Abstract

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self- and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type II second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self- and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.

© 2018 Chinese Laser Press

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References

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    [Crossref]

2017 (3)

W. Zhang, J. Wang, F. Li, L. Chen, and E. Karimi, “Revealing optical vortices with a small number of photons,” Laser Photon. Rev. 11, 1600163 (2017).
[Crossref]

L. J. Pereira, W. T. Buono, D. S. Tasca, K. Dechoum, and A. Z. Khoury, “Orbital-angular-momentum mixing in type-II second-harmonic generation,” Phys. Rev. A 96, 053856 (2017).
[Crossref]

X. Fang, Z. Kuang, P. Chen, H. Yang, Q. Li, W. Hu, Y. Lu, Y. Zhang, and M. Xiao, “Examining second-harmonic generation of high-order Laguerre-Gaussian modes through a single cylindrical lens,” Opt. Lett. 42, 4387–4390 (2017).
[Crossref]

2016 (5)

Z. Zhu, W. Gao, C. Mu, and H. Li, “Reversible orbital angular momentum photon-phonon conversion,” Optica 3, 212–217 (2016).
[Crossref]

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

Z. Zhou, S. Liu, Y. Li, D. Ding, W. Zhang, S. Shi, M. Dong, B. Shi, and C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
[Crossref]

P. Chen, S. Ge, L. Ma, W. Hu, V. Chigrinov, and Y. Lu, “Generation of equal-energy orbital angular momentum beams via photopatterned liquid crystals,” Phys. Rev. Appl. 5, 044009 (2016).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10, 327–332 (2016).
[Crossref]

2015 (2)

2014 (4)

Z. Zhou, D. Ding, Y. Jiang, Y. Li, S. Shi, X. Wang, and B. Shi, “Orbital angular momentum light frequency conversion and interference with quasi-phase matching crystals,” Opt. Express 22, 20298–20310 (2014).
[Crossref]

L. Chen, J. Lei, and J. Romero, “Quantum digital spiral imaging,” Light Sci. Appl. 3, e153 (2014).
[Crossref]

W. T. Buono, L. F. C. Moraes, J. A. O. Huguenin, C. F. R. Souza, and A. Z. Khoury, “Arbitrary orbital angular momentum addition in second harmonic generation,” New J. Phys. 16, 093041 (2014).
[Crossref]

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref]

2013 (2)

R. Barboza, U. Bortolozzo, M. G. Clerc, S. Residori, and E. Vidal-Henriquez, “Optical vortex induction via light-matter interaction in liquid-crystal media,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88, 053831 (2013).
[Crossref]

2012 (3)

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108, 087801 (2012).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref]

2011 (4)

2009 (1)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

2008 (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

2007 (2)

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

S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46, 7862–7867 (2007).
[Crossref]

2006 (1)

2005 (1)

2004 (4)

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293–304 (2004).
[Crossref]

M. Martinelli, J. A. O. Huguenin, P. Nussenzveig, and A. Z. Khoury, “Orbital angular momentum exchange in an optical parametric oscillator,” Phys. Rev. A 70, 013812 (2004).
[Crossref]

K. Ladavac and D. Grier, “Microoptomechanical pumps assembled and driven by holographic optical cortex arrays,” Opt. Express 12, 1144–1149 (2004).
[Crossref]

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

2003 (1)

2002 (3)

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, and A. Z. Khoury, “Conservation of orbital angular momentum in stimulated down-conversion,” Phys. Rev. A 66, 041801(R) (2002).

G. Molina-Terriza, J. P. Torres, and L. Torne, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref]

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

2001 (2)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[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]

1998 (1)

L. Yu, W. Huang, M. Huang, Z. Zhu, X. Zeng, and W. Ji, “The Laguerre-Gaussian series representation of two-dimensional fractional Fourier transform,” J. Phys. A 31, 9353–9357 (1998).
[Crossref]

1997 (1)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[Crossref]

1996 (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[Crossref]

1995 (1)

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

1994 (1)

M. W. Beijersbergen, R. P. C. Coewinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdma, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[Crossref]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdma, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Almeida, M. P.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, and A. Z. Khoury, “Conservation of orbital angular momentum in stimulated down-conversion,” Phys. Rev. A 66, 041801(R) (2002).

