Abstract

Optical vortex arrays (OVAs) have successfully aroused substantial interest from researchers for their promising prospects ranging from classical to quantum physics. Previous reported OVAs still show a lack of controllable dimensions which may hamper their applications. Taking an isolated perfect optical vortex (POV) as an array element, whose diameter is independent of its topological charge (TC), this paper proposes combined phase-only holograms to produce sophisticated POV arrays. The contributed scheme enables dynamically controllable multi-ring, TC, eccentricity, size, and the number of optical vortices (OVs). Apart from traditional single ring POV element, we set up a βg library to obtain optimized double ring POV element. With multiple selective degrees of freedom to be chosen, a series of POV arrays are generated which not only elucidate versatility of the method but also unravel analytical relationships between the set parameters and intensity patterns. More exotic structures are formed like the “Bear POV” to manifest the potential of this approach in tailoring customized structure beams. The experimental results show robust firmness with the theoretical simulations. As yet, these arrays make their public debut so far as we know, and will find miscellaneous applications especially in multi-microparticle trapping, large-capacity optical communications, novel pumping lasers and so on.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2020 (9)

H. Sroor, Y.-W. Huang, B. Sephton, D. Naidoo, A. Vallés, V. Ginis, C.-W. Qiu, A. Ambrosio, F. Capasso, and A. Forbes, “High-purity orbital angular momentum states from a visible metasurface laser,” Nat. Photonics 14(8), 498–503 (2020).
[Crossref]

Z. Zhang, X. Qiao, B. Midya, K. Liu, J. Sun, T. Wu, W. Liu, R. Agarwal, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, “Tunable topological charge vortex microlaser,” Science 368(6492), 760–763 (2020).
[Crossref]

W. Wang, C. Jiang, H. Dong, X. Lu, J. Li, R. Xu, Y. Sun, L. Yu, Z. Guo, X. Liang, Y. Leng, R. Li, and Z. Xu, “Hollow plasma acceleration driven by a relativistic reflected hollow laser,” Phys. Rev. Lett. 125(3), 034801 (2020).
[Crossref]

F. Tamburini, B. Thidé, and M. D. Valle, “Measurement of the spin of the m87 black hole from its observed twisted light,” Mon. Not. R. Astron. Soc.: Lett. 492(1), L22–L27 (2020).
[Crossref]

Y. Wang, H. Ma, L. Zhu, Y. Tai, and X. Li, “Orientation-selective elliptic optical vortex array,” Appl. Phys. Lett. 116(1), 011101 (2020).
[Crossref]

X. Li and H. Zhang, “Anomalous ring-connected optical vortex array,” Opt. Express 28(9), 13775–13785 (2020).
[Crossref]

J. Yu, C. Miao, J. Wu, and C. Zhou, “Circular dammann gratings for enhanced control of the ring profile of perfect optical vortices,” Photonics Res. 8(5), 648–658 (2020).
[Crossref]

S. Fu, Y. Zhai, J. Zhang, X. Liu, R. Song, H. Zhou, and C. Gao, “Universal orbital angular momentum spectrum analyzer for beams,” PhotoniX  1(1), 19 (2020).
[Crossref]

J. Pinnell, I. Nape, M. D. Oliveira, N. Tabebordbar, and A. Forbes, “Experimental demonstration of 11-dimensional 10-party quantum secret sharing,” Laser Photonics Rev. 14(9), 2000012 (2020).
[Crossref]

2019 (4)

2018 (10)

K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light: Sci. Appl. 7(3), 17156 (2018).
[Crossref]

X. Qiu, F. Li, H. Liu, X. Chen, and L. Chen, “Optical vortex copier and regenerator in the fourier domain,” Photonics Res. 6(6), 641–646 (2018).
[Crossref]

L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, D. N. Neshev, G. G. Paulus, and A. Dreischuh, “Far-field pattern formation by manipulating the topological charges of square-shaped optical vortex lattices,” J. Opt. Soc. Am. B 35(2), 402–409 (2018).
[Crossref]

X. Li, H. Ma, H. Zhang, Y. Tai, H. Li, M. Tang, J. Wang, J. Tang, and Y. Cai, “Close-packed optical vortex lattices with controllable structures,” Opt. Express 26(18), 22965–22975 (2018).
[Crossref]

H. Ma, X. Li, H. Zhang, J. Tang, Z. Nie, H. Li, M. Tang, J. Wang, Y. Tai, and Y. Wang, “Adjustable elliptic annular optical vortex array,” IEEE Photonics Technol. Lett. 30(9), 813–816 (2018).
[Crossref]

