Abstract

Shaping complex fields with a digital micromirror device (DMD) has attracted much attention recently due to its potential application in optical communication and microscopy. In this paper, we present an optimized Lee method to achieve dynamic shaping of orbital-angular-momentum (OAM) beams using a binary DMD. An error diffusion algorithm is introduced to enhance the accuracy for binary-amplitude hologram design, making it possible to achieve high fidelity wavefront shaping while retaining a high resolution. As a proof of concept, we apply this method to create different classes of OAM beams. The numerical simulations verify that a fidelity of F > 0.985 can be achieved for all the test OAM fields with fully independent phase and amplitude modulation. Moreover, we experimentally demonstrate the dynamic shaping of different OAM beams including pure modes and mixed modes with a switching rate of up to 17.8 kHz. On this basis, accurate information encoding into the generated multiplexed OAM beams is accomplished, which provides access to high speed classical and quantum communications that employ spatial mode encoding.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]

2017 (6)

B. Ndagano, N. Mphuthi, G. Milione, and A. Forbes, “Comparing mode-crosstalk and mode-dependent loss of laterally displaced orbital angular momentum and Hermite-Gaussian modes for free-space optical communication,” Opt. Lett. 42(20), 4175–4178 (2017).
[Crossref] [PubMed]

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molisch, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. A Math. Phys. Eng. Sci. 375(2087), 20150439 (2017).
[Crossref] [PubMed]

C. Aaron, G.-M. Pascuala, V. Asticio, and M. Ignacio, “Vortex beam generation and other advanced optics experiments reproduced with a twisted-nematic liquid-crystal display with limited phase modulation,” Eur. J. Phys. 38(1), 014005 (2017).
[Crossref]

R. Neal, F. O. Rachel, S. Adam, and F.-A. Sonja, “Optimisation of arbitrary light beam generation with spatial light modulators,” J. Opt. 19(9), 095605 (2017).
[Crossref]

C. Shi, M. Dubois, Y. Wang, and X. Zhang, “High-speed acoustic communication by multiplexing orbital angular momentum,” Proc. Natl. Acad. Sci. U.S.A. 114(28), 7250–7253 (2017).
[Crossref] [PubMed]

J. Yang, L. Gong, X. Xu, P. Hai, Y. Shen, Y. Suzuki, and L. V. Wang, “Motionless volumetric photoacoustic microscopy with spatially invariant resolution,” Nat. Commun. 8(1), 780 (2017).
[Crossref] [PubMed]

2016 (8)

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

O. S. Magaña-Loaiza, M. Mirhosseini, R. M. Cross, S. M. H. Rafsanjani, and R. W. Boyd, “Hanbury Brown and Twiss interferometry with twisted light,” Sci. Adv. 2(4), e1501143 (2016).
[Crossref] [PubMed]

J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
[Crossref] [PubMed]

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector Vortex Beam Generation with a Single Plasmonic Metasurface,” ACS Photonics 3(9), 1558–1563 (2016).
[Crossref]

T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24(6), 6249–6264 (2016).
[Crossref] [PubMed]

K. J. Mitchell, S. Turtaev, M. J. Padgett, T. Čižmár, and D. B. Phillips, “High-speed spatial control of the intensity, phase and polarisation of vector beams using a digital micro-mirror device,” Opt. Express 24(25), 29269–29282 (2016).
[Crossref] [PubMed]

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. Ben Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6(1), 27674 (2016).
[Crossref] [PubMed]

2015 (5)

P. Chen, W. Ji, B.-Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum Storage of Orbital Angular Momentum Entanglement in an Atomic Ensemble,” Phys. Rev. Lett. 114(5), 050502 (2015).
[Crossref] [PubMed]

Y. X. Ren, R. D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

2014 (8)

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” Opt. Express 22(15), 17999–18009 (2014).
[Crossref] [PubMed]

B. Rodenburg, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “Experimental generation of an optical field with arbitrary spatial coherence properties,” J. Opt. Soc. Am. B 31(6), A51–A55 (2014).
[Crossref]

L. Gong, X.-Z. Qiu, Y.-X. Ren, H.-Q. Zhu, W.-W. Liu, J.-H. Zhou, M.-C. Zhong, X.-X. Chu, and Y.-M. Li, “Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device,” Opt. Express 22(22), 26763–26776 (2014).
[Crossref] [PubMed]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref] [PubMed]

