Abstract

The optical rotational Doppler effect of light beams with angular momentum has recently found applications in the remote sensing of spinning objects. However, most of the reported experimental demonstrations rely on the particular condition of normal incidence, while the general case of oblique incidence has not been addressed yet. Herein, we investigate the optical rotational Doppler effect at oblique incidence based on a local scattering model and formulate the quantitative relation between the Doppler frequency shift and the tilt angle. The analytic results indicate that even if the rotational axis of the spinning object is oriented at a specific tilt angle relative to the light propagation direction, the rotational speed can still be extracted from an asymmetrically broadened Doppler signal. The geometric mean value of the extreme frequency shift is a constant despite the variation of the incident angle. An experiment with obliquely incident and superimposed optical vortices is executed to verify our theoretical predictions, achieving a successful detection of the rotational speed at relatively large tilt angles with a relative error less than 2%. The scheme proposed in this study may be useful for practical applications of rotational Doppler effect in remote sensing and metrology.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  31. M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7, 46 (2005).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  35. A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A: Pure Appl. Opt. 6(5), S170–S174 (2004).
    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (2)

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

S. Qiu, T. Liu, Z. Li, C. Wang, Y. Ren, Q. Shao, and C. Xing, “Influence of lateral misalignment on the optical rotational Doppler effect,” Appl. Opt. 58(10), 2650–2655 (2019).
[Crossref]

2018 (1)

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

2017 (5)

2016 (1)

2015 (2)

N. Cvijetic, G. Milione, E. Ip, and T. Wang, “Detecting Lateral Motion using Light’s Orbital Angular Momentum,” Sci. Rep. 5(1), 15422 (2015).
[Crossref]

Y. Liu, Y. Ke, J. Zhou, H. Luo, and S. Wen, “Manipulating the spin-dependent splitting by geometric Doppler effect,” Opt. Express 23(13), 16682–16692 (2015).
[Crossref]

2014 (3)

2013 (2)

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light's orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
[Crossref]

2011 (1)

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

2006 (2)

V. C. Chen, F. Li, S. S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: Phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006).
[Crossref]

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14(25), 11919–11924 (2006).
[Crossref]

2005 (2)

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Angular momentum of a rotating light beam,” Opt. Commun. 249(4-6), 367–378 (2005).
[Crossref]

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7, 46 (2005).
[Crossref]

2004 (1)

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A: Pure Appl. Opt. 6(5), S170–S174 (2004).
[Crossref]

2003 (1)

2001 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref]

1998 (1)

K. D. J. Courtial, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the Rotational Frequency Shift Imparted to a Rotating Light Beam Possessing Orbital Angular Momentum,” Phys. Rev. Lett. 80(15), 3217–3219 (1998).
[Crossref]

1997 (1)

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational Frequency Shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

1996 (1)

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
[Crossref]

1995 (2)

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

1989 (1)

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[Crossref]

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

1984 (1)

B. Sheva, “Theory of the Doppler effect: Fact, fiction and approximation,” Radio Sci. 19(4), 1027–1040 (1984).
[Crossref]

1982 (1)

1981 (1)

B. A. Garetz, “Angular Doppler effect,” J. Opt. Soc. Am. A 71(5), 609–611 (1981).
[Crossref]

1974 (1)

1972 (1)

L. M. Barker and R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43(11), 4669–4675 (1972).
[Crossref]

Allen, L.

K. D. J. Courtial, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the Rotational Frequency Shift Imparted to a Rotating Light Beam Possessing Orbital Angular Momentum,” Phys. Rev. Lett. 80(15), 3217–3219 (1998).
[Crossref]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Barker, L. M.

L. M. Barker and R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43(11), 4669–4675 (1972).
[Crossref]

Barnett, S. M.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light's orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

Basistiy, I. V.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Bekshaev, A. Y.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Angular momentum of a rotating light beam,” Opt. Commun. 249(4-6), 367–378 (2005).
[Crossref]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A: Pure Appl. Opt. 6(5), S170–S174 (2004).
[Crossref]

Belmonte, A.

