Abstract

Bessel-Gauss beams carrying orbital angular momentum are widely known for their non-diffractive or self-reconstructing performance, and have been applied in lots of domains. Here we demonstrate that, by illuminating a rotating object with high-order Bessel-Gauss beams, a frequency shift proportional to the rotating speed and the topological charge is observed. Moreover, the frequency shift is still present once an obstacle exists in the path, in spite of the decreasing of received signals. Our work indicates the feasibility of detecting rotating objects free of obstructions, and has potential as obstruction-immune rotation sensors in engine monitoring, aerological sounding, and so on.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  39. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
    [Crossref]
  40. V. Arrizón, D. Sánchez-de-la-Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett. 34(9), 1456–1458 (2009).
    [Crossref] [PubMed]
  41. M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
    [Crossref] [PubMed]
  42. N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
    [Crossref] [PubMed]

2016 (9)

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6(1), 30765 (2016).
[Crossref] [PubMed]

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6(1), 21877 (2016).
[Crossref] [PubMed]

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

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] [PubMed]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

J. A. Davis, I. Moreno, K. Badham, M. M. Sánchez-López, and D. M. Cottrell, “Nondiffracting vector beams where the charge and the polarization state vary with propagation distance,” Opt. Lett. 41(10), 2270–2273 (2016).
[Crossref] [PubMed]

A. Ryabtsev, S. Pouya, A. Safaripour, M. Koochesfahani, and M. Dantus, “Fluid flow vorticity measurement using laser beams with orbital angular momentum,” Opt. Express 24(11), 11762–11767 (2016).
[Crossref] [PubMed]

S. Fu, T. Wang, and C. Gao, “Generating perfect polarization vortices through encoding liquid-crystal display devices,” Appl. Opt. 55(23), 6501–6505 (2016).
[Crossref] [PubMed]

S. Fu, C. Gao, T. Wang, S. Zhang, and Y. Zhai, “Simultaneous generation of multiple perfect polarization vortices with selective spatial states in various diffraction orders,” Opt. Lett. 41(23), 5454–5457 (2016).
[Crossref] [PubMed]

2015 (5)

2014 (6)

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

A. G. Hayrapetyan, O. Matula, A. Aiello, A. Surzhykov, and S. Fritzsche, “Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 112(13), 134801 (2014).
[Crossref] [PubMed]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Optical angular momentum in a rotating frame,” Opt. Lett. 39(10), 2944–2946 (2014).
[Crossref] [PubMed]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “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. Ornigotti and A. Aiello, “Generalized Bessel beams with two indices,” Opt. Lett. 39(19), 5618–5621 (2014).
[Crossref] [PubMed]

2013 (2)

M. P. J. 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]

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

2012 (2)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
[Crossref] [PubMed]

2011 (4)

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107(17), 174802 (2011).
[Crossref] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
[Crossref] [PubMed]

I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19(18), 16760–16771 (2011).
[Crossref] [PubMed]

2009 (2)

V. Arrizón, D. Sánchez-de-la-Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett. 34(9), 1456–1458 (2009).
[Crossref] [PubMed]

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

2006 (2)

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref] [PubMed]

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] [PubMed]

2003 (1)

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

1998 (1)

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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]

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]

1987 (2)

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

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[Crossref]

1983 (1)

1981 (2)

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

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys., A Mater. Sci. Process. 25, 179–194 (1981).

Aadhi, A.

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6(1), 21877 (2016).
[Crossref] [PubMed]

Agnew, M.

Ahmed, N.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Aiello, A.

Allen, L.

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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]

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]

Almaiman, A.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

Apurv Chaitanya, N.

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6(1), 21877 (2016).
[Crossref] [PubMed]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Arrizón, V.

Asakura, T.

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys., A Mater. Sci. Process. 25, 179–194 (1981).

Ashrafi, S.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

Badham, K.

Barnett, S. M.

Barreiro, S.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref] [PubMed]

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]

Belmonte, A.

A. Belmonte, C. Rosales-Guzmán, and J. P. Torres, “Measurement of flow vorticity with helical beams of light,” Optica 2(11), 1002–1005 (2015).
[Crossref]

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

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]

Bliokh, K. Y.

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107(17), 174802 (2011).
[Crossref] [PubMed]

Boyd, R. W.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
[Crossref] [PubMed]

Cheng, H.

Cottrell, D. M.

Courtial, J.

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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]

Dantus, M.

Davis, J. A.