L. Li, C. Chang, X. Yuan, C. Yuan, S. Feng, S. Nie, and J. Ding, “Generation of optical vortex array along arbitrary curvilinear arrangement,” Opt. Express 26(8), 9798–9812 (2018).
[Crossref]

Y. Liang, M. Lei, S. Yan, M. Li, Y. Cai, Z. Wang, X. Yu, and B. Yao, “Rotating of low-refractive-index microparticles with a quasi-perfect optical vortex,” Appl. Opt. 57(1), 79–84 (2018).
[Crossref]

J. Yu, J. Wu, C. Xiang, H. Cao, L. Zhu, and C. Zhou, “A generalized circular dammann grating with controllable impulse ring profile,” IEEE Photonics Technol. Lett. 30(9), 801–804 (2018).
[Crossref]

D. Li, C. Chang, S. Nie, S. Feng, J. Ma, and C. Yuan, “Generation of elliptic perfect optical vortex and elliptic perfect vector beam by modulating the dynamic and geometric phase,” Appl. Phys. Lett. 113(12), 121101 (2018).
[Crossref]

X. Li, H. Ma, C. Yin, J. Tang, H. Li, M. Tang, J. Wang, Y. Tai, X. Li, and Y. Wang, “Controllable mode transformation in perfect optical vortices,” Opt. Express 26(2), 651–662 (2018).
[Crossref]

2017 (5)

2016 (3)

2015 (4)

2014 (2)

2013 (1)

2012 (4)

2011 (1)

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

2010 (1)

E. Brasselet, M. Malinauskas, A. Zukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

2009 (1)

G.-X. Wei, L.-L. Lu, and C.-S. Guo, “Generation of optical vortex array based on the fractional talbot effect,” Opt. Commun. 282(14), 2665–2669 (2009).
[Crossref]

2007 (4)

2006 (1)

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref]

2005 (2)

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[Crossref]

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]

1999 (1)

I. Amidror, “Fourier spectra of radially periodic images with a non-symmetric radial period,” J. Opt. Soc. Am. A 1(5), 621–625 (1999).
[Crossref]

1997 (1)

1994 (1)

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

1992 (2)

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]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref]

Agarwal, G. S.

D. Bhatti, J. V. Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91(6), 062303 (2015).
[Crossref]

Agarwal, R.

Z. Zhang, X. Qiao, B. Midya, K. Liu, J. Sun, T. Wu, W. Liu, R. Agarwal, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, “Tunable topological charge vortex microlaser,” Science 368(6492), 760–763 (2020).
[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. Photonics 6(7), 488–496 (2012).
[Crossref]

Albero, J.

Allen, L.

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

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]

Ambrosio, A.

H. Sroor, Y.-W. Huang, B. Sephton, D. Naidoo, A. Vallés, V. Ginis, C.-W. Qiu, A. Ambrosio, F. Capasso, and A. Forbes, “High-purity orbital angular momentum states from a visible metasurface laser,” Nat. Photonics 14(8), 498–503 (2020).
[Crossref]

Amidror, I.

I. Amidror, “Fourier spectra of radially periodic images with a non-symmetric radial period,” J. Opt. Soc. Am. A 1(5), 621–625 (1999).
[Crossref]

I. Amidror, “Fourier spectrum of radially periodic images,” J. Opt. Soc. Am. A 14(4), 816–826 (1997).
[Crossref]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref]

Anwar, A.

Anzolin, G.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

Arnold, A. S.

Arrizon, V.

Banerji, J.

Barnett, S. M.

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

Beijersbergen, M. W.

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]

Bernet, S.

Bhatti, D.

D. Bhatti, J. V. Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91(6), 062303 (2015).
[Crossref]

Brasselet, E.

E. Brasselet, M. Malinauskas, A. Zukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

Cai, Y.

Cao, H.

J. Yu, J. Wu, C. Xiang, H. Cao, L. Zhu, and C. Zhou, “A generalized circular dammann grating with controllable impulse ring profile,” IEEE Photonics Technol. Lett. 30(9), 801–804 (2018).
[Crossref]

Cao, W.

Capasso, F.

H. Sroor, Y.-W. Huang, B. Sephton, D. Naidoo, A. Vallés, V. Ginis, C.-W. Qiu, A. Ambrosio, F. Capasso, and A. Forbes, “High-purity orbital angular momentum states from a visible metasurface laser,” Nat. Photonics 14(8), 498–503 (2020).
[Crossref]

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Appl. Opt. (4)

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IEEE Photonics Technol. Lett. (2)

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Supplementary Material (4)

NameDescription
» Supplement 1       Derivation of double ring POV and beta_g library
» Visualization 1       Visualization 1 is a video about POV arrays with different sizes.
» Visualization 2       Visualization 2 is a video about POV arrays with different eccentricities.
» Visualization 3       Visualization 3 is a video about the "Bear POV" with different facial expressions.

