Abstract

We report a technique for encoding both amplitude and phase variations onto a laser beam using a single digital micro-mirror device (DMD). Using this technique, we generate Laguerre-Gaussian and vortex orbital-angular-momentum (OAM) modes, along with modes in a set that is mutually unbiased with respect to the OAM basis. Additionally, we have demonstrated rapid switching among the generated modes at a speed of 4 kHz, which is much faster than the speed regularly achieved by phase-only spatial light modulators (SLMs). The dynamic control of both phase and amplitude of a laser beam is an enabling technology for classical communication and quantum key distribution (QKD) systems that employ spatial mode encoding.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]

2013

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] [PubMed]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett.38, 3546–35490 (2013).
[CrossRef] [PubMed]

2012

2011

R. W. Boyd, A. K. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. SPIE7948, 79480L (2011).

2010

2009

2008

2006

P. J. Rodrigo, I. R. Perch-Nielsen, and J. Glückstad, “High-speed phase modulation using the RPC method with a digital micromirror-array device,” Opt. Express14, 5588–5593 (2006).
[CrossRef] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

2004

2003

J. A. Davis, K. Olea Valadez, and D. M. Cottrell, “Encoding amplitude and phase information onto a binary phase-only spatial light modulator,” Appl. Opt.43, 2003–2008 (2003).
[CrossRef]

2002

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

N. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002).
[CrossRef] [PubMed]

M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002).
[CrossRef]

1999

1998

L. J. Hornbeck, “From cathode rays to digital micromirrors: a history of electronic projection display technology,” Tex. Instrum. Tech. J.15, 7–46 (1998).

1996

1992

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

1979

1972

1971

1969

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev.13, 160–168 (1969).
[CrossRef]

Ahmed, N.

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. Photonics6, 488–496 (2012).
[CrossRef]

Allen, L.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Ando, T.

Barnett, S. M.

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proc. IEEE Int. Conf. (Bangalore, 1984), pp. 175–179.

Bent, N.

Berkhout, G. C. G.

Bjork, G.

M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002).
[CrossRef]

Bolduc, E.

Bourennane, M.

M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002).
[CrossRef]

N. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002).
[CrossRef] [PubMed]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

Boyd, R. W.

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proc. IEEE Int. Conf. (Bangalore, 1984), pp. 175–179.

Brown, B. R.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev.13, 160–168 (1969).
[CrossRef]

Campos, J.

Cerf, N.

N. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002).
[CrossRef] [PubMed]

Cerf, N. J.

M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002).
[CrossRef]

Chu, D. C.

Cohn, R. W.

Cottrell, D. M.

J. A. Davis, K. Olea Valadez, and D. M. Cottrell, “Encoding amplitude and phase information onto a binary phase-only spatial light modulator,” Appl. Opt.43, 2003–2008 (2003).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt.38, 5004–5013 (1999).
[CrossRef]

Courtial, J.

Davis, J. A.

J. A. Davis, K. Olea Valadez, and D. M. Cottrell, “Encoding amplitude and phase information onto a binary phase-only spatial light modulator,” Appl. Opt.43, 2003–2008 (2003).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt.38, 5004–5013 (1999).
[CrossRef]

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. Photonics6, 488–496 (2012).
[CrossRef]

Drori, Y.

Dudley, D.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” in Micromachining and Microfabrication, H. Urey, ed. (SPIE, 2003), pp. 14–25.

Duncan, W. M.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” in Micromachining and Microfabrication, H. Urey, ed. (SPIE, 2003), pp. 14–25.

Dymale, R. C.

Edgar, M. P.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

Fajardo, O.

P. Zhu, O. Fajardo, J. Shum, Y.-P. Zhang Schärer, and R. W. Friedrich, “High-resolution optical control of spatiotemporal neuronal activity patterns in zebrafish using a digital micromirror device,” Nat. Protoc.7, 1410–1425 (2012).
[CrossRef] [PubMed]

Fazal, I. M.

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. Photonics6, 488–496 (2012).
[CrossRef]

Franke-Arnold, S.

Friedrich, R. W.

P. Zhu, O. Fajardo, J. Shum, Y.-P. Zhang Schärer, and R. W. Friedrich, “High-resolution optical control of spatiotemporal neuronal activity patterns in zebrafish using a digital micromirror device,” Nat. Protoc.7, 1410–1425 (2012).
[CrossRef] [PubMed]

Fukuchi, N.

Gao, H.-F.

Gauthier, D. J.

R. W. Boyd, A. K. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. SPIE7948, 79480L (2011).

Gibson, G.

Gisin, N.

N. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002).
[CrossRef] [PubMed]

M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Glückstad, J.

Goodman, J. W.

Goodman, Joseph W.

Joseph W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2004).

Gruneisen, M. T.

Hornbeck, L. J.

L. J. Hornbeck, “From cathode rays to digital micromirrors: a history of electronic projection display technology,” Tex. Instrum. Tech. J.15, 7–46 (1998).

Huang, H.

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. Photonics6, 488–496 (2012).
[CrossRef]

Huang, K.

Inoue, T.

Jha, A. K.

R. W. Boyd, A. K. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. SPIE7948, 79480L (2011).

Jones, A. L.

