Abstract

We report an experimental method to determine the generalized Stokes parameters for a pair of points in the cross section of an electromagnetic beam, e.g., an expanded laser beam, with the help of a Young’s interferometer and a set of polarizers and quarter-wave plates. The method is investigated theoretically using the electromagnetic spectral interference law. The generalized Stokes parameters, owing to their two-point nature, determine the behavior of the single-point polarization properties of the electromagnetic beam at a field point. The present method offers a unique means to determine the two-point parameters (correlation functions) by measuring the usual Stokes parameters (intensities) and the contrast parameters (visibilities) of the beam. The method might be applicable to determine the polarization dependent changes in various optical measurements.

© 2009 Optical Society of America

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References

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  1. J. Ellis and A. Dogariu, Opt. Lett. 29, 536 (2004).
    [CrossRef] [PubMed]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  3. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).
  4. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [CrossRef] [PubMed]
  5. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
    [CrossRef]
  6. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  7. E. Wolf, Opt. Lett. 28, 1078 (2003).
    [CrossRef] [PubMed]
  8. E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  9. T. Setala, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2208 (2006).
    [CrossRef] [PubMed]
  10. T. Setala, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2669 (2006).
    [CrossRef] [PubMed]
  11. O. Korotkova, Opt. Lett. 261, 218 (2006).
  12. B. Kanseri and H. C. Kandpal, Opt. Lett. 33, 2410 (2008).
    [CrossRef] [PubMed]

Dogariu, A.

Ellis, J.

Friberg, A. T.

James, D. F. V.

Kandpal, H. C.

Kanseri, B.

Korotkova, O.

Mandel, L.

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

Setala, T.

Stokes, G. G.

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

Tervo, J.

Wolf, E.

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

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

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

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

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

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Lett. A

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

Trans. Cambridge Philos. Soc.

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

Other

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 (2)

Fig. 1
Fig. 1

Schematics of the experimental arrangement. BE is a beam expander, T 1 and T 2 are stops, Q is a polarizer, and W is a quarter-wave plate. SP is a spectrometer coupled with a fiber F and DP is a data processor. Other notations have their usual meaning.

Fig. 2
Fig. 2

(a) Interference fringes due to the interferometer, obtained at the observation plane. (b) The spectrum of the laser beam (peak wavelength = 632.8 nm ) obtained at point P using the spectrometer.

Tables (2)

Tables Icon

Table 1 Single Beam S n ( 1 ) ( r , ω ) and Two Beam Usual Stokes Parameters S n ( r , ω ) (for n = 0 , 1 , 2 , 3 ) Determined at Point P in the Observation Plane

Tables Icon

Table 2 Contrast Parameters C n ( r , ω ) and the Generalized Stokes Parameters S n ( r 1 , r 2 , ω ) (for n = 0 , 1 , 2 , 3 ) Determined for the Expanded Laser Beam

Equations (10)

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S n ( r , ω ) = S n ( 1 ) ( r , ω ) + S n ( 2 ) ( r , ω ) + 2 S 0 ( 1 ) ( r , ω ) S 0 ( 2 ) ( r , ω ) μ n ( r 1 , r 2 , ω ) cos β n ,
μ n ( r 1 , r 2 , ω ) = S n max ( r , ω ) S n min ( r , ω ) S 0 max ( r , ω ) + S 0 min ( r , ω ) = C n ( r , ω ) ,
μ n ( r 1 , r 2 , ω ) = S n ( r 1 , r 2 , ω ) φ 0 ( r 1 , ω ) φ 0 ( r 2 , ω ) ,
cos β n = S n ( r , ω ) 2 S n ( 1 ) ( r , ω ) 2 S 0 ( 1 ) ( r , ω ) × C n ( r , ω ) for ( n = 0 , 1 , 2 , 3 ) .
S n ( r 1 , r 2 , ω ) = μ n ( r 1 , r 2 , ω ) ( cos β n + i sin β n ) × φ 0 ( r 1 , ω ) φ 0 ( r 2 , ω ) .
S 0 1 ( r , ω ) = φ ( 0 ° , 0 ° ) + φ ( 90 ° , 0 ° ) ,
S 1 1 ( r , ω ) = φ ( 0 ° , 0 ° ) φ ( 90 ° , 0 ° ) ,
S 2 1 ( r , ω ) = φ ( 45 ° , 0 ° ) φ ( 135 ° , 0 ° ) ,
S 3 1 ( r , ω ) = φ ( 45 ° , 45 ° ) φ ( 135 ° , 45 ° ) .
μ n ( r 1 , r 2 , ω ) = μ n ( r 1 , r 2 , ω ) = S n ( r , ω ) 2 S n ( 1 ) ( r , ω ) 2 S 0 ( 1 ) ( r , ω ) .

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