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Figures (8)

Fig. 1.
Fig. 1. Optimization of double ring POV. Irregular ring profiles of POV with topological charges (a) m=2, (b) 5 and (c) 8 and fixed $\beta = $3π/4. Global searching process of ${\beta _g}$ to produce uniform double ring POV with topological charges (d) m=2, (e) 5 and (f) 8 (see Table S1 of Supplement 1 for detailed ${\beta _g}$ library). Corresponding double ring POV with optimal ${\beta _g}$ under different topological charges (g) m=2, (h) 5 and (i) 8.
Fig. 2.
Fig. 2. (a) General formation of holographic grating to produce POV array. (b) The experimental layout. LD, laser diode; SMF, single mode fiber; Col., collimator; HWP1-2, half wave plate; PBS, polarized beam splitter; SLM, spatial light modulator; FL, Fourier lens; BE, beams expander; M1-2, mirrors; BS, beam splitter; CCD, infrared CCD camera. The content of the dotted box in subfigure (b) is the interference optical path.
Fig. 3.
Fig. 3. Simulated and experimental results of a 1D POV array with variable topological charges 2, 4, 6, 8 from left to right. (a) and (b) are theoretical intensity patterns of the array and its interference field with Gaussian beams. (c) and (d) are corresponding experimental patterns. The insets of (a) and (c) display the details of double ring POV among the array.
Fig. 4.
Fig. 4. Definitions of the diameters of (a) single ring POV and (b) double ring POV. (c) The respective ring diameters of experimental results versus the topological charges.
Fig. 5.
Fig. 5. Simulated and experimental results of a 1D POV array with variable sizes. The relative size parameters are set as $\alpha = $ $2\pi \cdot 2,\,\; R = $ $4$,$\; R = $ $6$ and$\; \alpha = 2\pi \cdot 8$ for POV elements from left to right in (a) and (b). (c) The areas of POV elements versus the size parameters $\alpha /2\pi \; $or R. In subfigure (c), two scatter diagrams denote experimental results of single and double ring POV and two dotted lines are corresponding fitting curves.
Fig. 6.
Fig. 6. Simulated and experimental results of a 1D POV array with variable eccentricities. The stretching factor are set as 0.5, 0.8, 1.0, 0.8, 0.5 for POV elements from left to right in (a) and (b). (c) The eccentricities and (d) areas of elliptic POV elements versus the stretching factor s. In subfigure (c) and (d), scatter diagrams denote experimental results of single and double ring POV. The dotted line of subfigure (c) denotes theoretical equation$\; e = \sqrt {1 - {s^2}} $ and two dotted lines of subfigure (d) are fitting curves of area versus s.
Fig. 7.
Fig. 7. Simulated and experimental results of a 2D POV array with variable parameters. Top row: $\{{S\textrm{|}4\textrm{|}3\textrm{|}0} \}$; middle row: $\{{D\textrm{|}2\textrm{|}4\textrm{|}0.6} \},\,\; \{{D\textrm{|}4\textrm{|}4\textrm{|}0} \}\; $and$\; \{{D\textrm{|}2\textrm{|}4\textrm{|}0.8} \}$; bottom row: $\{{S\textrm{|}4\textrm{|}5\textrm{|}0} \}$
Fig. 8.
Fig. 8. Simulated and experimental results of the Bear POV. The “bear” becomes more astonished from left to right.

Equations (11)

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E(r,θ)=Jm(αr)exp(imθ),
E(ρ,φ)rE(r,θ)exp[i2πρrcos(θφ)]drdθ=imαexp(imφ)δ(ρ - α2π),
cos(2πRr)FourierorHankeltransformRπ1(ρ+R)3/2δ(1/2)(Rρ),
cosβcos(2πRr)sinβsin(2πRr)FourierorHankeltransformcosβRπδ(1/2)(Rρ)(ρ+R)3/2sinβRπδ(1/2)(ρR)(ρ+R)3/2.
E(r,θ)=cos(2πRr+β)exp(imθ),
E(ρ,φ)rE(r,θ)exp[i2πρrcos(θφ)]drdθ=im2πexp(imφ)(cosβMsinβN),
η(β)=wowi,
w=Ω|E(ρ,φ)|2ρdρdφΩρdρdφ,
{r=x2+y2θ=arctanyxstretch{r=(sx)2+y2θ=arctanysx,
T(x,y)=p,q=+bp,qexp[i(pγxx+qγyy)],
Tphase(x,y)=exp[iϕ(x,y)]=T(x,y)|T(x,y)|.

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