Abstract

The Huygens–Fresnel principle provides a conceptual understanding for wave propagation and diffraction. Recently the principle has been reexamined to suggest that it is also valid in the near field. We reformulate the problem in terms of nonradiative optics, focusing particularly on the obliquity factor inherent in the forward-directed propagation of light. In the near field of matter no explicit obliquity factor exists.

© 1995 Optical Society of America

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References

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  1. C. Huygens, Traité de la Lumiére (Leyden, 1690) [English translation by S. P. Thompson, Treatise on Light (Macmillan, London, 1912)].
  2. A. Fresnel, Ann. Chem. Phys. 1, 239 (1816).
  3. G. Kirchhoff, Ann. Physik. 18, 663 (1883).
    [CrossRef]
  4. D. Pohl, European patent0112401(filed December27, 1982); D. Pohl, U.S. patent4,604,520(filed December20, 1983).
  5. D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
    [CrossRef]
  6. A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).
  7. A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
    [CrossRef]
  8. D. A. Miller, Opt. Lett. 16, 1370 (1991).
    [CrossRef] [PubMed]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, p. 378.
  10. E. Wolf, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 2, 886 (1985).
    [CrossRef]
  11. F. Depasse, J. M. Vigoureux, “Nonradiative optics. I. General presentation, mathematical tools, and applications to near-field microscopy,” Phys. Rev. B (to be published).

1991 (1)

1985 (1)

1984 (2)

A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

1983 (1)

A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).

1883 (1)

G. Kirchhoff, Ann. Physik. 18, 663 (1883).
[CrossRef]

1816 (1)

A. Fresnel, Ann. Chem. Phys. 1, 239 (1816).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, p. 378.

Denk, W.

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Depasse, F.

F. Depasse, J. M. Vigoureux, “Nonradiative optics. I. General presentation, mathematical tools, and applications to near-field microscopy,” Phys. Rev. B (to be published).

Fresnel, A.

A. Fresnel, Ann. Chem. Phys. 1, 239 (1816).

Harootunian, A.

A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).

Huygens, C.

C. Huygens, Traité de la Lumiére (Leyden, 1690) [English translation by S. P. Thompson, Treatise on Light (Macmillan, London, 1912)].

Isaacson, M.

A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).

Kirchhoff, G.

G. Kirchhoff, Ann. Physik. 18, 663 (1883).
[CrossRef]

Lanz, M.

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Lewis, A.

A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).

Miller, D. A.

Murray, A.

A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Murray, M. A.

A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).

Nieto-Vesperinas, M.

Pohl, D.

D. Pohl, European patent0112401(filed December27, 1982); D. Pohl, U.S. patent4,604,520(filed December20, 1983).

Pohl, D. W.

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Vigoureux, J. M.

F. Depasse, J. M. Vigoureux, “Nonradiative optics. I. General presentation, mathematical tools, and applications to near-field microscopy,” Phys. Rev. B (to be published).

Wolf, E.

E. Wolf, M. Nieto-Vesperinas, J. Opt. Soc. Am. A 2, 886 (1985).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, p. 378.

Ann. Chem. Phys. (1)

A. Fresnel, Ann. Chem. Phys. 1, 239 (1816).

Ann. Physik. (1)

G. Kirchhoff, Ann. Physik. 18, 663 (1883).
[CrossRef]

Appl. Phys. Lett. (1)

D. W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Biophys. J. (1)

A. Lewis, M. Isaacson, M. A. Murray, A. Harootunian, Biophys. J. 41, 405 (1983).

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

Opt. Lett. (1)

Ultramicroscopy (1)

A. Lewis, M. Isaacson, A. Harootunian, A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 8, p. 378.

F. Depasse, J. M. Vigoureux, “Nonradiative optics. I. General presentation, mathematical tools, and applications to near-field microscopy,” Phys. Rev. B (to be published).

D. Pohl, European patent0112401(filed December27, 1982); D. Pohl, U.S. patent4,604,520(filed December20, 1983).

C. Huygens, Traité de la Lumiére (Leyden, 1690) [English translation by S. P. Thompson, Treatise on Light (Macmillan, London, 1912)].

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Equations (16)

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f ( θ ) = 1 + cos θ 2
ϕ ( r 1 , t ) = 1 4 π d S { - 1 r [ ϕ n ] + [ ϕ ] n 1 r - 1 c r r n [ ϕ t ] } .
[ ϕ ] 4 π r { i k ( 1 + cos θ ) + cos θ r } .
ϕ = a d exp [ i ( ω t - k r ) ] 4 π r { i k ( 1 + cos θ ) + cos θ r } .
ϕ ˜ ( k x , k y , 0 ) = 1 ( 2 π ) 2 d x d y ϕ ( x ' , y , 0 ) × exp [ - i ( k x x + k y y ) ] ,
ϕ ˜ ( k x , k y , z ) = ϕ ˜ ( k x , k y , 0 ) exp [ i z ( K 2 - k x 2 - k y 2 ) 1 / 2 ] ,
ϕ ( x , y , z ) = 1 ( 2 π ) 2 d x d y ' ϕ ( x , y , 0 ) × d k x d k y exp { i [ ( x - x ) k x + ( y - y ) k y + z ( K 2 - k x 2 - k y 2 ) 1 / 2 ] } .
ϕ ( x , y , z ) = 1 ( 2 π ) 2 d x d y ϕ ( x , y ' , 0 ) × [ cos θ exp ( i K r ) r 2 ( K r + i ) ] ,
cos θ exp ( i K r ) r 2 ( K r + i ) = - i d d z [ exp ( i K r ) r ] .
P ( t ) = α E i exp ( - i Ω t ) ,
Π ( t , r ) = [ P ( t , r ) ] r .
Π ˜ ( k ) = 1 ( 2 π ) 3 d r 3 Π ( r ) exp ( - i k · r ) .
Π ( r ) = d k 3 Π ˜ ( k ) exp ( i k r ) ,
Π ( r ) = α ( 2 π ) 2 K E i ( 0 ) d k 3 exp ( i k · r ) × lim η 0 + ( 1 k - K - i η - 1 k + K + i η ) .
Π ( r ) = α 2 π i K r E i ( 0 ) d k k [ exp ( i k r ) - exp ( i k r ) ] × lim η 0 + ( 1 k - K - i η - 1 k + K + i η ) ,
Π ( r ) = α 2 π i K r E i ( 0 ) [ 2 π i K exp ( i K r ) + 0 d u u exp ( - r u ) ( 1 i u - K - 1 i u + K ) - 0 d u u exp ( r u cos θ max ) × ( 1 i u - K - 1 i u + K ) ] .

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