Abstract

The angular acceleration of a spinning object can be estimated by probing the object with Laguerre-Gauss (LG) beams and analyzing the rotational Doppler frequency shift of returned signals. The frequency shift is time dependent because of the change of the rotational angular velocity over time. The detection system is built to collect the beating signals of LG beams back-scattered from a non-uniform spinning body. Then a time-frequency analysis method is proposed to study the evolution of the angular velocity in time. The experimental results of different angular accelerations of the rotator are consistent with expectations. The measurement errors of different probe beams with various topological charges from l = ± 10 to l = ± 100 are also investigated.

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

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References

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2019 (1)

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]

2018 (4)

V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, “Astigmatic laser beams with a large orbital angular momentum,” Opt. Express 26(1), 141–156 (2018).
[Crossref] [PubMed]

S. Xiao, L. Zhang, D. Wei, F. Liu, Y. Zhang, and M. Xiao, “Orbital angular momentum-enhanced measurement of rotation vibration using a Sagnac interferometer,” Opt. Express 26(2), 1997–2005 (2018).
[Crossref] [PubMed]

W. H. Zhang, J. S. 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. Appl. 10(4), 044014 (2018).
[Crossref]

F. Xia, Y. Zhao, H. Hu, and Y. Zhang, “Optical fiber sensing technology based on Mach-Zehnder interferometer and orbital angular momentum beam,” Appl. Phys. Lett. 112(22), 221105 (2018).
[Crossref]

2017 (8)

T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, “Rotational superradiant scattering in a vortex flow,” Nat. Phys. 13(9), 833–836 (2017).
[Crossref]

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] [PubMed]

Y. Liu, Z. Liu, J. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Measurements of Pancharatnam-Berry phase in mode transformations on hybrid-order Poincaré sphere,” Opt. Lett. 42(17), 3447–3450 (2017).
[Crossref] [PubMed]

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

Z. Liu, Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Geometric phase Doppler effect: when structured light meets rotating structured materials,” Opt. Express 25(10), 11564–11573 (2017).
[Crossref] [PubMed]

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. L. Sounas and A. Alù, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11(12), 774–783 (2017).
[Crossref]

H. L. Zhou, D. Z. Fu, J. J. Dong, P. Zhang, D. X. Chen, X. L. Cai, F. L. Li, and X. L. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6(4), e16251 (2017).
[Crossref] [PubMed]

2016 (5)

2015 (7)

2014 (4)

2013 (3)

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[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] [PubMed]

Y. S. Rumala and A. E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B 30(3), 615–621 (2013).
[Crossref]

2011 (1)

2009 (1)

E. Sejdić, I. Djurović, and J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” Digit. Signal Process. 19(1), 153–183 (2009).
[Crossref]

2006 (1)

M. Padgett, “Electromagnetism: like a speeding watch,” Nature 443(7114), 924–925 (2006).
[Crossref] [PubMed]

2005 (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(1), 46 (2005).
[Crossref]

2003 (2)

2002 (1)

I. V. Basistiy, A. Y. Bekshaev, M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, “Observation of the rotational Doppler effect for optical beams with helical wave front using spiral zone plate,” JETP Lett. 76(8), 486–489 (2002).
[Crossref]

1998 (2)

J. Courtial, K. Dholakia, 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]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational Frequency Shift of a Light Beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

1996 (1)

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

1990 (1)

F. Bretenaker and A. L. Floch, “Energy exchanges between a rotating retardation plate and a laser beam,” Phys. Rev. Lett. 65(18), 2316–2319 (1990).
[Crossref] [PubMed]

1988 (1)

R. Simon, H. J. Kimble, and E. C. Sudarshan, “Evolving geometric phase and its dynamical manifestation as a frequency shift: An optical experiment,” Phys. Rev. Lett. 61(1), 19–22 (1988).
[Crossref] [PubMed]

1979 (1)

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31(1), 1–3 (1979).
[Crossref]

1967 (1)

P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15(2), 70–73 (1967).
[Crossref]

Allen, L.