Dennis, M. R.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

K. Y. Bliokh, M. R. Dennis, and F. Nori, “Relativistic electron vortex beams: angular momentum and spin-orbit interaction,” Phys. Rev. Lett. 107(17), 174802 (2011).
[Crossref] [PubMed]

Dholakia, K.

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[Crossref] [PubMed]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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).
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J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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).
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Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Dong, J.

Dudley, A.

Durnin, J.

Failache, H.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Forbes, A.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
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M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
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I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19(18), 16760–16771 (2011).
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I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
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V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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Fritzsche, S.

A. G. Hayrapetyan, O. Matula, A. Aiello, A. Surzhykov, and S. Fritzsche, “Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 112(13), 134801 (2014).
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Fu, S.

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Gazzadi, G. C.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
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V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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Guattari, G.

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

Hayrapetyan, A. G.

A. G. Hayrapetyan, O. Matula, A. Aiello, A. Surzhykov, and S. Fritzsche, “Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 112(13), 134801 (2014).
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Hermosa, N.

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

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6(1), 21877 (2016).
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Jia, W.

Karimi, E.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondi racting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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Koochesfahani, M.

Lavery, M. P. J.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Optical angular momentum in a rotating frame,” Opt. Lett. 39(10), 2944–2946 (2014).
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M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “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).
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M. P. J. 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).
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Leach, J.

Lezama, A.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
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Li, L.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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Li, P.

Liao, P.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

Litvin, I.

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

Litvin, I. A.

Liu, S.

Love, G. D.

Lu, Y.

Ma, C.

Matula, O.

A. G. Hayrapetyan, O. Matula, A. Aiello, A. Surzhykov, and S. Fritzsche, “Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 112(13), 134801 (2014).
[Crossref] [PubMed]

McGloin, D.

McLaren, M.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
[Crossref] [PubMed]

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

Mellado-Villaseñor, G.

Méndez, G.

Meynart, R.

Mhlanga, T.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Molisch, A. F.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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Nori, F.

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Ornigotti, M.

Ostrovsky, A. S.

Padgett, M. J.

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “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]

F. C. Speirits, M. P. J. Lavery, M. J. Padgett, and S. M. Barnett, “Optical angular momentum in a rotating frame,” Opt. Lett. 39(10), 2944–2946 (2014).
[Crossref] [PubMed]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

M. P. J. 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]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
[Crossref] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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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).
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J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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]

Padovani, C.

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

Pouya, S.

Ren, Y.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Robertson, D. A.

J. Courtial, K. Dholakia, D. A. Robertson, K. Dholakia, 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).
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A. Belmonte, C. Rosales-Guzmán, and J. P. Torres, “Measurement of flow vorticity with helical beams of light,” Optica 2(11), 1002–1005 (2015).
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C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
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Roux, F. S.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20(21), 23589–23597 (2012).
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Ruiz, U.

Rusch, L.

Ryabtsev, A.

Safaripour, A.

Samanta, G. K.

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6(1), 21877 (2016).
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Sánchez-de-la-Llave, D.

Sánchez-López, M. M.

Saunter, C.

Speirits, F. C.

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).
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A. G. Hayrapetyan, O. Matula, A. Aiello, A. Surzhykov, and S. Fritzsche, “Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses,” Phys. Rev. Lett. 112(13), 134801 (2014).
[Crossref] [PubMed]

Tabosa, J. W. R.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
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T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys., A Mater. Sci. Process. 25, 179–194 (1981).

Torres, J. P.

A. Belmonte, C. Rosales-Guzmán, and J. P. Torres, “Measurement of flow vorticity with helical beams of light,” Optica 2(11), 1002–1005 (2015).
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C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3(1), 2815 (2013).
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N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Wang, J.

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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Wang, Z.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

Willner, A. E.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
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Wu, J.

Xie, G.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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Yu, J.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Zhang, P.

Zhang, S.

Zhang, X.

Zhang, Y.

Zhao, J.

Zhao, Z.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimeter-wave communication links,” Sci. Rep. 6(1), 22082 (2016).
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Zhou, C.

Zhou, H.

Zhu, L.

Adv. Opt. Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (2)

Appl. Phys., A Mater. Sci. Process. (1)

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys., A Mater. Sci. Process. 25, 179–194 (1981).

