Abstract

A study of the spectral shifts of a well-known type of partially coherent field, namely, one formed by Gaussian Schell model beams, propagating beyond an optical system reveals that there are no shifts in the geometric-image plane, whereas the greatest (blue) shift occurs in the back focal plane. These results are relevant for spectroradiometric measurements.

© 1997 Optical Society of America

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References

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  1. E. Wolf and D. F. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]
  2. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef] [PubMed]
  3. H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
    [CrossRef]
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  5. F. Gori, Opt. Commun. 34, 301 (1980).
    [CrossRef]
  6. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  7. F. Gori, Opt. Commun. 46, 149 (1983).
    [CrossRef]

1996 (1)

E. Wolf and D. F. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

1989 (1)

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

1986 (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

1983 (1)

F. Gori, Opt. Commun. 46, 149 (1983).
[CrossRef]

1980 (1)

F. Gori, Opt. Commun. 34, 301 (1980).
[CrossRef]

Gori, F.

F. Gori, Opt. Commun. 46, 149 (1983).
[CrossRef]

F. Gori, Opt. Commun. 34, 301 (1980).
[CrossRef]

James, D. F.

E. Wolf and D. F. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Joshi, K. C.

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

Kandpal, H. C.

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

Mandel, L.

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

Siegman, A.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Vaishya, J. S.

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

Wolf, E.

E. Wolf and D. F. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

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

Opt. Commun. (3)

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, Opt. Commun. 73, 169 (1989).
[CrossRef]

F. Gori, Opt. Commun. 34, 301 (1980).
[CrossRef]

F. Gori, Opt. Commun. 46, 149 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

E. Wolf and D. F. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Other (2)

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

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (2)

Fig. 1
Fig. 1

Plots of Mz1, f; ν versus ν (in terahertz) for f=30 mm, z1/f=2, M2=10, w0=1  mm, and for values of z2/f=0.2, 0.6, 0.7, 0.8, 1.0, from bottom to top.

Fig. 2
Fig. 2

Plots of the relative spectral shift η=ν¯0-ν0/ν0, amplified by a factor of 106, versus z2, for f=30  mm, z1/f=2, M2=90, w0=1  mm.

Equations (9)

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

Wr1, r2, 0; ν=S0; νexp-r1+r22+M4r1-r222w02,
M2=1+4σI2σμ21/2.
Wr1, r2, z1; ν=S0; ν1+cM2z1πνw022×exp{-iπνr12-r22cz11+πνw02cM2z12}×exp{-r1+r22+M4r1-r222w021+cM2z1πνw022}.
τr; ν=exp-iπνr2cf.
Ir, z2; ν=S0; ν1-z2f2+cM2πνw022z1+z2-z1z2f2exp{-2r22w021-z2f2+cM2πνw022z1+z2-z1z2f2}.
I0, z2; ν=S0; ν1-z2f2+cM2πνw022z1+z2-z1z2f2=S0; νMz1, z2; ν,
Mz1, z2; ν-11-z2f2+cM2πνw022z1+z2-z1z2f2
Mz1, f; ν=πw02cM2f2ν2,
S0; ν=Δ2ν0ν-ν02+Δ2ν0,

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