Abstract

In usual measurements of the phase of an optical field it is generally assumed that the field is monochromatic. In reality this assumption is never justified. The distinction between monochromaticity and complete spatial coherence is first discussed, and it is then shown that with every spatially coherent field (e.g., a laser mode) one can associate a monochromatic wave that, in a well-defined sense, represents the average behavior of the field. Its phase can be measured by standard interferometric techniques and also by techniques developed in recent years for the measurement of the spectral degree of coherence of fields of arbitrary states of coherence.

© 2003 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [Crossref]
  2. L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
    [Crossref]
  3. D. F. V. James and E. Wolf, Opt. Commun. 145, 1 (1998).
    [Crossref]
  4. S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
    [Crossref]
  5. V. N. Kumar and D. N. Rao, J. Mod. Opt. 48, 1455 (2001).
  6. A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. (to be published).
  7. E. Wolf, Nuovo Cimento XII, 184 (1954).
  8. G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
    [Crossref]

2002 (1)

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[Crossref]

2001 (1)

V. N. Kumar and D. N. Rao, J. Mod. Opt. 48, 1455 (2001).

2000 (1)

S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
[Crossref]

1998 (1)

D. F. V. James and E. Wolf, Opt. Commun. 145, 1 (1998).
[Crossref]

1981 (1)

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[Crossref]

1954 (1)

E. Wolf, Nuovo Cimento XII, 184 (1954).

Dogariu, A.

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[Crossref]

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. (to be published).

James, D. F. V.

D. F. V. James and E. Wolf, Opt. Commun. 145, 1 (1998).
[Crossref]

Kandpal, H. C.

S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
[Crossref]

Kumar, V. N.

V. N. Kumar and D. N. Rao, J. Mod. Opt. 48, 1455 (2001).

Mandel, L.

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[Crossref]

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

Popescu, G.

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[Crossref]

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. (to be published).

Rao, D. N.

V. N. Kumar and D. N. Rao, J. Mod. Opt. 48, 1455 (2001).

Titus, S. S. K.

S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
[Crossref]

Vaishya, J. S.

S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
[Crossref]

Wasan, A.

S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
[Crossref]

Wolf, E.

D. F. V. James and E. Wolf, Opt. Commun. 145, 1 (1998).
[Crossref]

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[Crossref]

E. Wolf, Nuovo Cimento XII, 184 (1954).

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

J. Mod. Opt. (1)

V. N. Kumar and D. N. Rao, J. Mod. Opt. 48, 1455 (2001).

Nuovo Cimento (1)

E. Wolf, Nuovo Cimento XII, 184 (1954).

Opt. Commun. (3)

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[Crossref]

D. F. V. James and E. Wolf, Opt. Commun. 145, 1 (1998).
[Crossref]

S. S. K. Titus, A. Wasan, J. S. Vaishya, and H. C. Kandpal, Opt. Commun. 173, 45 (2000).
[Crossref]

Phys. Rev. Lett. (1)

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[Crossref]

Other (2)

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

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. (to be published).

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Equations (13)

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V1t=aeiϕ1t, V2t=aeiϕ2t,
I12=2a2cosϕ2t-ϕ1t,
I12=2a2 cosα2-α1.
ϕ2t=ϕ1t+β.
I=2a2 cos β
Wr1,r2,ω=12π-V*r1,tVr2,t+τeiωτdτ,
μr1,r2,ω=Wr1,r2,ωSr1,ωSr2,ω.
Sr,ω=Wr,r,ω
Wr1,r2,ω=U*r1,ωUr2,ω,
2Ur,ω+k2Ur,ω=0,
Ur,ω=Ur,ωeiϕr,ω,
μr1,r2,ω=expiϕr2,ω-ϕr1,ω.
Vr,t=Ur,ωeiωt.

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