weiglhofer, “Evanescent plane waves and the far field: resolution of a controversy,” J. Mod. Opt. 47, 759–763 (2000).
  27. J. van Kranendonk and J. E. Sipe, “Foundations of the macroscopic electromagnetic theory of dielectric media,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. 25, pp. 246, ff.
  28. O. Keller, “Local fields in the electrodynamics of mesoscopic media,” Phys. Rep. 268, 85–262 (1996).
  29. O. Keller, “Attached and radiated electromagnetic fields of an electric point dipole,” J. Opt. Soc. Am. B 16, 835–847 (1999).
  30. J. D. Jackson, Classical Electrodynamics, 2th ed. (Wiley, New York, 1975), p. 141.
  31. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995), Sec. 3.2.4.
  32. O. Keller, “Screened electromagnetic propagators in nonlocal metal optics,” Phys. Rev. B 34, 3883–3899 (1986).
  33. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 275–276.
  34. N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1975), Chap. 3.
  35. M. V. Berry, “Asymptotics of evanescence,” J. Mod. Opt. 48, 1535–1541 (2001).
  36. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Special Functions, Vol. 2 of Integrals and Series (Gordon & Breach, New York, 1986), p. 188, no. 2.12.10.3. It should be noted that this formula contains a misprint. Here, [exp(ia ...)...] should read [−i exp(ia ...)...].
  37. D. C. Bertilone, “The contributions of homogeneous and evanescent plane waves to the scalar optical field: exact diffraction formulae,” J. Mod. Opt. 38, 865–875 (1991).
  38. D. C. Bertilone, “Wave theory for a converging spherical incident wave in an infinite-aperture system,” J. Mod. Opt. 38, 1531–1536 (1991).
  39. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK, 1922), p. 537.
  40. Page 487 of Ref. 15.
  41. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, Calif., 1995), p. 847.

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