Abstract

The rotational frequency shift is studied for fields of arbitrary states of coherence and polarization. It is shown that the power spectrum of the field in the rotating frame is influenced both by the degree of polarization and the degree of coherence. Examples for some model field classes are given.

© 2006 Optical Society of America

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References

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  1. B. A. Garetz, J. Opt. Soc. Am. 71, 609 (1981).
    [CrossRef]
  2. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
    [CrossRef]
  3. G. Nienhuis, Opt. Commun. 132, 8 (1996).
    [CrossRef]
  4. I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
    [CrossRef]
  5. M. Hautakorpi, T. Setälä, and M. Kaivola, J. Opt. Soc. Am. A 23, 1159 (2006).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  7. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1944), Chap. 11.2.
  8. K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
    [CrossRef] [PubMed]
  9. E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]

2006

2000

1998

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

1997

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

1996

G. Nienhuis, Opt. Commun. 132, 8 (1996).
[CrossRef]

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

1981

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

Brown, T. G.

Courtial, J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Dholakia, K.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Garetz, B. A.

Hautakorpi, M.

James, D. F. V.

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

Kaivola, M.

Mandel, L.

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

Nienhuis, G.

G. Nienhuis, Opt. Commun. 132, 8 (1996).
[CrossRef]

Padgett, M. J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Setälä, T.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1944), Chap. 11.2.

Wolf, E.

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

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

Youngworth, K. S.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

G. Nienhuis, Opt. Commun. 132, 8 (1996).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Rep. Prog. Phys.

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

Other

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

G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1944), Chap. 11.2.

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Figures (2)

Fig. 1
Fig. 1

Changes in the (normalized) spectrum of a Bessel-correlated field for (a) a circularly polarized field at different rates of rotation Ω normalized by linewidth Δ ω and (b) a partially polarized field with different degrees of polarization P, with Ω Δ ω = 1 . In both cases, r σ μ = 10 , where r is the radial distance from the center of rotation and σ μ is the correlation length. The power spectrum in the nonrotating frame is Lorentzian.

Fig. 2
Fig. 2

Changes in the (normalized) spectrum of a partially polarized and partially coherent field for P = 0.1 (dashed curve) and P = 0.75 (solid curve), with Ω Δ ω = 10 and r σ μ = 0.25 .

Equations (16)

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Γ ( r 1 , r 2 , τ ) = [ E + * ( r 1 , t 1 ) E + ( r 2 , t 2 ) E + * ( r 1 , t 1 ) E ( r 2 , t 2 ) E * ( r 1 , t 1 ) E + ( r 2 , t 2 ) E * ( r 1 , t 1 ) E ( r 2 , t 2 ) ] ,
R c ( t ) = [ exp [ i Ω t ] 0 0 exp [ i Ω t ] ] .
Γ ( r ) ( r 1 , r 2 , τ , T ) = [ Γ ̃ + + exp [ i Ω τ ] Γ ̃ + exp [ 2 i Ω T ] Γ ̃ + exp [ 2 i Ω T ] Γ ̃ exp [ i Ω τ ] ] ,
Γ ̃ i j = Γ i j [ R Ω ( t 1 ) r 1 , R Ω ( t 2 ) r 2 , τ ] ,
R Ω ( t ) = [ cos Ω t sin Ω t sin Ω t cos Ω t ] .
W ( r ) ( r 1 , r 2 , ω , T ) = 1 2 π Γ ( r ) ( r 1 , r 2 , τ , T ) exp [ i ω τ ] d τ .
Γ ( r 1 , r 2 , τ ) = I 0 P 0 exp [ r 1 2 2 σ I 2 ] exp [ r 2 2 2 σ I 2 ] J 0 [ r 2 r 1 σ μ ] g ( τ ) ,
P 0 = ( 1 P ) [ 1 0 0 1 ] + 2 P [ a 2 a * b b * a b 2 ] ,
J 0 ( r 2 r 1 σ μ ) = J n ( r 1 σ μ ) J n ( r 2 σ μ ) exp [ i n ( ϕ 2 ϕ 1 ) ] ,
W ( r ) ( r 1 , r 2 , ω ) = I 0 n = P n ( ω , T ) exp [ i n ( ϕ 2 ϕ 1 ) ] exp [ r 1 2 2 σ I 2 ] exp [ r 2 2 2 σ I 2 ] × J n ( r 1 σ μ ) J n ( r 2 σ μ ) ,
P n ( ω , T ) = [ [ ( 1 P ) + 2 P a 2 ] g ̃ ( ω + Ω n Ω ) 2 P a * b g ̃ ( ω n Ω ) exp [ 2 i Ω T ] 2 P b * a exp [ 2 i Ω T ] g ̃ ( ω n Ω ) [ ( 1 P ) + 2 P b 2 ] g ̃ ( ω Ω n Ω ) ]
S ( r ) ( r , ω ) = W + + ( r ) ( r , r , ω ) + W ( r ) ( r , r , ω ) ,
S ( r ) ( r , ω ) = I 0 n = [ [ ( 1 P ) + 2 P a 2 ] g ̃ ( ω + Ω n Ω ) + [ ( 1 P ) + 2 P b 2 ] g ̃ ( ω Ω n Ω ) ] exp [ r 2 σ I 2 ] [ J n ( r σ μ ) ] 2 .
Γ ( r 1 , r 2 , τ ) = I 0 P 0 J 1 ( r 1 σ μ ) J 1 ( r 2 σ μ ) exp [ i ( ϕ 2 ϕ 1 ) ] g ( τ ) .
S ( r ) ( r , ω ) = I 0 [ J 1 ( r σ μ ) ] 2 { [ ( 1 P ) + 2 P a 2 ] g ̃ ( ω ) + [ ( 1 P ) + 2 P b 2 ] g ̃ ( ω 2 Ω ) } .
S ( r ) ( r , ω ) = I 0 [ J 1 ( r σ μ ) ] 2 [ ( 1 + P ) g ̃ ( ω ) + ( 1 P ) g ̃ ( ω 2 Ω ) ] .

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