Abstract

A new experimental procedure for determining the (second-order) coherence time of a light beam is described that is based on a combination of conventional interferometry with an intensity-correlation technique. It permits measurements of coherence times that are several orders of magnitude shorter than the resolving times of the detectors, which ordinarily limit correlation measurements. The validity of the method is demonstrated by an experiment in which the transverse fluorescent light from a dye laser is measured.

© 1989 Optical Society of America

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References

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  1. See, for example, M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.
  2. R. Hanbury Brown and R. Q. Twiss, Nature 177, 27; Nature 178, 1046, 1447 (1956).
  3. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
    [Crossref]
  4. Z. Y. Ou and L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. (to be published).
  5. G. Richter, Abh. Akad. Wiss. DDR 7N, 245 (1977).
  6. L. Mandel, Phys. Rev. A 28, 929 (1983).
    [Crossref]
  7. Z. Y. Ou, Phys. Rev. A 37, 1607 (1988).
    [Crossref] [PubMed]
  8. R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
    [Crossref] [PubMed]
  9. R. Ghosh and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
    [Crossref] [PubMed]
  10. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
    [Crossref] [PubMed]
  11. Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988).
    [Crossref] [PubMed]

1988 (2)

Z. Y. Ou, Phys. Rev. A 37, 1607 (1988).
[Crossref] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988).
[Crossref] [PubMed]

1987 (2)

R. Ghosh and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[Crossref] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

1986 (1)

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
[Crossref] [PubMed]

1983 (1)

L. Mandel, Phys. Rev. A 28, 929 (1983).
[Crossref]

1977 (1)

G. Richter, Abh. Akad. Wiss. DDR 7N, 245 (1977).

1965 (1)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[Crossref]

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

Ghosh, R.

R. Ghosh and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[Crossref] [PubMed]

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
[Crossref] [PubMed]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, Nature 177, 27; Nature 178, 1046, 1447 (1956).

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
[Crossref] [PubMed]

Mandel, L.

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988).
[Crossref] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

R. Ghosh and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[Crossref] [PubMed]

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
[Crossref] [PubMed]

L. Mandel, Phys. Rev. A 28, 929 (1983).
[Crossref]

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[Crossref]

Z. Y. Ou and L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. (to be published).

Ou, Z. Y.

Z. Y. Ou, Phys. Rev. A 37, 1607 (1988).
[Crossref] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988).
[Crossref] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
[Crossref] [PubMed]

Z. Y. Ou and L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. (to be published).

Richter, G.

G. Richter, Abh. Akad. Wiss. DDR 7N, 245 (1977).

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, Nature 177, 27; Nature 178, 1046, 1447 (1956).

Wolf, E.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[Crossref]

See, for example, M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

Abh. Akad. Wiss. DDR (1)

G. Richter, Abh. Akad. Wiss. DDR 7N, 245 (1977).

Nature (1)

R. Hanbury Brown and R. Q. Twiss, Nature 177, 27; Nature 178, 1046, 1447 (1956).

Phys. Rev. A (3)

L. Mandel, Phys. Rev. A 28, 929 (1983).
[Crossref]

Z. Y. Ou, Phys. Rev. A 37, 1607 (1988).
[Crossref] [PubMed]

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. A 34, 3962 (1986).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

R. Ghosh and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[Crossref] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[Crossref] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[Crossref]

Other (2)

Z. Y. Ou and L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. (to be published).

See, for example, M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

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Figures (4)

Fig. 1
Fig. 1

Mach–Zehnder type of interferometer for determining coherence time by second-order interference. Differential time difference τ = τ1τ2.

Fig. 2
Fig. 2

Intensity correlator for determination of the fourth-order correlation time.

Fig. 3
Fig. 3

Schematic of the experimental setup for determining the second-order coherence time by fourth-order interference.

Fig. 4
Fig. 4

Results of photoelectric coincidence measurements with their standard deviations as a function of differential time delay δτ. The solid curve is the theoretical prediction given by Eq. (18) with R = 1/2 = T and γ00(τ) given by inequality (19).

