Abstract

It is shown that orbital angular momentum (OAM) is a promising new resource in future classical and quantum communications. However, the separation of OAM modes is still a big challenge. In this paper, we propose a simple and efficient separation method with a radial varying phase. In the method, specific radial varying phases are designed and modulated for different OAM modes. The resultant beam is focused to the spots with different horizontal and vertical positions after a convex lens, when the coordinate transformation, including two optical elements with coordinate transformation phase and correct phase, operates on the received beam. The horizontal position of the spot is determined by the vortex phases, and the vertical position of the spot is dependent on the radial varying phases. The simulation and experimental results show that the proposed method is feasible both for separation of two OAM modes and separation of three OAM modes. The proposed separation method is available in principle for any neighboring OAM modes because the radial varying phase is controlled. Additionally, no extra instruments are introduced, and there is no diffraction and narrowing process limitation for the separation.

© 2017 Chinese Laser Press

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References

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  1. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, and Y. Yan, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
    [Crossref]
  2. L. Li, G. Xie, Y. Ren, N. Ahmed, and H. Huang, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55, 2098–2103 (2016).
    [Crossref]
  3. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
    [Crossref]
  4. H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100  Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39, 197–200 (2014).
    [Crossref]
  5. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref]
  6. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, and V. Pas’ko, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [Crossref]
  7. R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (3)

L. Li, G. Xie, Y. Ren, N. Ahmed, and H. Huang, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55, 2098–2103 (2016).
[Crossref]

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

C. Li, R. Jiang, L. Wang, and S. Zhao, “Simulations of high efficient separation of orbital-angular-momentum of light,” J. Nanjing Univ. Post Telecommun. 36, 4752 (2016).

2014 (1)

2013 (2)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, and J. Courtial, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

2012 (3)

2010 (1)

G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

2004 (2)

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, and V. Pas’ko, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

2002 (1)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

2001 (1)

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

1974 (1)

Ahmed, N.

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

Beijersbergen, M. W.

G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Berkhout, G. C.

G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Berkhout, G. C. G.

Birnbaum, K. M.

Boyd, R. W.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20, 24444–24449 (2012).
[Crossref]

Bryngdahl, O.

Courtial, J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, and J. Courtial, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, and V. Pas’ko, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Dolinar, S. J.

Erkmen, B. I.

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, and Y. Yan, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Gibson, G.

Huang, H.

Jiang, R.

C. Li, R. Jiang, L. Wang, and S. Zhao, “Simulations of high efficient separation of orbital-angular-momentum of light,” J. Nanjing Univ. Post Telecommun. 36, 4752 (2016).

Kuskoa, C.

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

Lavery, M. P.

G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

Lavery, M. P. J.

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

Li, C.

C. Li, R. Jiang, L. Wang, and S. Zhao, “Simulations of high efficient separation of orbital-angular-momentum of light,” J. Nanjing Univ. Post Telecommun. 36, 4752 (2016).

Li, L.

Love, G. D.

Mair, A.

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

Malik, M.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20, 24444–24449 (2012).
[Crossref]

Mihailescuc, M.

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

Mirhosseini, M.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20, 24444–24449 (2012).
[Crossref]

Nanc, A.

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

O’Sullivan, M. N.

Padgett, M. J.

Pas’ko, V.

Paunc, I.

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

Ren, Y.

Robertson, D. J.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, and J. Courtial, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, and M. J. Padgett, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20, 2110–2115 (2012).
[Crossref]

Rogawski, D.

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

Sponselli, A.

M. P. J. Lavery, D. J. Robertson, A. Sponselli, and J. Courtial, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

Tudora, R.

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

Tur, M.

Vasnetsov, M.

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

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

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, and Y. Yan, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Wang, L.

C. Li, R. Jiang, L. Wang, and S. Zhao, “Simulations of high efficient separation of orbital-angular-momentum of light,” J. Nanjing Univ. Post Telecommun. 36, 4752 (2016).

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

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

Willner, A. E.

Willner, M. J.

Xie, G.

Yan, Y.

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, and Y. Yan, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yue, Y.

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

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

Zhao, S.

C. Li, R. Jiang, L. Wang, and S. Zhao, “Simulations of high efficient separation of orbital-angular-momentum of light,” J. Nanjing Univ. Post Telecommun. 36, 4752 (2016).

Appl. Opt. (1)

J. Nanjing Univ. Post Telecommun. (1)

C. Li, R. Jiang, L. Wang, and S. Zhao, “Simulations of high efficient separation of orbital-angular-momentum of light,” J. Nanjing Univ. Post Telecommun. 36, 4752 (2016).

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, and Y. Yan, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Nature (1)

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

New J. Phys. (1)

M. P. J. Lavery, D. J. Robertson, A. Sponselli, and J. Courtial, “Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013).
[Crossref]

Opt. Commun. (1)

R. Tudora, M. Mihailescuc, C. Kuskoa, I. Paunc, and A. Nanc, “Simultaneous and spatially separated detection of multiple orbital angular momentum states,” Opt. Commun. 368, 141–149 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (3)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[Crossref]

G. C. Berkhout, M. P. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1.

OAM separation method with radial varying phase. U0(r,θ),,U5(x,y) are the electric fields, l1,l2 denote different OAM modes, and m1,m2 represent different radial varying phases. Image e is the superposition beam. Image f is the unfolded beam from image e by the coordinate transformation. FSO: free space optical channel. Images a and c are the horizontal distribution phases that unfolded from the vortex phases, and images b and d are the vertical distribution phases unfolded from the radial varying phases.

Fig. 2.
Fig. 2.

Schematic setup for the experiment. L1–L5, lenses; BS, beam splitter; M1 and M2, mirrors; A1 and A2, apertures.

Fig. 3.
Fig. 3.

Demonstration of the propagation properties of the radial varying phase.

Fig. 4.
Fig. 4.

Simulation and experimental results for the proposed separation method with two OAM modes.

Fig. 5.
Fig. 5.

Simulation and experimental results for the proposed separation method with three OAM modes.

Fig. 6.
Fig. 6.

Comparisons of the separation methods based on coordinate transformation and their corresponding separation efficiency. (a) illustrates the method in Ref. [9]; (b) illustrates the method in Ref. [12]; (c) illustrates the proposed method.

Equations (10)

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

U0(r,θ)=A(r)exp(iθ),
ϕ1(r)={m2πlnrlnR(Rmin<r<Rmax)0(others),
U1(r,θ)=U0(r,θ)exp[iϕ1(r)].
U2(r,θ)=,mA(r)exp(iθ)exp(im2πlnrlnR).
U3(u,v)=U2(r,θ)exp[iϕ2(x,y)]exp(ikxv+yuf)dxdy,
U4(u,v)=U3(u,v)exp[iϕ3(u,v)].
U4(u,v)=,mrect(v2πa)rect(ualnR)exp(iva)exp(im2πualnR),
U5(x,y)=U4(u,v)·exp(ikxv+yuf)dudv,
U5(x,y)=,m(2πa)sinc(xΔΔ)(alnR)sinc(yΛmΛ),
x=Δ,y=Λm,

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