Abstract

We analyze the coherence properties of a partially coherent optical field emerging from two pinholes in a plane opaque screen. We show that at certain pairs of points in the region of superposition the light is fully coherent, regardless of the state of coherence of the light at the pinholes. In particular, this result also holds if each pinhole is illuminated by a different laser.

© 2003 Optical Society of America

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References

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  1. T. Young, Philos. Trans. R. Soc. London 92, 26 (1802).
  2. T. Young, in A Course of Lectures on Natural Philosophy and the Mechanical Arts, P. Kelland, ed. (Taylor and Walton, London, 1845), Vol. 1, p. 364.
  3. D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
    [CrossRef]
  4. H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
    [CrossRef]
  5. M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
    [CrossRef]
  6. H. Rauch, Phys. Lett. A 173, 240 (1993).
    [CrossRef]
  7. D. L. Jacobson, S. A. Werner, and H. Rauch, Phys. Rev. A 49, 3196 (1994).
    [CrossRef] [PubMed]
  8. G. S. Agarwal, Found. Phys. 25, 219 (1995).
    [CrossRef]
  9. S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
    [CrossRef]
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]

1999

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

1995

G. S. Agarwal, Found. Phys. 25, 219 (1995).
[CrossRef]

1994

D. L. Jacobson, S. A. Werner, and H. Rauch, Phys. Rev. A 49, 3196 (1994).
[CrossRef] [PubMed]

1993

H. Rauch, Phys. Lett. A 173, 240 (1993).
[CrossRef]

1992

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

1991

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

1802

T. Young, Philos. Trans. R. Soc. London 92, 26 (1802).

Agarwal, G. S.

G. S. Agarwal, Found. Phys. 25, 219 (1995).
[CrossRef]

Chander, M.

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

Gori, F.

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

Jacobson, D. L.

D. L. Jacobson, S. A. Werner, and H. Rauch, Phys. Rev. A 49, 3196 (1994).
[CrossRef] [PubMed]

James, D. F. V.

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

Joshi, K. C.

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

Kandpal, H. C.

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

Mandel, L.

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

Metha, D. S.

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

Ponomarenko, S. A.

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

Rauch, H.

D. L. Jacobson, S. A. Werner, and H. Rauch, Phys. Rev. A 49, 3196 (1994).
[CrossRef] [PubMed]

H. Rauch, Phys. Lett. A 173, 240 (1993).
[CrossRef]

Santarsiero, M.

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

Saxena, K.

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

Vaishya, J. S.

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

Werner, S. A.

D. L. Jacobson, S. A. Werner, and H. Rauch, Phys. Rev. A 49, 3196 (1994).
[CrossRef] [PubMed]

Wolf, E.

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

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

Young, T.

T. Young, Philos. Trans. R. Soc. London 92, 26 (1802).

T. Young, in A Course of Lectures on Natural Philosophy and the Mechanical Arts, P. Kelland, ed. (Taylor and Walton, London, 1845), Vol. 1, p. 364.

Found. Phys.

G. S. Agarwal, Found. Phys. 25, 219 (1995).
[CrossRef]

Opt. Commun.

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

D. F. V. James and E. Wolf, Opt. Commun. 81, 150 (1991).
[CrossRef]

Philos. Trans. R. Soc. London

T. Young, Philos. Trans. R. Soc. London 92, 26 (1802).

Phys. Rev. A

D. L. Jacobson, S. A. Werner, and H. Rauch, Phys. Rev. A 49, 3196 (1994).
[CrossRef] [PubMed]

Phys. Lett. A

H. C. Kandpal, J. S. Vaishya, M. Chander, K. Saxena, D. S. Metha, and K. C. Joshi, Phys. Lett. A 167, 114 (1992).
[CrossRef]

M. Santarsiero and F. Gori, Phys. Lett. A 167, 123 (1992).
[CrossRef]

H. Rauch, Phys. Lett. A 173, 240 (1993).
[CrossRef]

Other

T. Young, in A Course of Lectures on Natural Philosophy and the Mechanical Arts, P. Kelland, ed. (Taylor and Walton, London, 1845), Vol. 1, p. 364.

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

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Figures (2)

Fig. 1
Fig. 1

Illustration of the notation relating to interference patterns formed with partially coherent light in Young’s experiment.

Fig. 2
Fig. 2

Contour lines of μr1,r2,ω, with r1 kept fixed at 0,0,1.5 m and r2 varying in the plane z=1.5 m. In this example d=1 mm, ω=1015 s-1, and μ0Q1,Q2,ω=0.2+0.2i.

Equations (21)

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

W0r1,r2,ω=S0r1,ωS0r2,ω1/2μ0r1,r2,ω.
Wr1,r2,ω=12π2z=0W0r1,r2,ωik+1R1×-ik+1R2expikR2-R1R1R2×cosθ1 cosθ2d2r1d2r2,
Wr1,r2,ω=δA2π2S1ωK11*K12+S2ωK21*K22+S1ωS2ωμ0Q1,Q2,ωK11*K22+μ0*Q1,Q2,ωK12K21*,
Kij=-ik+1RijexpikRijRijcosθij,    i,j=1,2,
Sr0,ω Wr0,r0,ω=δA2π2S1ωK102+S2ωK202+2S1ωS2ωReμ0Q1,Q2,ωK10*K20,
r¯1=d/2,0,0,    r¯2=-d/2,0,0,
r1=0,y1,z1,    r2=0,y2,z2,
K11=K21,    K12=K22.
Wr1,r2,ω=δA2π2K11*K12S1ω+S2ω+2S1ωS2ωReμ0Q1,Q2,ω.
Sri,ω=δA2π2K1i2S1ω+S2ω+2S1ωS2ωReμ0Q1,Q2,ω, i=1,2.
μP1,P2,ω=K11*K12K11K12,
=expikR12-R11×ik+1/R11-ik+1/R12ik+1/R11-ik+1/R12,
=expikR12-R11expiϕ1-ϕ2,
cosϕi=1/R1iDi,    sinϕi=k/Di,
Di=k2+1/R1i2.
μr1,r2,ω=1,
K11=K12,    K21=K22.
Wr1,r2,ω=δA2π2S1ωK112+S2ωK212+2S1ωS2ω×ReK11*K22μ0Q1,Q2,ω.
Sr1,ω=Sr2,ω
=δA2π2S1ωK112+S2ωK222+2S1ωS2ω×ReK11*K22μ0Q1,Q2,ω,
μr1,r2,ω=1.

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