Abstract

We observe the rotational Doppler shift of an orbital angular momentum (OAM)-carrying white-light beam after it is backscattered from a rotating object. Unlike the well known linear shift, this rotational shift is independent of the optical frequency, and hence each spectral component of the scattered light is shifted by the same value. Consequently, even a white-light source can give rise to a single-valued frequency shift. We show that the size of this shift is proportional to the OAM of the light and that superpositions of different OAM states give rise to multiple frequency sidebands. The observability of this rotational shift for white-light illumination highlights the potential for the rotational Doppler effect to form the basis of a rotational sensor for the remote detection of spinning objects.

© 2014 Optical Society of America

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2014

2013

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

C. Rosales-Guzmån, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 3, 2851 (2013).
[CrossRef]

2011

2008

2007

2006

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, Opt. Express 14, 11919 (2006).
[CrossRef]

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, Phys. Rev. Lett. 97, 113601 (2006).
[CrossRef]

2005

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[CrossRef]

2003

M. Harwit, Astrophys. J. 597, 1266 (2003).
[CrossRef]

1998

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

1997

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

1994

L. Allen, M. Babiker, and W. L. Power, Opt. Commun. 112, 141 (1994).
[CrossRef]

1992

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

1990

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

1983

1981

B. A. Garetz, J. Opt. Soc. Am. 71, 609 (1981).
[CrossRef]

T. Asakura and N. Takai, Appl. Phys. 25, 179 (1981).
[CrossRef]

Allen, L.

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

L. Allen, M. Babiker, and W. L. Power, Opt. Commun. 112, 141 (1994).
[CrossRef]

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

Arnold, A. S.

Asakura, T.

T. Asakura and N. Takai, Appl. Phys. 25, 179 (1981).
[CrossRef]

Babiker, M.

L. Allen, M. Babiker, and W. L. Power, Opt. Commun. 112, 141 (1994).
[CrossRef]

Barnett, S. M.

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, Opt. Lett. 39, 2944 (2014).
[CrossRef]

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

Barreiro, S.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, Phys. Rev. Lett. 97, 113601 (2006).
[CrossRef]

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Beijersbergen, M. W.

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

Belmonte, A.

C. Rosales-Guzmån, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 3, 2851 (2013).
[CrossRef]

A. Belmonte and J. P. Torres, Opt. Lett. 36, 4437 (2011).
[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, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Ellinas, D.

Failache, H.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, Phys. Rev. Lett. 97, 113601 (2006).
[CrossRef]

Franke-Arnold, S.

Garetz, B. A.

Gibson, G. M.

Girkin, J. M.

Harwit, M.

M. Harwit, Astrophys. J. 597, 1266 (2003).
[CrossRef]

Hermosa, N.

C. Rosales-Guzmån, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 3, 2851 (2013).
[CrossRef]

Keen, S.

Lavery, M. P. J.

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, Opt. Lett. 39, 2944 (2014).
[CrossRef]

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

Leach, J.

Lembessis, V. E.

Lezama, A.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, Phys. Rev. Lett. 97, 113601 (2006).
[CrossRef]

Love, G. D.

Meynart, R.

Öhberg, P.

Padgett, M. J.

Pas’ko, V. A.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[CrossRef]

Power, W. L.

L. Allen, M. Babiker, and W. L. Power, Opt. Commun. 112, 141 (1994).
[CrossRef]

Robertson, D. A.

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Rosales-Guzmån, C.

C. Rosales-Guzmån, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 3, 2851 (2013).
[CrossRef]

Saunter, C.

Soskin, M. S.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Speirits, F. C.

Sperits, F. C.

M. P. J. Lavery, F. C. Sperits, 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]

Tabosa, J. W. R.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, Phys. Rev. Lett. 97, 113601 (2006).
[CrossRef]

Takai, N.

T. Asakura and N. Takai, Appl. Phys. 25, 179 (1981).
[CrossRef]

Torres, J. P.

C. Rosales-Guzmån, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 3, 2851 (2013).
[CrossRef]

A. Belmonte and J. P. Torres, Opt. Lett. 36, 4437 (2011).
[CrossRef]

Vasnetsov, M. V.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Woerdman, J. P.

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

Wright, A. J.

Yao, A. M.

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys.

T. Asakura and N. Takai, Appl. Phys. 25, 179 (1981).
[CrossRef]

Astrophys. J.

M. Harwit, Astrophys. J. 597, 1266 (2003).
[CrossRef]

J. Opt. Soc. Am.

JETP Lett.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

New J. Phys.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).
[CrossRef]

Opt. Commun.

L. Allen, M. Babiker, and W. L. Power, Opt. Commun. 112, 141 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. Lett.

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

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, Phys. Rev. Lett. 97, 113601 (2006).
[CrossRef]

Sci. Rep.

C. Rosales-Guzmån, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 3, 2851 (2013).
[CrossRef]

Science

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

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Figures (5)

Fig. 1.
Fig. 1.

For a helically phased beam (i.e., one carrying orbital angular momentum), the local ray direction is inclined by an angle β = / k 0 r with respect to the propagation direction. When used to illuminate a spinning object, this incline results in a frequency shift of the scattered light similar to that obtained in Doppler velocimetry.

Fig. 2.
Fig. 2.

A supercontinuum laser source is coupled into a single-mode fiber (SMF) to produce a spatially coherent beam of white light, which is then collimated by a lens, L1, and illuminates a spatial light modulator (SLM). The SLM is encoded with a combination of fork diffraction patterns, such that the first-order diffracted beam is of the desired OAM superposition . A spatial filter, AP, is placed in the focal plane of a lens, L2, and used to select the first-order diffracted beam of all the wavelength components. To compensate for chromatic dispersion resulting from the diffraction grating, the first-order beam is then reimaged onto a prism, yielding a white-light OAM-carrying beam within which all the wavelength components are coaxial. This white OAM is reimaged onto the spinning rough surface, and the backscattered light is collected by a photodetector, PD, to measure the intensity modulation frequency.

Fig. 3.
Fig. 3.

The recorded time sequence of the intensity backscattered from the spinning surface is Fourier transformed to give a power spectrum from which the peak modulation frequency in this backscattered light can be measured. The power normalization is with respect to the noise floor of the detector (0 dB). The inset shows the intensity cross section of the OAM superposition = ± 12 .

Fig. 4.
Fig. 4.

Observed modulation frequency plotted as a function of rotation rate for four different superpositions of illuminating OAM, = ± 8 , ± 10 , ± 12 , ± 14 . The predicted frequency of the intensity modulation is f mod = Ω | 1 2 | / 2 π , shown as a solid line. The insets show the intensity cross section of the various OAM superpositions.

Fig. 5.
Fig. 5.

The observed power spectrum in the intensity modulation of the scattered light obtained spinning surface is illuminated with a superposition of = ± 14 & ± 15 . This superposition results in a cluster of peaks, corresponding to the integer differences between the various OAM components of the illuminating light. The power normalization is with respect to the noise floor of the detector (0 dB). The inset shows the intensity cross section of the OAM superposition = ± 14 & ± 15 .

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