Abstract

It is well established that light carrying orbital angular momentum (OAM) can be used to induce a mechanical torque causing an object to spin. We consider the complementary scenario: will an observer spinning relative to the beam axis measure a change in OAM as a result of their rotational velocity? Remarkably, although a linear Doppler shift changes the linear momentum of a photon, the angular Doppler shift induces no change in the angular momentum. Further, we examine the rotational Doppler shift in frequency imparted to the incident light due to the relative motion of the beam with respect to the observer and consider what must happen to the measured wavelength if the speed of light c is to remain constant. We show specifically that the OAM of the incident beam is not affected by the rotating observer and that the measured wavelength is shifted by a factor equal and opposite to that of the frequency shift induced by the rotational Doppler effect.

© 2014 Optical Society of America

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References

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  1. J. H. Poynting, Proc. R. Soc. London A 82, 560 (1909).
    [CrossRef]
  2. W. A. Shurcliff, Polarized Light: Production and Use (Harvard, 1962).
  3. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  4. B. A. Garetz, J. Opt. Soc. Am. 71, 609 (1981).
    [CrossRef]
  5. G. Nienhuis, Opt. Commun. 132, 8 (1996).
    [CrossRef]
  6. J. Javanainen, S. M. Paik, and S. M. Yoo, Phys. Rev. A 58, 580 (1998).
    [CrossRef]
  7. A. Y. Okulov, J. Opt. Soc. Am. B 29, 714 (2012).
    [CrossRef]
  8. M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
    [CrossRef]
  9. J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
    [CrossRef]
  10. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
    [CrossRef]
  11. I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
    [CrossRef]
  12. M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, Pis’ma v Zh. Èksper. Teoret. Fiz. 81, 699 (2005).
  13. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
    [CrossRef]
  14. F. C. Speirits and S. M. Barnett, Phys. Rev. Lett. 111, 103602 (2013).
    [CrossRef]

2013 (2)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
[CrossRef]

F. C. Speirits and S. M. Barnett, Phys. Rev. Lett. 111, 103602 (2013).
[CrossRef]

2012 (1)

2005 (1)

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, Pis’ma v Zh. Èksper. Teoret. Fiz. 81, 699 (2005).

2002 (2)

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

1998 (2)

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

J. Javanainen, S. M. Paik, and S. M. Yoo, Phys. Rev. A 58, 580 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

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

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1981 (1)

1909 (1)

J. H. Poynting, Proc. R. Soc. London A 82, 560 (1909).
[CrossRef]

Allen, L.

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

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Arlt, J.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
[CrossRef]

F. C. Speirits and S. M. Barnett, Phys. Rev. Lett. 111, 103602 (2013).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[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]

Courtial, J.

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

Dholakia, K.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

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

Garetz, B. A.

Javanainen, J.

J. Javanainen, S. M. Paik, and S. M. Yoo, Phys. Rev. A 58, 580 (1998).
[CrossRef]

Lavery, M. P. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
[CrossRef]

MacDonald, M. P.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

Nienhuis, G.

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

Okulov, A. Y.

Padgett, M. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
[CrossRef]

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

Paik, S. M.

J. Javanainen, S. M. Paik, and S. M. Yoo, Phys. Rev. A 58, 580 (1998).
[CrossRef]

Pas’ko, V. A.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, Pis’ma v Zh. Èksper. Teoret. Fiz. 81, 699 (2005).

Paterson, L.

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

Poynting, J. H.

J. H. Poynting, Proc. R. Soc. London A 82, 560 (1909).
[CrossRef]

Robertson, D. A.

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

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard, 1962).

Sibbett, W.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

Soskin, M. S.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, Pis’ma v Zh. Èksper. Teoret. Fiz. 81, 699 (2005).

Speirits, F. C.

F. C. Speirits and S. M. Barnett, Phys. Rev. Lett. 111, 103602 (2013).
[CrossRef]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Vasnetsov, M. V.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, Pis’ma v Zh. Èksper. Teoret. Fiz. 81, 699 (2005).

Volke-Sepulveda, K.

J. Arlt, M. P. MacDonald, L. Paterson, W. Sibbett, K. Volke-Sepulveda, and K. Dholakia, Opt. Express 10, 844 (2002).
[CrossRef]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yoo, S. M.

J. Javanainen, S. M. Paik, and S. M. Yoo, Phys. Rev. A 58, 580 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, Opt. Commun. 201, 21 (2002).
[CrossRef]

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

Opt. Express (1)

Phys. Rev. A (2)

J. Javanainen, S. M. Paik, and S. M. Yoo, Phys. Rev. A 58, 580 (1998).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett. (3)

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]

F. C. Speirits and S. M. Barnett, Phys. Rev. Lett. 111, 103602 (2013).
[CrossRef]

Pis’ma v Zh. Èksper. Teoret. Fiz. (1)

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, Pis’ma v Zh. Èksper. Teoret. Fiz. 81, 699 (2005).

Proc. R. Soc. London A (1)

J. H. Poynting, Proc. R. Soc. London A 82, 560 (1909).
[CrossRef]

Science (1)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, Science 341, 537 (2013).
[CrossRef]

Other (1)

W. A. Shurcliff, Polarized Light: Production and Use (Harvard, 1962).

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Figures (3)

Fig. 1.
Fig. 1.

Wavelength λ is defined as the distance along the beam between two points with the same phase, shown for (a) a Gaussian beam with flat phase fronts and (b) an =1 beam with helical phase fronts.

Fig. 2.
Fig. 2.

Change in ϕ coordinate from ϕ (black arrow) to ϕ (white arrow) due to the rotation of the observer can be seen in (a), while the corresponding relative change in wavelength δλ is shown in (b).

Fig. 3.
Fig. 3.

Effect of an observer’s rotation around the beam axis can be seen to either increase, kz, or decrease, kz, the measured wavelength, compared with the wavelength in the non-rotating case kz.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

J=S+L.
ψ=J(κρ)eikzeiϕeiωt,
Ωκc,
ϕ=ϕΩt.
ψ=J(κρ)eikzei(ϕ+Ωt)eiωt,
ψ=J(κρ)eikzeiϕei(ωtΩt),
iϕψ(ρ,ϕ)=ψ(ρ,ϕ).
iϕψ(ρ,ϕ)=ψ(ρ,ϕ).
kzδz=δϕ.
δλλ=ΩckzΩω.
δk=Ωωk,
k=k(1Ωω).
ω=ωΩ=ω(1Ωω).
ωk=ωk=c.
eikΔzeiΔϕ=1.
kΔz+Δϕ=2π,
Δz=Δz(1+Ωck).
k=k(1Ωck),

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