Karimi, E.

Karlsson, A.

M. Bourennane, A. Karlsson, G. Bjork, N. Gisin, and N. J. Cerf, “Quantum key distribution using multilevel encoding: security analysis,” J. Phys. A35, 10065–10076 (2002).
[CrossRef]

N. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88, 127902 (2002).
[CrossRef] [PubMed]

Katz, N.

Kirk, J. P.

Lavery, M. P. J.

Leach, J.

Lee, W. H.

Lerner, V.

Li, M.

Li, Y.-M.

Liang, M.

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev.13, 160–168 (1969).
[CrossRef]

Love, G. D.

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] [PubMed]

M. Malik, M. N. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express20, 13195–13200 (2012).
[CrossRef] [PubMed]

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. Express20, 24444–24449 (2012).
[CrossRef]

R. W. Boyd, A. K. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. SPIE7948, 79480L (2011).

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Matsumoto, N.

Miller, W. A.

Mirhosseini, M.

Miyaji, G.

Miyanaga, N.

Moreno, I.

Nakatsuka, M.

O’Sullivan, C.

R. W. Boyd, A. K. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. SPIE7948, 79480L (2011).

O’Sullivan, M. N.

Ohtake, T.

Olea Valadez, K.

J. A. Davis, K. Olea Valadez, and D. M. Cottrell, “Encoding amplitude and phase information onto a binary phase-only spatial light modulator,” Appl. Opt.43, 2003–2008 (2003).
[CrossRef]

Padgett, M. J.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96, 163905 (2006).
[CrossRef] [PubMed]

Pas’ko, V.

Perch-Nielsen, I. R.

Ren, 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. Photonics6, 488–496 (2012).
[CrossRef]

Ren, Y.-X.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Robertson, D. J.

Rodenburg, B.

M. Malik, M. N. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express20, 13195–13200 (2012).
[CrossRef] [PubMed]

R. W. Boyd, A. K. Jha, M. Malik, C. O’Sullivan, B. Rodenburg, and D. J. Gauthier, “Quantum key distribution in a high-dimensional state space: exploiting the transverse degree of freedom of the photon,” Proc. SPIE7948, 79480L (2011).

Rodrigo, P. J.

Santamato, E.

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] [PubMed]

Shum, J.

P. Zhu, O. Fajardo, J. Shum, Y.-P. Zhang Schärer, and R. W. Friedrich, “High-resolution optical control of spatiotemporal neuronal activity patterns in zebrafish using a digital micromirror device,” Nat. Protoc.7, 1410–1425 (2012).
[CrossRef] [PubMed]

Shwa, D.

Slaughter, J.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” in Micromachining and Microfabrication, H. Urey, ed. (SPIE, 2003), pp. 14–25.

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
[CrossRef] [PubMed]

Sueda, K.

Sun, B.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

Sweiti, A. M.

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2002).
[CrossRef]

Tur, M.

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. Photonics6, 488–496 (2012).
[CrossRef]

Vasnetsov, M.

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

Wang, J.

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. Photonics6, 488–496 (2012).
[CrossRef]

Wang, Z.-Q.

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science340, 844–847 (2013).
[CrossRef] [PubMed]

Willner, A. E.

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. Photonics6, 488–496 (2012).
[CrossRef]

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992).
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Figures (5)

Fig. 1
Fig. 1

Binary hologram for generating (a) = 2 vortex OAM mode, (b) = −5 vortex OAM mode, (c) LG22 and (d) LG21.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup for a) measuring intensity profiles and phase interferograms. b) switching among three OAM modes and detecting them in real time.

Fig. 3
Fig. 3

Intensity and interferograms of three vortex modes (to the left) and LG modes (to the right). The interferograms demonstrate the phase structure of the beams and have been obtained by interfering the generated modes with a plane wave.

Fig. 4
Fig. 4

Intensity patterns for ANG modes constructed from superposition of vortex OAM modes from the set ∈ [−2 : 2].

Fig. 5
Fig. 5

Detected power as function of time for three vortex OAM modes of = 5, = −5 and = 0. It is seen that the generated mode can be changed on a time-scale of 0.25 ms (measured at FWHM) corresponding to a switching rate of 4 kHz. The detecter power is divided to its maximum value in each case.

Equations (9)

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T ( x ) = m = rect [ x ( m + p ) x 0 w x 0 ] ,
rect ( u ) = { 1 if | u | 1 / 2 , 0 else .
T ( x ) = m = T m exp [ i 2 π m ( x x 0 ) ] .
T m = sin ( π m w ) π m e i 2 π m p ,
T 1 ( x ) = 1 π sin [ π w ( x ) ] e i 2 π p ( x ) .
T ( x , y ) = 1 / 2 + 1 / 2 sgn ( cos [ 2 π x / x 0 + π p ( x , y ) ] cos [ π w ( x , y ) ] ) .
w ( x , y ) = 1 π arcsin [ 𝒜 ( x , y ) ] ,
p ( x , y ) = 1 π φ ( x , y ) .
θ j , N ( r , φ ) = 1 2 N + 1 = L L u ( r , φ ) e i 2 π j / ( 2 N + 1 ) .

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