Abstract

Evanescent waves have become of considerable interest in recent years because of developments in near-field optics. Claims have been made that such waves contribute to the radiation fields of sources and to the far fields of scatterers. We show, by considering a spherical scalar wave and a linear electric dipole field, that these claims are misleading and that such contributions are without physical consequences. Our conclusions apply to a much broader class of fields than those considered in this Letter.

© 1998 Optical Society of America

Full Article  |  PDF Article

Corrections

Emil Wolf and John T. Foley, "Do evanescent waves contribute to the far field??Errata," Opt. Lett. 23, 1142-1142 (1998)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-23-14-1142

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  2. See, for example, M. A. Paesler and P. J. Moyer, Near-Field Optics (Wiley, New York, 1996).
  3. In this connection see E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110, especially pp. 90 and 91.
    [CrossRef]
  4. H. P. Baltes and H. G. Schmidt-Weimar, Phys. Lett. A 60, 275 (1977).
    [CrossRef]
  5. H. P. Baltes and B. Steinle, Nuovo Cimento B 41, 428 (1977).
    [CrossRef]
  6. J. T. Foley and E. Wolf, J. Opt. Soc. Am. 69, 761 (1979).
    [CrossRef]
  7. Mufei Xio, Opt. Commun. 132, 403 (1996).
    [CrossRef]
  8. Mufei Xio, Chem. Lett. 258, 363 (1996).
    [CrossRef]
  9. Mufei Xio, J. Mod. Opt. 44, 327 (1997).
    [CrossRef]
  10. For the classic definition of the Stokes phenomenon see, for example, E. T. Copson, Asymptotic Expansions (Cambridge Press, Cambridge, 1967, p. 12; P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper and Row, New York, 1967), p. 321. For a fuller discussion of the Stokes phenomenon see R. B. Dingle, Asymptotic Expansions:?Their Derivation and Interpretation (Academic, New York, 1973), Secs.??1.2 and 21.6.
  11. The traditional definition of the Stokes phenomenon has been generalized by M. Berry See, for example, M. Berry, in Asymptotics beyond All Orders, H. Segur, T. Tanvee, and H. Levine, eds. (Plenum, New York, 1991), p. 1.
  12. H. F. Arnoldus and T. F. George, Phys. Rev. A 43, 3675 (1991).
    [CrossRef] [PubMed]
  13. Asymptotic approximation??(9) follows at once from Eq.??(3.3–95) of Ref.??1, with the substitutions k0=k, ap, q=ik/2?/m, m=z/r, appropriate to integral representation??(7a) of fhr.
  14. G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
    [CrossRef]
  15. G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
    [CrossRef]
  16. See Ref.??14, Eqs.??(8), (10), and (12), for the case Up, q, k=1.
  17. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993), Sec. 2.2.3, Eq.??(64). That equation differs from Eq.??(14) of the present Letter by a factor of 1/4??0 because of a different choice of units.

1997 (1)

Mufei Xio, J. Mod. Opt. 44, 327 (1997).
[CrossRef]

1996 (2)

Mufei Xio, Opt. Commun. 132, 403 (1996).
[CrossRef]

Mufei Xio, Chem. Lett. 258, 363 (1996).
[CrossRef]

1991 (1)

H. F. Arnoldus and T. F. George, Phys. Rev. A 43, 3675 (1991).
[CrossRef] [PubMed]

1979 (1)

1977 (2)

H. P. Baltes and H. G. Schmidt-Weimar, Phys. Lett. A 60, 275 (1977).
[CrossRef]

H. P. Baltes and B. Steinle, Nuovo Cimento B 41, 428 (1977).
[CrossRef]

1976 (1)

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

1973 (1)

G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
[CrossRef]

Arnoldus, H. F.

H. F. Arnoldus and T. F. George, Phys. Rev. A 43, 3675 (1991).
[CrossRef] [PubMed]

Baltes, H. P.

H. P. Baltes and H. G. Schmidt-Weimar, Phys. Lett. A 60, 275 (1977).
[CrossRef]

H. P. Baltes and B. Steinle, Nuovo Cimento B 41, 428 (1977).
[CrossRef]

Berry, M.

The traditional definition of the Stokes phenomenon has been generalized by M. Berry See, for example, M. Berry, in Asymptotics beyond All Orders, H. Segur, T. Tanvee, and H. Levine, eds. (Plenum, New York, 1991), p. 1.

The traditional definition of the Stokes phenomenon has been generalized by M. Berry See, for example, M. Berry, in Asymptotics beyond All Orders, H. Segur, T. Tanvee, and H. Levine, eds. (Plenum, New York, 1991), p. 1.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993), Sec. 2.2.3, Eq.??(64). That equation differs from Eq.??(14) of the present Letter by a factor of 1/4??0 because of a different choice of units.

Copson, E. T.

For the classic definition of the Stokes phenomenon see, for example, E. T. Copson, Asymptotic Expansions (Cambridge Press, Cambridge, 1967, p. 12; P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper and Row, New York, 1967), p. 321. For a fuller discussion of the Stokes phenomenon see R. B. Dingle, Asymptotic Expansions:?Their Derivation and Interpretation (Academic, New York, 1973), Secs.??1.2 and 21.6.