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Measuring the translational and rotational velocities of particles in helical motion using structured light,” Opt. Express 22(13), 16504–16509 (2014).
[Crossref]

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
[Crossref]

Berkhout, G. C. G.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational Frequency Shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational Frequency Shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

Bland-Hawthorn, J.

Chen, L.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Chen, V. C.

V. C. Chen, F. Li, S. S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: Phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006).
[Crossref]

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[Crossref]

Courtial, J.

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

Courtial, K. D. J.

K. D. J. Courtial, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the Rotational Frequency Shift Imparted to a Rotating Light Beam Possessing Orbital Angular Momentum,” Phys. Rev. Lett. 80(15), 3217–3219 (1998).
[Crossref]

Cvijetic, N.

N. Cvijetic, G. Milione, E. Ip, and T. Wang, “Detecting Lateral Motion using Light’s Orbital Angular Momentum,” Sci. Rep. 5(1), 15422 (2015).
[Crossref]

Dandliker, R.

Dong, J.

Durst, F.

Fang, L.

L. Fang, M. J. Padgett, and J. Wang, “Sharing a Common Origin Between the Rotational and Linear Doppler Effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

Fickler, R.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Fischer, A.

A. Fischer, “Model-based review of Doppler global velocimetry techniques with laser frequency modulation,” Opt. Lasers. Eng. 93, 19–35 (2017).
[Crossref]

Friese, M. E.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref]

Fu, D.

Fu, S.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

S. Fu, C. Gao, T. Wang, Y. Zhai, and Z. Zhang, “Non-diffractive Bessel-Gauss beams for the detection of rotating object free of obstructions,” Opt. Express 25(17), 20098–20108 (2017).
[Crossref]

Gao, C.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

S. Fu, C. Gao, T. Wang, Y. Zhai, and Z. Zhang, “Non-diffractive Bessel-Gauss beams for the detection of rotating object free of obstructions,” Opt. Express 25(17), 20098–20108 (2017).
[Crossref]

Gao, J.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Garetz, B. A.

B. A. Garetz, “Angular Doppler effect,” J. Opt. Soc. Am. A 71(5), 609–611 (1981).
[Crossref]

Gibson, G. M.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Gil, L.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[Crossref]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

He, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref]

He, Y.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Heckenberg, N. R.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref]

Hermosa, N.

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Measuring the translational and rotational velocities of particles in helical motion using structured light,” Opt. Express 22(13), 16504–16509 (2014).
[Crossref]

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
[Crossref]

Ho, S. S.

V. C. Chen, F. Li, S. S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: Phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006).
[Crossref]

Hollenbach, R. E.

L. M. Barker and R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43(11), 4669–4675 (1972).
[Crossref]

Howe, B. M.

Ip, E.

N. Cvijetic, G. Milione, E. Ip, and T. Wang, “Detecting Lateral Motion using Light’s Orbital Angular Momentum,” Sci. Rep. 5(1), 15422 (2015).
[Crossref]

Iten, P. D.

Ke, Y.

Keen, S.

Lavery, M. P.

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light's orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

Lavery, M. P. J.

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

Leach, J.

Lee, M. P.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Leon-Saval, S.

Li, F.

V. C. Chen, F. Li, S. S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: Phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006).
[Crossref]

Li, Z.

Ling, X.

Liu, T.

Liu, Y.

Liu, Z.

Love, G. D.

Luo, H.

Milione, G.

N. Cvijetic, G. Milione, E. Ip, and T. Wang, “Detecting Lateral Motion using Light’s Orbital Angular Momentum,” Sci. Rep. 5(1), 15422 (2015).
[Crossref]

Molina-Terriza, G.

R. Neo, S. Leon-Saval, J. Bland-Hawthorn, and G. Molina-Terriza, “OAM interferometry: the detection of the rotational Doppler shift,” Opt. Express 25(18), 21159–21170 (2017).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref]

Neo, R.

Nienhuis, G.

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
[Crossref]

Padgett, M. J.