J. Courtial, K. Dholakia, 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]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational Frequency Shift of a Light Beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[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] [PubMed]

Alù, A.

D. L. Sounas and A. Alù, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11(12), 774–783 (2017).
[Crossref]

Arnold, S.

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31(1), 1–3 (1979).
[Crossref]

Averbukh, I. S.

O. Faucher, E. Prost, E. Hertz, F. Billard, B. Lavorel, A. A. Milner, V. A. Milner, J. Zyss, and I. S. Averbukh, “Rotational Doppler effect in harmonic generation from spinning molecules,” Phys. Rev. A (Coll. Park) 94(5), 051402 (2016).
[Crossref]

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Barnett, S. M.

Basistiy, I. V.

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

I. V. Basistiy, A. Y. Bekshaev, M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, “Observation of the rotational Doppler effect for optical beams with helical wave front using spiral zone plate,” JETP Lett. 76(8), 486–489 (2002).
[Crossref]

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] [PubMed]

Bekshaev, A. Y.

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

I. V. Basistiy, A. Y. Bekshaev, M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, “Observation of the rotational Doppler effect for optical beams with helical wave front using spiral zone plate,” JETP Lett. 76(8), 486–489 (2002).
[Crossref]

Belmonte, A.

Bendoula, R.

Billard, F.

O. Faucher, E. Prost, E. Hertz, F. Billard, B. Lavorel, A. A. Milner, V. A. Milner, J. Zyss, and I. S. Averbukh, “Rotational Doppler effect in harmonic generation from spinning molecules,” Phys. Rev. A (Coll. Park) 94(5), 051402 (2016).
[Crossref]

Bland-Hawthorn, J.

Bretenaker, F.

F. Bretenaker and A. L. Floch, “Energy exchanges between a rotating retardation plate and a laser beam,” Phys. Rev. Lett. 65(18), 2316–2319 (1990).
[Crossref] [PubMed]

Cai, X. L.

H. L. Zhou, D. Z. Fu, J. J. Dong, P. Zhang, D. X. Chen, X. L. Cai, F. L. Li, and X. L. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6(4), e16251 (2017).
[Crossref] [PubMed]

Chen, D. X.

H. L. Zhou, D. Z. Fu, J. J. Dong, P. Zhang, D. X. Chen, X. L. Cai, F. L. Li, and X. L. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6(4), e16251 (2017).
[Crossref] [PubMed]

Chen, L.

W. H. Zhang, J. S. 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. Appl. 10(4), 044014 (2018).
[Crossref]

Chomet, B.

Courtial, J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational Frequency Shift of a Light Beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

J. Courtial, K. Dholakia, 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]

Coutant, A.

T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, “Rotational superradiant scattering in a vortex flow,” Nat. Phys. 13(9), 833–836 (2017).
[Crossref]

Dantus, M.

Dholakia, K.

J. Courtial, K. Dholakia, 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]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational Frequency Shift of a Light Beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

Ding, D.

S. Shi, D. Ding, Z. Zhou, Y. Li, W. Zhang, and B. Shi, “Magnetic-field-induced rotation of light with orbital angular momentum,” Appl. Phys. Lett. 106(26), 261110 (2015).
[Crossref]

Djurovic, I.

E. Sejdić, I. Djurović, and J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” Digit. Signal Process. 19(1), 153–183 (2009).
[Crossref]

Dong, J.

Dong, J. J.

H. L. Zhou, D. Z. Fu, J. J. Dong, P. Zhang, D. X. Chen, X. L. Cai, F. L. Li, and X. L. Zhang, “Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect,” Light Sci. Appl. 6(4), e16251 (2017).
[Crossref] [PubMed]

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]

Faucher, O.

O. Faucher, E. Prost, E. Hertz, F. Billard, B. Lavorel, A. A. Milner, V. A. Milner, J. Zyss, and I. S. Averbukh, “Rotational Doppler effect in harmonic generation from spinning molecules,” Phys. Rev. A (Coll. Park) 94(5), 051402 (2016).
[Crossref]

Fickler, R.