Devaney, A. J.

G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
[CrossRef]

Foley, J. T.

George, T. F.

H. F. Arnoldus and T. F. George, Phys. Rev. A 43, 3675 (1991).
[CrossRef] [PubMed]

Lalor, É.

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Moyer, P. J.

See, for example, M. A. Paesler and P. J. Moyer, Near-Field Optics (Wiley, New York, 1996).

Paesler, M. A.

See, for example, M. A. Paesler and P. J. Moyer, Near-Field Optics (Wiley, New York, 1996).

Schmidt-Weimar, H. G.

H. P. Baltes and H. G. Schmidt-Weimar, Phys. Lett. A 60, 275 (1977).
[CrossRef]

Sherman, G. C.

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
[CrossRef]

Stamnes, J. J.

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
[CrossRef]

Steinle, B.

H. P. Baltes and B. Steinle, Nuovo Cimento B 41, 428 (1977).
[CrossRef]

Wolf, E.

J. T. Foley and E. Wolf, J. Opt. Soc. Am. 69, 761 (1979).
[CrossRef]

In this connection see E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110, especially pp. 90 and 91.
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993), Sec. 2.2.3, Eq.??(64). That equation differs from Eq.??(14) of the present Letter by a factor of 1/4??0 because of a different choice of units.

Xio, Mufei

Mufei Xio, J. Mod. Opt. 44, 327 (1997).
[CrossRef]

Mufei Xio, Opt. Commun. 132, 403 (1996).
[CrossRef]

Mufei Xio, Chem. Lett. 258, 363 (1996).
[CrossRef]

Chem. Lett. (1)

Mufei Xio, Chem. Lett. 258, 363 (1996).
[CrossRef]

J. Math. Phys. (1)

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

J. Mod. Opt. (1)

Mufei Xio, J. Mod. Opt. 44, 327 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Nuovo Cimento B (1)

H. P. Baltes and B. Steinle, Nuovo Cimento B 41, 428 (1977).
[CrossRef]

Opt. Commun. (2)

Mufei Xio, Opt. Commun. 132, 403 (1996).
[CrossRef]

G. C. Sherman, J. J. Stamnes, A. J. Devaney, and É. Lalor, Opt. Commun. 8, 271 (1973).
[CrossRef]

Phys. Lett. A (1)

H. P. Baltes and H. G. Schmidt-Weimar, Phys. Lett. A 60, 275 (1977).
[CrossRef]

Phys. Rev. A (1)

H. F. Arnoldus and T. F. George, Phys. Rev. A 43, 3675 (1991).
[CrossRef] [PubMed]

Other (8)

Asymptotic approximation??(9) follows at once from Eq.??(3.3–95) of Ref.??1, with the substitutions k0=k, ap, q=ik/2?/m, m=z/r, appropriate to integral representation??(7a) of fhr.

For the classic definition of the Stokes phenomenon see, for example, E. T. Copson, Asymptotic Expansions (Cambridge Press, Cambridge, 1967, p. 12; P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper and Row, New York, 1967), p. 321. For a fuller discussion of the Stokes phenomenon see R. B. Dingle, Asymptotic Expansions:?Their Derivation and Interpretation (Academic, New York, 1973), Secs.??1.2 and 21.6.

The traditional definition of the Stokes phenomenon has been generalized by M. Berry See, for example, M. Berry, in Asymptotics beyond All Orders, H. Segur, T. Tanvee, and H. Levine, eds. (Plenum, New York, 1991), p. 1.

See Ref.??14, Eqs.??(8), (10), and (12), for the case Up, q, k=1.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993), Sec. 2.2.3, Eq.??(64). That equation differs from Eq.??(14) of the present Letter by a factor of 1/4??0 because of a different choice of units.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

See, for example, M. A. Paesler and P. J. Moyer, Near-Field Optics (Wiley, New York, 1996).

In this connection see E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110, especially pp. 90 and 91.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (18)

Equations on this page are rendered with MathJax. Learn more.

pt=p0 cosωt,
Er, t=ReE0rexp-iωt
E0r=14π0k2p0+p0·expikrr,
k=ω/c,
E0r=p04π0k2zˆ+zexpikrr,
expikrr=fhr+fer.
fhr=ik2πp2+q211mexpikpx+qy+mzdpdq,
fer=ik2πp2+q2>11mexpikpx+qy+mzdpdq,
m=+1-p2-q2  when p2+q21,
=+ip2+q2-1  when p2+q2>1.
fhrsexpikr/r as kr, s fixed.
fh0, 0, z=expikzz-1z,
fe0, 0, z=1z,
fhx, y, 0=isinkx2+y2x2+y2,
fex, y, 0=coskx2+y2x2+y2,
E0rh=p04π0k2zˆ+zfhr.
E0rshp04π0k2zˆ+zexpikrrkr, s2=1, s fixed,
E0rsh-k2p04π0sin θexpikrrθˆkr, s2=1, s fixed,

Metrics