L. Fang, M. J. Padgett, and J. Wang, “Sharing a Common Origin Between the Rotational and Linear Doppler Effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light's orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14(25), 11919–11924 (2006).
[Crossref]

K. D. J. Courtial, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the Rotational Frequency Shift Imparted to a Rotating Light Beam Possessing Orbital Angular Momentum,” Phys. Rev. Lett. 80(15), 3217–3219 (1998).
[Crossref]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

Pas’ko, V. A.

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7, 46 (2005).
[Crossref]

Phillips, D. B.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Qiu, S.

Ren, Y.

Richter, G.

Robertson, D. A.

K. D. J. Courtial, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the Rotational Frequency Shift Imparted to a Rotating Light Beam Possessing Orbital Angular Momentum,” Phys. Rev. Lett. 80(15), 3217–3219 (1998).
[Crossref]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[Crossref]

Rosales-Guzman, C.

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Measuring the translational and rotational velocities of particles in helical motion using structured light,” Opt. Express 22(13), 16504–16509 (2014).
[Crossref]

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
[Crossref]

Rubinsztein-Dunlop, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref]

Saunter, C.

Shao, Q.

Sheva, B.

B. Sheva, “Theory of the Doppler effect: Fact, fiction and approximation,” Radio Sci. 19(4), 1027–1040 (1984).
[Crossref]

Shu, W.

Simpson, S. H.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Slyusar, V. V.

Soskin, M. S.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Angular momentum of a rotating light beam,” Opt. Commun. 249(4-6), 367–378 (2005).
[Crossref]

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7, 46 (2005).
[Crossref]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A: Pure Appl. Opt. 6(5), S170–S174 (2004).
[Crossref]

I. V. Basistiy, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, and B. A. Ya, “Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam,” Opt. Lett. 28(14), 1185–1187 (2003).
[Crossref]

Speirits, F. C.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light's orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

Spreeuw, R. J.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref]

Torres, J. P.

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Measuring the translational and rotational velocities of particles in helical motion using structured light,” Opt. Express 22(13), 16504–16509 (2014).
[Crossref]

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref]

Vasnetsov, M. V.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Angular momentum of a rotating light beam,” Opt. Commun. 249(4-6), 367–378 (2005).
[Crossref]

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7, 46 (2005).
[Crossref]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A: Pure Appl. Opt. 6(5), S170–S174 (2004).
[Crossref]

I. V. Basistiy, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, and B. A. Ya, “Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam,” Opt. Lett. 28(14), 1185–1187 (2003).
[Crossref]

Wang, C.

Wang, J.

L. Fang, M. J. Padgett, and J. Wang, “Sharing a Common Origin Between the Rotational and Linear Doppler Effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

Wang, T.

S. Fu, C. Gao, T. Wang, Y. Zhai, and Z. Zhang, “Non-diffractive Bessel-Gauss beams for the detection of rotating object free of obstructions,” Opt. Express 25(17), 20098–20108 (2017).
[Crossref]

N. Cvijetic, G. Milione, E. Ip, and T. Wang, “Detecting Lateral Motion using Light’s Orbital Angular Momentum,” Sci. Rep. 5(1), 15422 (2015).
[Crossref]

Wechsler, H.

V. C. Chen, F. Li, S. S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: Phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006).
[Crossref]

Wen, S.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Xing, C.

Xu, T.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Ya, B. A.

Yin, C.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

Zhai, Y.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

S. Fu, C. Gao, T. Wang, Y. Zhai, and Z. Zhang, “Non-diffractive Bessel-Gauss beams for the detection of rotating object free of obstructions,” Opt. Express 25(17), 20098–20108 (2017).
[Crossref]

Zhang, D.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Zhang, J.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

Zhang, P.

Zhang, R.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

Zhang, W.

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

Zhang, X.

Zhang, Z.

Zhou, H.

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

H. Zhou, D. Fu, J. Dong, P. Zhang, and X. Zhang, “Theoretical analysis and experimental verification on optical rotational Doppler effect,” Opt. Express 24(9), 10050–10056 (2016).
[Crossref]

Zhou, J.

