Abstract

We show that an increase of the coherence length of a statistically homogeneous planar source diminishes the contribution of surface waves to the spatial coherence of the near field, as well as producing changes in the enhancement of the near-field spectrum.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. E. Wolf, Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  3. R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
    [CrossRef]
  4. A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
    [CrossRef] [PubMed]
  5. H. Roychowdhury and E. Wolf, Opt. Lett. 28, 170 (2003).
    [CrossRef] [PubMed]
  6. A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
    [CrossRef] [PubMed]
  7. E. Wolf and W. H. Carter, Opt. Commun. 50, 131 (1984).
    [CrossRef]
  8. This way of expressing correlation functions is customary in several studies of statistical fields. See, e.g., Eqs. (2.13) and (3.4) in Section 6.3.2 of Ref. .
  9. H. Raether, Surface Plasmons (Springer-Verlag, 1988).
  10. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, 2nd ed. (World Science, 2006), Chaps. 7 and 11.

2003 (2)

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

H. Roychowdhury and E. Wolf, Opt. Lett. 28, 170 (2003).
[CrossRef] [PubMed]

2000 (1)

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

1999 (1)

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

1984 (1)

E. Wolf and W. H. Carter, Opt. Commun. 50, 131 (1984).
[CrossRef]

Apostol, A.

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

Carminati, R.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

Carter, W. H.

E. Wolf and W. H. Carter, Opt. Commun. 50, 131 (1984).
[CrossRef]

Dogariu, A.

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

Greffet, J. J.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

Joulain, K.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, 2nd ed. (World Science, 2006), Chaps. 7 and 11.

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

Roychowdhury, H.

Shchegrov, A. V.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

Wolf, E.

H. Roychowdhury and E. Wolf, Opt. Lett. 28, 170 (2003).
[CrossRef] [PubMed]

E. Wolf and W. H. Carter, Opt. Commun. 50, 131 (1984).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

E. Wolf, Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Opt. Commun. (1)

E. Wolf and W. H. Carter, Opt. Commun. 50, 131 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (3)

R. Carminati and J. J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef] [PubMed]

Other (5)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

E. Wolf, Theory of Coherence and Polarization of Light (Cambridge University, 2007).

This way of expressing correlation functions is customary in several studies of statistical fields. See, e.g., Eqs. (2.13) and (3.4) in Section 6.3.2 of Ref. .

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, 2nd ed. (World Science, 2006), Chaps. 7 and 11.

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.


Figures (3)

Fig. 1
Fig. 1

( 2 π / k ) 2 S ( ω ) 1 W ( ρ , z , ω ) in arbitrary units (a.u.) versus ρ / λ at λ = 495.9 nm for different values of the source coherence length σ. (a) Evanescent part at the plane z = λ / 20 . The maximum normalized W e ( 0 ) for σ = 0 is 52.1   a.u. . The normalized homogeneous part W h ( 0 ) (not shown) is smaller than 1.2. (b) Homogeneous part at the plane z = 2 λ . The normalized evanescent part W h ( 0 ) (not shown) is smaller than 0.1.

Fig. 2
Fig. 2

( 2 π / k ) 2 S ( ω ) 1 G ( k s , ω ) in arbitrary units for a Gaussian-correlated source with an Au surface. The effect of the SPP excitation is characterized by the peaks of the Fresnel reflection coefficient magnitude | A | 2 in Eq. (4). The wavelength λ = 495.9 nm and the coherence lengths σ are the same as in Figs. 1a, 1b. For σ = 0 and λ / 8 , the SPP peaks of G are 11.97 at s SPP = ± 1.13 and 8.10 at s SPP = ± 1.12 , respectively. Notice that for σ = 0 , this normalized angular spectrum coincides with | A ( k s , ω ) | 2 .

Fig. 3
Fig. 3

Homogeneous and evanescent parts of the normalized cross-spectral density ( 2 π / k ) 2 S ( ω ) 1 W ( ρ , z , ω ) at z = λ / 20 , λ = 495.9 nm . (a)  σ = λ / 3 and 3 λ / 8 . (b)  σ = λ / 8 but with no SPP excitation. Notice the subwavelength width of the main lobe of W e when it dominates upon W h .

Equations (7)

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

W ( 0 ) ( ρ 1 , ρ 2 , ω ) = F ( ρ 1 ρ 2 , ω ) ,
μ ( 0 ) ( ρ 1 , ρ 2 , ω ) = F ( ρ 1 ρ 2 , ω ) / S ( 0 ) ( ω ) .
W ( r 1 , r 2 , ω ) = k 2 G ( k s , ω ) e i k ( s · r 1 s * · r 2 ) d 2 s ,
G ( k s , ω ) = S ( 0 ) ( ω ) μ ˜ ( 0 ) ( k s , ω ) | A ( k s , ω ) | 2 .
S ( 0 ) ( ω ) = S ( ω ) / ( 2 π σ 2 )
W h ( r 1 , r 2 , ω ) = W h ( ρ , z , ω ) = ( k / 2 π ) 2 S ( ω ) × s 2 1 e 1 2 ( k σ s ) 2 | A ( k s , ω ) | 2 e i k s · ρ d 2 s .
W e ( r 1 , r 2 , ω ) = ( k 2 π ) 2 S ( ω ) s 2 > 1 e 1 2 ( k σ s ) 2 × | A ( k s , ω ) | 2 e ( i k s · ρ ) e 2 k s x 2 + s y 2 1 z d 2 s .

Metrics