J. Yang, L. Qiu, W. Zhao, Y. Shen, and H. Jiang, “Laser differential confocal paraboloidal vertex radius measurement,” Opt. Lett. 39(4), 830–833 (2014).
[Crossref] [PubMed]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11(5), 541–544 (2014).
[Crossref] [PubMed]

2013 (3)

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]

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]

M. Mirhosseini, O. S. Magaña-Loaiza, C. Chen, B. Rodenburg, M. Malik, and R. W. Boyd, “Rapid generation of light beams carrying orbital angular momentum,” Opt. Express 21(25), 30196–30203 (2013).
[Crossref] [PubMed]

2012 (2)

V. Lerner, D. Shwa, Y. Drori, and N. Katz, “Shaping Laguerre-Gaussian laser modes with binary gratings using a digital micromirror device,” Opt. Lett. 37(23), 4826–4828 (2012).
[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]

2007 (1)

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

2005 (2)

2004 (1)

B. Zdenek and C. Radek, “Mixed vortex states of light as information carriers,” New J. Phys. 6, 131 (2004).
[Crossref]

2003 (1)

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

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

1993 (1)

K. T. Knox and R. Eschbach, “Threshold modulation in error diffusion,” J. Electron. Imaging 2(3), 185–192 (1993).
[Crossref]

1992 (2)

S. Weissbach and F. Wyrowski, “Error diffusion procedure: theory and applications in optical signal processing,” Appl. Opt. 31(14), 2518–2534 (1992).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. 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]

1979 (1)

1976 (1)

J. F. Jarvis, C. N. Judice, and W. Ninke, “A survey of techniques for the display of continuous tone pictures on bilevel displays,” Comput. Graph. Image Process. 5(1), 13–40 (1976).
[Crossref]

Aaron, C.

C. Aaron, G.-M. Pascuala, V. Asticio, and M. Ignacio, “Vortex beam generation and other advanced optics experiments reproduced with a twisted-nematic liquid-crystal display with limited phase modulation,” Eur. J. Phys. 38(1), 014005 (2017).
[Crossref]

Adam, S.

R. Neal, F. O. Rachel, S. Adam, and F.-A. Sonja, “Optimisation of arbitrary light beam generation with spatial light modulators,” J. Opt. 19(9), 095605 (2017).
[Crossref]

Ahmed, N.

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[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]

Alfano, R. R.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. 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]

Almazov, A. A.

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Arnold, A. S.

Arrizón, V.

Ashrafi, S.

A. E. Willner, Y. Ren, G. Xie, Y. Yan, L. Li, Z. Zhao, J. Wang, M. Tur, A. F. Molisch, and S. Ashrafi, “Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing,” Philos. Trans. A Math. Phys. Eng. Sci. 375(2087), 20150439 (2017).
[Crossref] [PubMed]

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

Asticio, V.

C. Aaron, G.-M. Pascuala, V. Asticio, and M. Ignacio, “Vortex beam generation and other advanced optics experiments reproduced with a twisted-nematic liquid-crystal display with limited phase modulation,” Eur. J. Phys. 38(1), 014005 (2017).
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Bao, C.

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ACS Photonics (1)

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector Vortex Beam Generation with a Single Plasmonic Metasurface,” ACS Photonics 3(9), 1558–1563 (2016).
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Ann. Phys. (1)

Y. X. Ren, R. D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527(7-8), 447–470 (2015).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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Eur. J. Phys. (1)

C. Aaron, G.-M. Pascuala, V. Asticio, and M. Ignacio, “Vortex beam generation and other advanced optics experiments reproduced with a twisted-nematic liquid-crystal display with limited phase modulation,” Eur. J. Phys. 38(1), 014005 (2017).
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L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
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Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
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Proc. Natl. Acad. Sci. U.S.A. (1)

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Figures (7)

