Abstract

It was shown some time ago that the space-time and the space-frequency degrees of polarization of a stochastic electromagnetic beam are not equivalent to each other. It is not possible, in general, to obtain a formal relationship between them. In this Letter, we discuss certain conditions under which they are directly related. These conditions lead to the concept of polarization-purity. If an optical beam obeys these conditions, its space-frequency degree of polarization has the same value at all frequencies present in the spectrum, and the value is equal to the space-time degree of polarization.

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References

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  1. G. G. Stokes, Trans. Cambr. Phil. Soc. 9, 399 (1852).
  2. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1995).
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    [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).
  7. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
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    [CrossRef]
  9. T. Setälä, F. Nunziata, and A. T. Friberg, Opt. Lett. 34, 2924 (2009).
    [CrossRef]
  10. M. Lahiri, Opt. Lett. 34, 2936 (2009).
    [CrossRef]
  11. M. Lahiri and E. Wolf, Phys. Lett. A 374, 997 (2010).
    [CrossRef]
  12. An equivalent condition is briefly discussed in [9].
  13. The term purity is inspired by the concept of cross-spectral purity introduced by Mandel [14]. Cross-spectral purity has similar significance relating to the spatial coherence properties of optical fields [15].
  14. L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
    [CrossRef]
  15. L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529(1976).
    [CrossRef]

2010

M. Lahiri and E. Wolf, Phys. Lett. A 374, 997 (2010).
[CrossRef]

2009

1994

1976

1961

1959

E. Wolf, Nuovo Cimento 13, 1165 (1959).
[CrossRef]

1852

G. G. Stokes, Trans. Cambr. Phil. Soc. 9, 399 (1852).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1995).

Friberg, A. T.

James, D. F. V.

Lahiri, M.

M. Lahiri and E. Wolf, Phys. Lett. A 374, 997 (2010).
[CrossRef]

M. Lahiri, Opt. Lett. 34, 2936 (2009).
[CrossRef]

Mandel, L.

Nunziata, F.

Poincaré, H.

H. Poincaré, Théorie Mathématique de la Lumière (Georges Carré, 1892), Vol. 2.

Setälä, T.

Stokes, G. G.

G. G. Stokes, Trans. Cambr. Phil. Soc. 9, 399 (1852).

Wiener, N.

N. Wiener, J. Math. Phys. 7, 109 (1927–28).

Wolf, E.

M. Lahiri and E. Wolf, Phys. Lett. A 374, 997 (2010).
[CrossRef]

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529(1976).
[CrossRef]

E. Wolf, Nuovo Cimento 13, 1165 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

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

J. Math. Phys.

N. Wiener, J. Math. Phys. 7, 109 (1927–28).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nuovo Cimento

E. Wolf, Nuovo Cimento 13, 1165 (1959).
[CrossRef]

Opt. Lett.

Phys. Lett. A

M. Lahiri and E. Wolf, Phys. Lett. A 374, 997 (2010).
[CrossRef]

Trans. Cambr. Phil. Soc.

G. G. Stokes, Trans. Cambr. Phil. Soc. 9, 399 (1852).

Other

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1995).

H. Poincaré, Théorie Mathématique de la Lumière (Georges Carré, 1892), Vol. 2.

An equivalent condition is briefly discussed in [9].

The term purity is inspired by the concept of cross-spectral purity introduced by Mandel [14]. Cross-spectral purity has similar significance relating to the spatial coherence properties of optical fields [15].

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

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

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