Abstract

We report an experimental method to determine the elements of the electric cross-spectral density matrix for laser light. For this purpose an additional setup consisting of mirrors and reflecting prisms is utilized with the conventional Young’s interferometer to overcome existing experimental limitations. The generalized Stokes parameters, which are the characteristics of two spatial points of the electromagnetic field, are also obtained for a pair of points. The knowledge of these two quantities might be useful in determining the change in polarization properties of light in propagation and their effects in optical measurements.

© 2008 Optical Society of America

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References

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  1. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  2. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
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  3. G. P. Agrawal and E. Wolf, J. Opt. Soc. Am. A 17, 2019 (2000).
    [CrossRef]
  4. E. Wolf, Opt. Lett. 28, 1078 (2003).
    [CrossRef] [PubMed]
  5. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  7. H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
    [CrossRef]
  8. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
    [CrossRef] [PubMed]
  9. E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  10. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [CrossRef] [PubMed]
  11. H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
    [CrossRef]

2006 (1)

2005 (2)

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

2003 (3)

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

E. Wolf, Opt. Lett. 28, 1078 (2003).
[CrossRef] [PubMed]

2000 (1)

1994 (1)

1852 (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Agrawal, G. P.

Borghi, R.

Gori, F.

James, D. F. V.

Korotkova, O.

Mandel, L.

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

Roychowdhury, H.

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

Santarsiero, M.

Stokes, G. G.

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Wolf, E.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

E. Wolf, Opt. Lett. 28, 1078 (2003).
[CrossRef] [PubMed]

G. P. Agrawal and E. Wolf, J. Opt. Soc. Am. A 17, 2019 (2000).
[CrossRef]

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

E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Other (2)

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

E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Figures (3)

Fig. 1
Fig. 1

Schematics of the experimental setup. The inset illustrates the notations. Abbreviations are defined in the text.

Fig. 2
Fig. 2

(a–d) Interference fringes observed at the observation plane R for different direction of polarizations (DOPs) of the polarizers. (e) Data recorded by the spectrometer shows the spectral profile of laser beam.

Fig. 3
Fig. 3

Variation in the output intensity of the laser beam with different DOPs of the linear polarizer. 0° and 180° of the transmission axis correspond to the x axis polarization.

Tables (2)

Tables Icon

Table 1 Components of the Spectral Degree of Coherence and the Cross-Spectral Density Matrix Obtained for the Laser Light

Tables Icon

Table 2 Generalized Stokes Parameters for a Pair of Points in the Laser Beam

Equations (7)

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W ( r 1 , r 2 , ω ) = W i j ( r 1 , r 2 , ω ) = E i * ( r 1 , ω ) E j ( r 2 , ω ) , i = x , y , j = x , y ,
η ( r 1 , r 2 , ω ) = Tr W ( r 1 , r 2 , ω ) Tr W ( r 1 , r 1 , ω ) Tr W ( r 2 , r 2 , ω ) .
Tr W ( r 1 , r 2 , ω ) = S ( r 1 , ω ) S ( r 2 , ω ) η ( r 1 , r 2 , ω ) .
W ( r 1 , r 2 , ω ) = W i j ( r 1 , r 2 , ω ) = S i ( r 1 , ω ) S j ( r 2 , ω ) η i j ( r 1 , r 2 , ω ) , i = x , y , j = x , y .
S i ( r 1 , r 2 , ω ) = Tr [ W ( r 1 , r 2 , ω ) σ i ] ( i = 0 , 1 , 2 , 3 ) ,
S max S min S max + S min ,
W ( r 1 , r 2 , ω ) = [ 410.6 ± 4.0 118.2 ± 1.6 119.7 ± 1.8 366.4 ± 3.4 ] .

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