Abstract

We present a polarimetric technique that provides a complete description of a mixture of uncorrelated optical fields with different spectral and polarization properties. The second-order coherence theory is used to describe the superposition of two random optical fields, and an imaging experiment is reported that illustrates the capability to separate radiations with different spectral composition and to simultaneously determine their Stokes vectors.

© 2004 Optical Society of America

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References

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  1. E. Collett, Polarized Light (Marcel Dekker, New York, 1993), p. 103.
  2. M. J. Halmas, J. Samir, “Temporal coherence of laser fields analyzed by heterodyne interferometry,” Appl. Opt. 21, 265–273 (1982).
    [CrossRef]
  3. J. D. Cohen, “Electrooptic detector of temporally coherent radiation,” Appl. Opt. 30, 874–883 (1991).
    [CrossRef] [PubMed]
  4. D. A. Satorius, T. E. Dimmick, “Imaging detector of temporally coherent radiation,” Appl. Opt. 36, 2929–2935 (1997).
    [CrossRef] [PubMed]
  5. R. C. Cautinho, D. R. Selviah, H. A. French, “Detection of partially coherent optical emission sources,” in Optical Pattern Recognition XI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4043, 238–248 (2000).
    [CrossRef]
  6. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  7. E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28, 1078–1080 (2003).
    [CrossRef] [PubMed]
  8. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
    [CrossRef]
  9. A. Dogariu, E. Wolf, “Coherence theory of pairs of correlated wave fields,” J. Mod. Opt. 50, 1791–1796 (2003).
    [CrossRef]

2003 (2)

1997 (1)

1991 (1)

1982 (1)

1959 (1)

E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
[CrossRef]

Cautinho, R. C.

R. C. Cautinho, D. R. Selviah, H. A. French, “Detection of partially coherent optical emission sources,” in Optical Pattern Recognition XI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4043, 238–248 (2000).
[CrossRef]

Cohen, J. D.

Collett, E.

E. Collett, Polarized Light (Marcel Dekker, New York, 1993), p. 103.

Dimmick, T. E.

Dogariu, A.

A. Dogariu, E. Wolf, “Coherence theory of pairs of correlated wave fields,” J. Mod. Opt. 50, 1791–1796 (2003).
[CrossRef]

French, H. A.

R. C. Cautinho, D. R. Selviah, H. A. French, “Detection of partially coherent optical emission sources,” in Optical Pattern Recognition XI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4043, 238–248 (2000).
[CrossRef]

Halmas, M. J.

Mandel, L.

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

Samir, J.

Satorius, D. A.

Selviah, D. R.

R. C. Cautinho, D. R. Selviah, H. A. French, “Detection of partially coherent optical emission sources,” in Optical Pattern Recognition XI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4043, 238–248 (2000).
[CrossRef]

Wolf, E.

A. Dogariu, E. Wolf, “Coherence theory of pairs of correlated wave fields,” J. Mod. Opt. 50, 1791–1796 (2003).
[CrossRef]

E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28, 1078–1080 (2003).
[CrossRef] [PubMed]

E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
[CrossRef]

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

Appl. Opt. (3)

J. Mod. Opt. (1)

A. Dogariu, E. Wolf, “Coherence theory of pairs of correlated wave fields,” J. Mod. Opt. 50, 1791–1796 (2003).
[CrossRef]

Nuovo Cimento (1)

E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
[CrossRef]

Opt. Lett. (1)

Other (3)

E. Collett, Polarized Light (Marcel Dekker, New York, 1993), p. 103.

R. C. Cautinho, D. R. Selviah, H. A. French, “Detection of partially coherent optical emission sources,” in Optical Pattern Recognition XI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE4043, 238–248 (2000).
[CrossRef]

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

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Figures (4)

Fig. 1
Fig. 1

SBW-to-polarization transformer; a beamlike field, linearly polarized at 0 deg (x direction) at the input plane P. The orthogonal components Ex and Ey are temporally delayed by δ, when the beam reaches the output plane Q.

Fig. 2
Fig. 2

Schematic of the Stokes–SBW image analyzer. QWP1 and QWP3, rotating quarter-wave plates; QWP2, static quarter-wave plate. P1 and P2, static linear polarizers. BS, 50/50 nonpolarized beam splitter; M, mirror.

Fig. 3
Fig. 3

Intensity image corresponding to mixed input radiation. The image was recorded in a 12-bit format and has a scale factor of 3.4.

Fig. 4
Fig. 4

Images encoded in the components of Stokes vectors Sn and Sb for mixed radiation. Images are in a 12-bit format and have scale factors of 1.6 and 2.8 for Sn and Sb, respectively.

Equations (25)

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Wij(ρ, ω)=12πEi*(ρ, t)Ej(ρ, t+τ)exp(iωτ)dτ
Ex(ρ, t)=E(ρ, t+δ),
Ey(ρ, t)=E(ρ, t).
Wxx(ρ, ω)=12πE*(ρ, t+δ)×E(ρ, t+δ+τ)exp(iωτ)dτ,
Wyy(ρ, ω)=12πE*(ρ, t)×E(ρ, t+τ)exp(iωτ)dτ,
Wxy(ρ, ω)=12πE*(ρ, t+δ)×E(ρ, t+τ)exp(iωτ)dτ.
S(ρ, ω)Tr[W(ρ, ω)].
Π(ρ, ω)=1-4 Det[W(ρ, ω)]{Tr[W(ρ, ω)]}2.
{E(T)(ρ, t)}={E(A)(ρ, t)+E(B)(ρ, t)},
Wij(T)(ρ, ω)=12πEi(T)*(ρ, t)×Ej(T)(ρ, t+τ)exp(iωτ)dτ,
S(ρ, ω)=S(A)(ρ, ω)+S(B)(ρ, ω).
Π(ρ, ω)=S(A)(ρ, ω)S(A)(ρ, ω)+S(B)(ρ, ω).
Jxx(ρ)=Jyy(ρ)=12πE*(ρ, t)E(ρ, t+τ)exp(iωτ)dτdω
=Γ(ρ, 0),
Jxy(ρ)=Jyx*(ρ)=Γ(ρ, δ)=12πE*(ρ, t+δ)×E(ρ, t+δ+τ)exp(iωτ)dτdω=Γ(ρ, δ)
J(ρ)=Γ(ρ, 0)Γ(ρ, δ)Γ*(ρ, δ)Γ(ρ, 0)
Π(ρ)=1-4 Det[J(ρ)]{Tr[J(ρ)]}2=|Γ(ρ, δ)||Γ(ρ, 0)|=γ(ρ, δ).
J(ρ)=Γ(A)(ρ, 0)Γ(A)(ρ, δ)Γ(A)*(ρ, δ)Γ(A)(ρ, 0)+Γ(B)(ρ ,0)Γ(B)(ρ, δ)Γ(B)*(ρ, δ)Γ(B)(ρ ,0).
J(ρ)=I(A)(ρ)+I(B)(ρ)I(A)(ρ)I(A)*(ρ)I(A)(ρ)+I(B)(ρ).
Π(ρ)=1-4 Det[J(ρ)]{Tr[J(ρ)]}2=I(A)(ρ)I(A)(ρ)+I(B)(ρ),
I(ρ)=I(A)(ρ)+I(B)(ρ).
I(A)(ρ)=I(ρ)Π(ρ)
I(B)(ρ)=I(ρ)[1-Π(ρ)].
I0n,I1n,,INn,
I0b,I1b,,INb,

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