Appl. Opt. (3)

IEEE Trans. Aerosp. Electron. Syst. (1)

V. C. Chen, F. Li, S. S. Ho, and H. Wechsler, “Micro-Doppler effect in radar: Phenomenon, model, and simulation study,” IEEE Trans. Aerosp. Electron. Syst. 42(1), 2–21 (2006).
[Crossref]

J. Appl. Phys. (1)

L. M. Barker and R. E. Hollenbach, “Laser interferometer for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43(11), 4669–4675 (1972).
[Crossref]

J. Opt. (2)

Y. Zhai, S. Fu, R. Zhang, C. Yin, H. Zhou, J. Zhang, and C. Gao, “The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure,” J. Opt. 21(5), 054002 (2019).
[Crossref]

M. P. J. Lavery, G. C. G. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A: Pure Appl. Opt. 6(5), S170–S174 (2004).
[Crossref]

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

B. A. Garetz, “Angular Doppler effect,” J. Opt. Soc. Am. A 71(5), 609–611 (1981).
[Crossref]

Laser Photonics Rev. (1)

L. Fang, M. J. Padgett, and J. Wang, “Sharing a Common Origin Between the Rotational and Linear Doppler Effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

New J. Phys. (1)

M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7, 46 (2005).
[Crossref]

Opt. Commun. (5)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[Crossref]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Angular momentum of a rotating light beam,” Opt. Commun. 249(4-6), 367–378 (2005).
[Crossref]

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
[Crossref]

Opt. Express (6)

Opt. Lasers. Eng. (1)

A. Fischer, “Model-based review of Doppler global velocimetry techniques with laser frequency modulation,” Opt. Lasers. Eng. 93, 19–35 (2017).
[Crossref]

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (3)

W. Zhang, J. Gao, D. Zhang, Y. He, T. Xu, R. Fickler, and L. Chen, “Free-Space Remote Sensing of Rotation at the Photon-Counting Level,” Phys. Rev. A 10(4), 044014 (2018).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Phys. Rev. Lett. (4)

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational Frequency Shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector States of Angular Momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref]

K. D. J. Courtial, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the Rotational Frequency Shift Imparted to a Rotating Light Beam Possessing Orbital Angular Momentum,” Phys. Rev. Lett. 80(15), 3217–3219 (1998).
[Crossref]

Radio Sci. (1)

B. Sheva, “Theory of the Doppler effect: Fact, fiction and approximation,” Radio Sci. 19(4), 1027–1040 (1984).
[Crossref]

Sci. Rep. (2)

N. Cvijetic, G. Milione, E. Ip, and T. Wang, “Detecting Lateral Motion using Light’s Orbital Angular Momentum,” Sci. Rep. 5(1), 15422 (2015).
[Crossref]

C. Rosales-Guzman, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
[Crossref]

Science (1)