J. Opt. Soc. Am. (1)

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

Nat. Commun. (1)

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Opt. Commun. (3)

I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

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

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Opt. Express (5)

Opt. Lett. (12)

J. A. Davis, I. Moreno, K. Badham, M. M. Sánchez-López, and D. M. Cottrell, “Nondiffracting vector beams where the charge and the polarization state vary with propagation distance,” Opt. Lett. 41(10), 2270–2273 (2016).
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Figures (9)

Fig. 1
Fig. 1 Rotational Doppler shift of BG beams. The frequency shift results from relative velocity between the horizonal components of Poyting vector and the line speed indeed, determined by the topological charge l and the angular velocity Ω only.
Fig. 2
Fig. 2 Axicons can be employed to generate BG beams in the overlap region. BG beams can self-heal at the region behind zobs if an obstacle is placed in the path.
Fig. 3
Fig. 3 Experimental setup. LD, laser diode. Col., collimator. HWP, half wave plate. PBS1 & PBS2, polarized beams plitter. R, reflector. SLM, liquid-crystal spatial light modulator. L1 & L2, lens with focal length f = 100 mm. ID, iris diaphragm. BS, beam splitter. QWP, quarter wave plate. L3, lens with focal length f’ = 50 mm. PD, photodiode. CCD, infrared CCD camera. The rotating surface is placed at the distance of 0.38m from the origin where BG region start. The CCD and rotating surface have the same distance L (L = 0.16 m) from the beam splitter.
Fig. 4
Fig. 4 Angular velocity detection without obstractions. (a) & (b), signals outputted from photodiode when BG beams with topological charge ± 20 and ± 22 are incident, separately. Note that here we display part of the signals with 3ms, for clearly. (c) The frequency spectra of (a) and (b), where fmod can be acquired as the peak. For l = ± 20, fmod = 2462.5Hz, and for l = ± 22, fmod = 2750Hz.
Fig. 5
Fig. 5 Results under various angular velocities and topological charges. (a) Measured modulation frequency fmod vs angular velocity Ω of the rotating surface under four different topological charges. (b)-(e), intensity profiles of incident 2-fold multiplexed BG beams with topological charges of ± 16, ± 18, ± 20 and ± 22, respectively.
Fig. 6
Fig. 6 Angular velocity detection with obstractions under the condition L>zobs. (a) A cylinder with the diameter of 0.37 mm is placed vertically in the center of the path as the obstruction. (b)-(g) Intensity profiles of BG beams on the rotating surface without and with obstruction in various locations. (b), no obstruction. (c)-(g), with obstructions, their distance to the rotating surface are 380 mm, 330 mm, 280 mm, 230 mm, 190 mm, respectively. All of the profiles are recorded by the CCD. (h) Spectra of signals outputted by the photodiode with obstructions in various locations. The peaks in the spectra are apparent even with obstructions but have power losses.
Fig. 7
Fig. 7 Compared results of detecting angular velocity with obstructions for both BG beams and non-BG (Laguerre Gaussian, LG) beams. The obstruction is placed at the distance of 38 cm from the rotating surface. (a) BG beams; (b) LG beams.
Fig. 8
Fig. 8 Angular velocity detection with obstractions under various angular velocities. (a), intensity frequencies fmod and spectrum signals for various angular velocities with no obstruction. (b)-(d), intensity frequencies fmod and spectrum signals for various angular velocities with obstructions, the distance from which to the rotator is 380 mm, 320 mm and 250 mm, separately. The obstruction is a cylinder with the diameter of 1.19 mm. The BG beams can’t recover when placed 250 mm to the rotating surface in the propagation path.
Fig. 9
Fig. 9 Hologram to generate 2-fold multiplxed BG beams with opposite topological charges. The holographic axicon has three components, a SPP, an axicon, and a linear phase.

Equations (14)

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E( r,φ ) J l ( k r r )exp( ilφ )
E( r,φ ) J l ( k r r )exp( ilφ )exp( r 2 ω 0 2 )
α= lλ 2πr
Δf= f 0 v A sinα c = f 0 rΩ λ f 0 lλ 2πr = lΩ 2π
f mod = | l |Ω π
z max = Rd λ =Rcotβ
z obs = r 0 d λ
Δ f 1 = lΩ 2π
Δ f 2 = lΩ 2π
E 1 (t)=Acos( 2π f 1 t+σ )
E 2 (t)=Acos( 2π f 2 t+σ )
I( t )= ( E 1 + E 2 ) 2 = A 2 { 1+cos[ 2π( f 1 f 2 )t ]+cos[ 2π( f 1 + f 2 )t+2σ ] +0.5cos( 4π f 1 t+2σ )+0.5cos( 4π f 2 t+2σ ) }
I( t )= A 2 + A 2 cos[ 2π( f 1 f 2 )t ]
f mod = f 1 f 2 =| Δ f 1 |+| Δ f 2 |= | l |Ω π

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