W. H. Zhang, J. S. 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. Appl. 10(4), 044014 (2018).
[Crossref]

Floch, A. L.

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S. Shi, D. Ding, Z. Zhou, Y. Li, W. Zhang, and B. Shi, “Magnetic-field-induced rotation of light with orbital angular momentum,” Appl. Phys. Lett. 106(26), 261110 (2015).
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Appl. Opt. (1)

Appl. Phys. Lett. (2)

F. Xia, Y. Zhao, H. Hu, and Y. Zhang, “Optical fiber sensing technology based on Mach-Zehnder interferometer and orbital angular momentum beam,” Appl. Phys. Lett. 112(22), 221105 (2018).
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S. Shi, D. Ding, Z. Zhou, Y. Li, W. Zhang, and B. Shi, “Magnetic-field-induced rotation of light with orbital angular momentum,” Appl. Phys. Lett. 106(26), 261110 (2015).
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Digit. Signal Process. (1)

E. Sejdić, I. Djurović, and J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” Digit. Signal Process. 19(1), 153–183 (2009).
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Figures (9)

Fig. 1
Fig. 1 The transformation of OAM beams when passing through a non-uniform spinning SPP. l, the original topological charge. l(t), the topological charge behind the phase plate. Ω(t), the rotational angular velocity. SPP, the spiral phase plate.
Fig. 2
Fig. 2 Experimental setup. LD, laser diode. SMF, single mode fiber. Col., collimator. HWP, half wave plate. PBS1& PBS2, polarized beams splitter. R, reflector. SLM, liquid-crystal spatial light modulator. L1&L2, lenses with focal length f = 100 mm. ID, iris diaphragm. BS, beam splitter. L3, lens with focal length 300 mm. CCD, infrared CCD camera. L4, lens with focal length 50 mm. PD, photodiode. QWP, quarter wave plate.
Fig. 3
Fig. 3 The intensity distribution of 2-fold multiplexed LG beams with topological charges of (a) ± 50,(b) ± 25,respectively.
Fig. 4
Fig. 4 The experimental results. (a) The beat signals in 0-0.045 s and (c) the corresponding frequency spectrum when the rotational angular velocity is uniform; (b) The beat signal in 0-0.4 s and (d) the frequency spectrum in 0-10 s when the rotational angular velocity is non-uniform.
Fig. 5
Fig. 5 The time-frequency analysis results of the non-stationary returned signals by use of the STFT method. In STFT time-frequency spectrum, horizontal axis represents time t and vertical axis represents frequency f.
Fig. 6
Fig. 6 The time-frequency spectrums of different situations. (a) Ω0 = 94.25 rad/s and a(t) = 0 rad/s2. (b) Ω0 = 157.08rad/s and a(t) = −12.95 rad/s2. (c) Ω0 = 12.57rad/s and a(t) = 10.36 rad/s2. (d) a(t) is changing over time.
Fig. 7
Fig. 7 The experimental and theoretical data for various angular accelerations of the rotator.
Fig. 8
Fig. 8 The time-frequency spectrums of the 2-fold multiplexed beams with the topological charges of ± 60 (a) and ± 70 (b).
Fig. 9
Fig. 9 The comparison between the experimental and theoretical data of the probe beams with different topological charges. Df/dt - l curve is the theoretical data. Markers: experimental data.

Equations (7)

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M( r,θ,t )=exp( iΦ( r,θ t 0 t Ω( t )d t ) )= A n ( r ) exp( inθ )exp( in t 0 t Ω( t )d t ),
Ω( t )= Ω 0 + t 0 t a( t )d t.
E= B( r ) A n ( r )exp( i( l+n )θ )exp( i2πft )exp( in t 0 t Ω( t ) dt ).
Δf( t )= 1 2π dφ( t ) dt = nΩ( t ) ( 2π ) ,
a( t )= dΩ( t ) dt =( 2π/n ) dΔf( t ) dt ,
a( t )= dΩ( t ) dt = 2π ( l 1 l 2 ) × df( t ) dt .
STFT(t,f)= + s(u) g * (ut) exp(i2πfu)du,