Fig. 1
Fig. 1 Principle of the error diffusion algorithm and its performance in improving Lee holography. (a)-(c) Principle of the error diffusion algorithm. (d) The gray-scale hologram encoding the vortex mode with topological charge of l=1. (e, f) The binary holograms obtained with Lee method and error diffusion method, respectively. (g)-(i) The Fourier spectra of the three holograms. Insets at the top right corner are the zoom-in spectra that include the desired field information. The three dashed line boxes and the corresponding zoom-in plots indicate that undesired diffraction order beams and the binarization noise can be significantly suppressed by the error diffusion algorithm.
Fig. 2
Fig. 2 Simulation results of the LG11 beam. (a, d, g) The gray-value and binary DMD masks encoding the intensity (b) and phase (c) of the target LG11 mode. Insets are the zoom-in local parts of the binary patterns. (e, f) Calculated intensity and phase using Lee holography. (h, i) Calculated intensity and phase using optimized Lee method. Intensities are normalized to the maximum intensity.
Fig. 3
Fig. 3 Simulation results of a typical Bessel mode. (a, d, g) The gray-value and binary DMD masks encoding the intensity (b) and phase (c) of the target Bessel mode with topological charge of l=1. Insets are the zoom-in local parts of the binary patterns. (e, f) Calculated intensity and phase using Lee holography. (h, i) Calculated intensity and phase using our method. Intensities are normalized to the maximum intensity.
Fig. 4
Fig. 4 (a) Experimental setup. L: Lens; M: Mirror; BS: Beam splitter; P: Pinhole. (b) The target phase front to be encoded. (c, d) The intensity profiles of the generated vortex mode ( l=1) using the traditional Lee holography and the optimized Lee method, respectively.
Fig. 5
Fig. 5 Experimental generation of OAM beams. (a1, b1) Experimental results of the generated of the LG beams (LG10 and LG11) and (c1,d1) Bessel beams ( l=1; l=3) using the Lee method. (a2)-(d2) The corresponding results of the same modes generated with our proposed method. (a3)-(d3) and (a4)-(d4) The measured phase profiles of the generated OAM modes corresponding to the above intensity profiles.
Fig. 6
Fig. 6 Experimental results of dynamic shaping of mixed OAM modes. (a)-(e) Intensity patterns for ANG modes constructed with superposition of vortex modes from the set l ∈ [−3: 3]. (f) The recorded waveform (blue) of dynamic switching among the generated OAM modes together with the DMD trigger waveform (red). The green waveform demonstrates switching between the OAM modes and non-load mode. The fastest switching speed is up to 17.86 kHz.
Fig. 7
Fig. 7 Experimental demonstration of information encoding using multiplexed OAM beams. (a) Calculated intensities and phases of the multiplexed signal of the letters in the word ALP. (b) Measured optical field amplitude and phase profiles of the multiplexed OAM beams. The experimental results match with the ideal fields in (a). (c) Binary (ASCII) representations of the letters in the word ALP. Each letter contains 8 bits (byte) of information. Each byte contains the same amount of total amplitude, i.e., the signal bars in each letter sum up to unity. This amplitude amount is equally distributed into the vortex beams forming the multiplexed signal. A multiplexed beam formed by the eight orthogonal vortex beams with even OAM charges from −8 to + 8 is capable to convey the information of each letter. (d) Measured signals of the letters in the word ALP. The bars are calculated by forming the inner product between the measured fields of the multiplexed signal and the bases. The norms of the bases are normalized to unity.

Tables (1)

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Table 1 Calculated fidelities of different OAM modes for two methods

Equations (9)

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s(x,y)=A(x,y)exp(iϕ(x,y)),
T(x,y)= n sin(πnq) πn exp[ in(2π( u 0 x+ v 0 y)+2πδ) ],
U 1 (x,y)= U in × sin(πq) π exp(i2πδ)
q(x,y)= 1 π arcsin(A(x,y)),δ(x,y)= ϕ(x,y) 2π ,
h( x,y )=H[cos(2π( u 0 x+ v 0 y)2πδ(x,y))cos(πq(x,y))],
H(x){ 0 ifx<0 1 ifx0 .
h(x,y)=A(x,y)cos(2π( u 0 x+ v 0 y)2πδ(x,y)).
θ j, N l ( r,ϕ )= 1 2 N l +1 L L u l ( r,ϕ ) e i2πjl/ ( 2 N l +1 ) ,
I jl = p j p l da p l p l da ,

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