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light's orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Rotational Doppler effect in the case of normal incidence. (a) An optical vortex illuminates the rotating object in a direction coaxial with respect to its rotational axis, whereby the object’s rotational speed is $\Omega $, and the black line passing through the optical vortex beam represents the Poynting vector. (b) Magnified view of the local scatter area S on the object. For an arbitrary point, the distance from the axis is r and the linear speed is $v$.
Fig. 2.
Fig. 2. Transformation of OV profile and Poynting vector at oblique incidence. (a) If the incident OV axis is in the $yoz$ plane, $\gamma $ denotes the incident angle, r is the original OV profile radius, $r^{\prime}$ is the distance between any point on the elliptical ring and the ellipse center of the OV projection on the object, and ${\theta _z}$ is the angle between the orientation of each tiny scatterer and the x–axis, ${\vec{v}_\theta }$ shows the linear velocity direction. (b) If d is an arbitrary point, the Poynting vector at normal incidence is ${\vec{p}_0}$ and can be calculated by the Poynting vector at point ${x_0}$, while ${\vec{p}_\gamma }$ represents the Poynting vector at oblique incidence.
Fig. 3.
Fig. 3. Simulation of modulated frequency shift at l = 18 and $\Omega = 716$ rad/s. (a) The maximum of the modulated frequency varies at a faster rate than the minimum value as the incident angle $\gamma $ increases. (b) Frequency curve at $\gamma = 0.78$ rad. It is clear that ${f_{\bmod }}$ is at its maximum when ${\theta _z}$ has the values of $\pi /2$ and $3\pi /2$ and at a minimum when ${\theta _z}$ has the values of 0 and $\pi $ . (c) Frequency distribution map delineated by means of Eq. (8).
Fig. 4.
Fig. 4. Experimental setup. (A: attenuator. P: polarizer. L: lens. BS: beam splitter. SLM: spatial light modulator. SF: Spatial filter. f: focal length. D: distance. Charge couple device (CCD): laser CCD camera. γ: incidence angle. PD: photodetector). The CCD and the object have the same angles and distances. The oscilloscope can perform real-time Fourier transformations. The sampling time is 0.1 ms and the sampling frequency is 10 kHz.
Fig. 5.
Fig. 5. (a), (d), and (g), are the intensity distributions of OVs with topological charges $\pm 12$, $\pm 15$ and $\pm 18$ . (b), (e), and (h), are intensity curves in the time domain which longitudinal coordinates represent the voltage detected by the photodetector. (c), (f), and (i), are the corresponding Doppler shift signals. In all studied cases, the rotational velocity was set to 716 rad/s.
Fig. 6.
Fig. 6. Measured modulation frequency ${f_{\bmod }}$ vs. angular velocity Ω of the rotating object for three different topological charges. The measured results are shown as points, and the values predicted from Eq. (3) shown as solid lines.
Fig. 7.
Fig. 7. Experimental results for topological charge $l = \pm 18$ and rotation speed $\Omega = 716.3$ rad/s. (a) Measured Fourier spectrum signals. (b) Extreme value of the modulated frequency ${f_{\max }}$ and ${f_{\min }}$ varies as the incidence angle $\gamma $ . The blue dashed line stands for the symmetric graphics of ${f_{\min }}$ with the center frequency as axis. It is obviously the ${f_{\max }}$ varies faster than the ${f_{\min }}$ . (c) Relationship between the value of the center frequency and the incidence angle $\gamma $ .
Fig. 8.
Fig. 8. (a) and (c) show the maximum and minimum Doppler frequency shift variations as a function of incidence angle $\gamma $ for topological charges $l = \pm 15$ and $l = \pm 12$ . The blue dashed line stands for the symmetric graphics of ${f_{\min }}$ with the center frequency as axis. (b) and (d) are the corresponding center frequency variations as the incidence angle increase. The images shown in the inserts of (b) and (d) are light spot shapes captured by the CCD camera at an incident angle of $\gamma = 0.44$ rad. In all studied cases, the rotational velocity was set to 716.3 rad/s.

Equations (10)

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

Δ f = α f 0 v c
Δ f = f 0 v p c = l λ 2 π r ( f 0 Ω r c ) = l Ω 2 π
f mod = 2 Δ f = l Ω π
r = r 1 ( sin γ sin θ z ) 2
v θ = v x 0 M z ( θ z ) = ( sin θ z , cos θ z , 0 )
p γ = p x 0 M z ( θ z ) M x ( γ ) = ( l λ sin θ z , l λ cos θ z cos γ sin γ 4 π 2 r 2 l 2 λ 2 , l λ sin γ cos θ z cos γ 4 π 2 r 2 l 2 λ 2 )
Δ f = f v θ cos β c = l Ω ( sin 2 θ z + cos 2 θ z cos γ ) 2 π 1 ( sin θ z sin γ ) 2 + f Ω r cos θ z sin γ c 1 ( sin θ z sin γ ) 2
f mod = | l | Ω ( sin 2 θ z + cos γ cos 2 θ z ) π 1 ( sin γ sin θ z ) 2
f e x = { f max = l Ω 2 π cos γ f min = l Ω cos γ 2 π
f c = l Ω 2 π = f min f max

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