Abstract

In practical situations, one often generates a beam by superposition of two or more light beams. The beam generated by superposition displays, in general, different spectral properties than do the original beams. However, there are some optical beams, called cross-spectrally pure beams, which can generate a light beam of identical spectral distribution on superposition. The relationship between cross-spectral purity and spatial coherence has been the subject of investigations for some time. Recently, a concept of so-called statistical similarity has been introduced which provides a new way to elucidate complete spatial coherence. In this Letter, we discuss some implications of statistical similarity of an optical field on its cross-spectral purity.

© 2012 Optical Society of America

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References

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  1. L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
    [CrossRef]
  2. L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
    [CrossRef]
  3. D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
    [CrossRef]
  4. M. Lahiri and E. Wolf, Phys. Rev. Lett. 105, 063901 (2010).
    [CrossRef]
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  6. S. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
    [CrossRef]
  7. E. Wolf, Opt. Commun. 283, 4427 (2010).
    [CrossRef]
  8. The concept of “statistical similarity” originated in the work of Verdet [12,13], who estimated the size of the region on Earth’s surface throughout which vibrations of sunlight fluctuate in unison. His result is in agreement with the order of magnitude of coherence-area of sunlight on the Earth’s surface, as estimated by modern coherence theory [14].
  9. M. Lahiri and E. Wolf, Opt. Lett. 36, 2423 (2011).
    [CrossRef]
  10. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
    [CrossRef]
  11. E. Wolf, J. Opt. Soc. Am. A 3, 76 (1986).
    [CrossRef]
  12. E. Verdet, Leçons d’Optique Physique, Vol. 1 (L’Imprimierie Impériale, 1869).
  13. E. Verdet, Annales Scientifiques de l’E.N.S. 2, 291 (1865).
  14. G. S. Agarwal, G. Gbur, and E. Wolf, Opt. Lett. 29, 459 (2004).
    [CrossRef]

2011 (1)

2010 (2)

E. Wolf, Opt. Commun. 283, 4427 (2010).
[CrossRef]

M. Lahiri and E. Wolf, Phys. Rev. Lett. 105, 063901 (2010).
[CrossRef]

2005 (1)

S. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

2004 (1)

1997 (1)

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[CrossRef]

1986 (1)

1982 (1)

1976 (1)

1961 (1)

1865 (1)

E. Verdet, Annales Scientifiques de l’E.N.S. 2, 291 (1865).

Agarwal, G. S.

Gbur, G.

James, D. F. V.

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[CrossRef]

Lahiri, M.

M. Lahiri and E. Wolf, Opt. Lett. 36, 2423 (2011).
[CrossRef]

M. Lahiri and E. Wolf, Phys. Rev. Lett. 105, 063901 (2010).
[CrossRef]

Mandel, L.

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

L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
[CrossRef]

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

Ponomarenko, S.

S. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Roychowdhury, H.

S. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Verdet, E.

E. Verdet, Annales Scientifiques de l’E.N.S. 2, 291 (1865).

E. Verdet, Leçons d’Optique Physique, Vol. 1 (L’Imprimierie Impériale, 1869).

Wolf, E.

M. Lahiri and E. Wolf, Opt. Lett. 36, 2423 (2011).
[CrossRef]

E. Wolf, Opt. Commun. 283, 4427 (2010).
[CrossRef]

M. Lahiri and E. Wolf, Phys. Rev. Lett. 105, 063901 (2010).
[CrossRef]

S. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

G. S. Agarwal, G. Gbur, and E. Wolf, Opt. Lett. 29, 459 (2004).
[CrossRef]

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[CrossRef]

E. Wolf, J. Opt. Soc. Am. A 3, 76 (1986).
[CrossRef]

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
[CrossRef]

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

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

Annales Scientifiques de l’E.N.S. (1)

E. Verdet, Annales Scientifiques de l’E.N.S. 2, 291 (1865).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[CrossRef]

E. Wolf, Opt. Commun. 283, 4427 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

S. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

M. Lahiri and E. Wolf, Phys. Rev. Lett. 105, 063901 (2010).
[CrossRef]

Other (3)

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

The concept of “statistical similarity” originated in the work of Verdet [12,13], who estimated the size of the region on Earth’s surface throughout which vibrations of sunlight fluctuate in unison. His result is in agreement with the order of magnitude of coherence-area of sunlight on the Earth’s surface, as estimated by modern coherence theory [14].

E. Verdet, Leçons d’Optique Physique, Vol. 1 (L’Imprimierie Impériale, 1869).

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Figures (1)

Fig. 1.
Fig. 1.

Illustrating notation.

Equations (25)

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Γ(r1,r2;τ)V*(r1;t)V(r2;t+τ).
I(r)|V(r;t)|2=Γ(r,r;0).
γ(r1,r2;τ)Γ(r1,r2;τ)I(r1)I(r2).
|γ(r1,r2;τ0)|=1.
V(r2;t+τ0)=A(τ0)(r1,r2)V(r1;t).
|A(τ0)(r1,r2)|=I(r2)I(r1),
arg{A(τ0)(r1,r2)}=arg{γ(r1,r2;τ0)},
W(r1,r2;ω)=12πΓ(r1,r2;τ)eiωτdτ,
W(r1,r2;ω)=U*(r1;ω)U(r2;ω)ω,
W(r,r;ω)S(r,ω).
μ(r1,r2;ω)W(r1,r2;ω)S(r1,ω)S(r2,ω).
U(r2;ω)=B(r1,r2;ω)U(r1;ω),
|B(r1,r2;ω)|=S(r2;ω)S(r1;ω),
arg{B(r1,r2;ω)}=arg{μ(r1,r2;ω)}.
S(r1;ω)I(r1)=S(r2;ω)I(r2),
μ(r1,r2;ω)=γ(r1,r2;τ0)exp[iωτ0].
W(r1,r2;ω)=exp[iωτ0]A(τ0)(r1,r2)S(r1;ω)=exp[iωτ0]S(r2;ω){A(τ0)(r1,r2)}*.
S(r1;ω)=S(r2;ω)|A(τ0)(r1,r2)|2.
S(r1;ω)I(r1)=S(r2;ω)I(r2);
μ(r1,r2;ω)=A(τ0)(r1,r2)|A(τ0)(r1,r2)|exp[iωτ0].
μ(r1,r2;ω)=γ(r1,r2;τ0)exp[iωτ0];
S(r2;ω)S(r1;ω)=C(r1,r2),
B(r1,r2;ω)=f(r1;r2)exp[iωτ0],
|B(r1,r2;ω)|=I(r2)I(r1),
arg{B(r1,r2;ω)}=arg{γ(r1,r2;τ0)}+ωτ0.

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