Abstract

We put forward a technique to manipulate the size of orbital angular momentum (OAM) beams based on space diffraction compensation. Paraxial Fresnel diffraction which carries a negative spatial quadratic phase distribution can be regarded as a negative diffractive effect. To compensate the negative diffraction, we employ a 4f Fourier lens system containing a phase mask to generate an inverse quadratic phase. The size of OAM beams can be easily controlled by designing the phase mask profile without changing the OAM. The applications of space diffraction compensation in OAM demultiplexing, ring fiber coupling for OAM beams and optical manipulation of micro particles are also discussed.

© 2014 Optical Society of America

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  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]
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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] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2014 (2)

2013 (4)

2012 (1)

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

2009 (1)

N. Savage, “Digital spatial light modulators,” Nat. Photon. 3(3), 170–172 (2009).
[CrossRef]

2008 (1)

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

2005 (1)

2003 (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

2000 (1)

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

1996 (1)

J. W. Goodman and S. C. Gustafson, “Introduction to Fourier optics,” Opt. Eng. 35(5), 1513 (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]

Ahmed, N.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Allen, L.

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]

Almoro, P. F.

Arita, Y.

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.

Bernet, S.

Birnbaum, K. M.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Cai, Y.

Chen, M.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Damsgaard, H.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Dholakia, K.

Dolinar, S.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Dong, J.

Dong, Y.

Edvold, B.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Erkmen, B. I.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Fürhapter, S.

Goodman, J. W.

J. W. Goodman and S. C. Gustafson, “Introduction to Fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Grüner-Nielsen, L.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Gustafson, S. C.

J. W. Goodman and S. C. Gustafson, “Introduction to Fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[CrossRef]

Hanson, S. G.

Huang, D.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Jesacher, A.

Johansson, P.

Käll, M.

Knudsen, S. N.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Larsen, C. C.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Lehmuskero, A.

Li, Y.

Magnussen, D.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Mazilu, M.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Ritsch-Marte, M.

Savage, N.

N. Savage, “Digital spatial light modulators,” Nat. Photon. 3(3), 170–172 (2009).
[CrossRef]

Shi, L.

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] [PubMed]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Torres, J. P.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Veng, T.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

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] [PubMed]

Wright, E. M.

Yan, Y.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Yang, J.-Y.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Yang, Y.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Zhang, L.

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Zhang, X.

Zhao, C.

Zhou, H.

Appl. Opt. (1)

IEEE Photon. J. (1)

Y. Yue, Y. Yan, N. Ahmed, J.-Y. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, and S. Dolinar, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4(2), 535–543 (2012).
[CrossRef]

Nat. Photon. (1)

N. Savage, “Digital spatial light modulators,” Nat. Photon. 3(3), 170–172 (2009).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Nature (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Opt. Eng. (1)

J. W. Goodman and S. C. Gustafson, “Introduction to Fourier optics,” Opt. Eng. 35(5), 1513 (1996).
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (1)

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (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]

Phys. Rev. Lett. (1)

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Other (1)

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: Trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (Wiley-VCH Verlag, 2012).

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Figures (5)

Fig. 1
Fig. 1

The principle of (a) dispersion compensation and (b) space diffraction compensation.

Fig. 2
Fig. 2

Dependence of optical vortex's radius R on topological charge and RCQ. Inset: optical vortex's radius R is the distance from the maximum intensity position to the center.

Fig. 3
Fig. 3

Normalized intensity and phase of OAM beams on different planes when the optical vortex radii of output fields are all controlled at 2 mm. The left (right) legend is corresponding to the intensity (phase).

Fig. 4
Fig. 4

(a) Scheme and (b) simulation of the space diffraction compensation for OAM demultiplexing. Inset, assigned interval of RCQs.

Fig. 5
Fig. 5

(a) Structure of ring fiber. (b) Intensity and phase distribution of OAM modes in this fiber. (c) Dependence of optical vortex's radius R on RCQ. (d) Coupling efficiency dependence on RCQ for different TC. Inset: coupling efficiency dependence on beam radius.

Equations (6)

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

H(μ,ν)=exp(jkz)exp[jπλz( μ 2 + ν 2 )],
H id (μ,ν)=F[ U id (x,y)],
H out (μ,ν) H in1 (u,v)M(λfμ,λfν)exp[-jπλz( μ 2 + ν 2 )].
U in1 (r,θ)= (r/w) | l | exp( r 2 / w 2 )exp(ilθ),
H out (μ,ν) H in1 (u,v)exp[jπλδz( μ 2 + ν 2 )],
c l = F ( x , y ) ψ l * ( x , y ) d x d y / | F ( x , y ) | 2 d x d y

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