Equations (22)

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γ ( τ ) = V 0 * ( t ) V 0 ( t + τ ) / V 0 ( t ) 2 .
I 0 ( t ) I 0 ( t + τ ) = I 0 2 [ 1 + λ ( τ ) ] ,
λ ( τ ) = γ ( τ ) 2 .
V 01 ( t ) = T V 0 ( t - τ 1 ) ,
V 02 ( t ) = i R V 0 ( t - τ 1 ) exp [ i ϕ ( t ) ] ,
V 1 ( t ) = T V 01 ( t - τ 2 ) + i R V 02 ( t - τ 2 - δ τ ) ,
V 2 ( t ) = T V 02 ( t - τ 2 ) + i R V 01 ( t - τ 2 - δ τ ) ,
Γ ( 2 , 2 ) ( t , t + τ ) = V 1 * ( t ) V 2 * ( t + τ ) V 2 ( t + τ ) V 1 ( t ) .
Γ ( 2 , 2 ) ( t , t + τ ) = R T 3 [ I 0 ( t ) I 0 ( t + τ ) + I 0 ( t ) I 0 ( t + τ + δ τ ) ] + R 3 T [ I 0 ( t ) I 0 ( t + τ + δ τ ) + I 0 ( t ) I 0 ( t + τ + 2 δ τ ) ] - R 2 T 2 V 0 * ( t ) V 0 ( t + τ + δ τ ) V 0 * ( t + τ ) × V 0 ( t - δ τ ) exp { i [ ϕ ( t - δ τ ) - ϕ ( t + τ ) ] } + c . c .
I 0 ( t ) I 0 ( t + τ ) I 0 [ 1 + λ ( τ ) ] ,
Γ M = - ½ τ R ½ τ R d τ Γ ( 2 , 2 ) ( t , t + τ ) = R T I 0 2 ( T 2 { 2 τ R + - ½ τ R ½ τ R d τ [ λ ( τ ) + λ ( τ + δ τ ) ] } + R 2 { 2 τ R + - ½ τ R ½ τ R d τ [ λ ( τ + δ τ ) + λ ( τ + 2 δ τ ) ] } ) - R 2 T 2 - ½ τ R ½ τ R d τ V 0 * ( t ) V 0 ( t + τ + δ τ ) V 0 * ( t + τ ) × V 0 ( t - δ τ ) exp { i [ ϕ ( t - δ τ ) - ϕ ( t + τ ) ] } + c . c .
exp { i [ ϕ ( t - δ τ ) - ϕ ( t + τ ) ] }
- λ ( τ ) d τ ,
Γ M = R T I 0 2 2 ( T 2 + R 2 ) [ τ R + - λ ( τ ) d τ ] - R 2 T 2 - ½ τ R ½ τ R × V 0 * ( t ) V 0 ( t - δ τ ) V 0 * ( t + τ ) V 0 ( t + τ + δ τ ) + c . c .
f * ( t ) = V 0 ( t ) V 0 * ( t + δ τ ) ,
V 0 * ( t ) V 0 ( t - δ τ ) V 0 * ( t + τ ) V 0 ( t + τ + δ τ ) = V 0 * ( t + δ τ ) V 0 ( t ) V 0 * ( t + τ + δ τ ) V 0 ( t + τ + 2 δ τ ) = Δ f * ( t ) Δ f ( t + τ + δ τ ) + Γ 00 ( δ τ ) 2 ,
Γ 00 ( τ ) = V 0 * ( t ) V 0 ( t + τ )
τ R - λ ( τ ) d τ .
Γ M = 2 R T ( R 2 + T 2 ) I 0 2 τ R [ 1 - R T R 2 + T 2 γ 00 ( δ τ ) 2 ] ,
R c ( δ τ ) / r 1 r 2 τ R = 1 - [ R T / ( R 2 + T 2 ) ] γ 00 ( δ τ ) 2 .
γ 00 ( τ ) exp [ - ½ ( σ τ ) 2 ] .
τ c 1 2 - γ 00 ( τ ) d τ ,

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