Arecchi, F. T.

F. Lenzini, S. Residori, F. T. Arecchi, and U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 061801(R) (2011).
[Crossref]

Arie, A.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref]

Assanto, G.

Barboza, R.

R. Barboza, U. Bortolozzo, M. G. Clerc, G. Assanto, E. Vidal-Henriquez, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Adv. Opt. Photon. 7, 635–683 (2015).
[Crossref]

R. Barboza, U. Bortolozzo, M. G. Clerc, S. Residori, and E. Vidal-Henriquez, “Optical vortex induction via light-matter interaction in liquid-crystal media,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

Barnett, S. M.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coewinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdma, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Bloch, N. V.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref]

Bortolozzo, U.

R. Barboza, U. Bortolozzo, M. G. Clerc, G. Assanto, E. Vidal-Henriquez, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Adv. Opt. Photon. 7, 635–683 (2015).
[Crossref]

R. Barboza, U. Bortolozzo, M. G. Clerc, S. Residori, and E. Vidal-Henriquez, “Optical vortex induction via light-matter interaction in liquid-crystal media,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

F. Lenzini, S. Residori, F. T. Arecchi, and U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 061801(R) (2011).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003), p. 96.

Brasselet, E.

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108, 087801 (2012).
[Crossref]

Buono, W. T.

L. J. Pereira, W. T. Buono, D. S. Tasca, K. Dechoum, and A. Z. Khoury, “Orbital-angular-momentum mixing in type-II second-harmonic generation,” Phys. Rev. A 96, 053856 (2017).
[Crossref]

W. T. Buono, L. F. C. Moraes, J. A. O. Huguenin, C. F. R. Souza, and A. Z. Khoury, “Arbitrary orbital angular momentum addition in second harmonic generation,” New J. Phys. 16, 093041 (2014).
[Crossref]

Caetano, D. P.

D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, and A. Z. Khoury, “Conservation of orbital angular momentum in stimulated down-conversion,” Phys. Rev. A 66, 041801(R) (2002).

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

Carrasco, S.

Chen, L.

W. Zhang, J. Wang, F. Li, L. Chen, and E. Karimi, “Revealing optical vortices with a small number of photons,” Laser Photon. Rev. 11, 1600163 (2017).
[Crossref]

J. Zhou, W. Zhang, and L. Chen, “Experimental detection of high-order or fractional orbital angular momentum of light based on a robust mode converter,” Appl. Phys. Lett. 108, 111108 (2016).
[Crossref]

L. Chen, J. Lei, and J. Romero, “Quantum digital spiral imaging,” Light Sci. Appl. 3, e153 (2014).
[Crossref]

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref]

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88, 053831 (2013).
[Crossref]

Chen, P.

X. Fang, Z. Kuang, P. Chen, H. Yang, Q. Li, W. Hu, Y. Lu, Y. Zhang, and M. Xiao, “Examining second-harmonic generation of high-order Laguerre-Gaussian modes through a single cylindrical lens,” Opt. Lett. 42, 4387–4390 (2017).
[Crossref]

P. Chen, S. Ge, L. Ma, W. Hu, V. Chigrinov, and Y. Lu, “Generation of equal-energy orbital angular momentum beams via photopatterned liquid crystals,” Phys. Rev. Appl. 5, 044009 (2016).
[Crossref]

Chen, Y. F.

Chigrinov, V.

P. Chen, S. Ge, L. Ma, W. Hu, V. Chigrinov, and Y. Lu, “Generation of equal-energy orbital angular momentum beams via photopatterned liquid crystals,” Phys. Rev. Appl. 5, 044009 (2016).
[Crossref]

S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19, 4085–4090 (2011).
[Crossref]

Clerc, M. G.

R. Barboza, U. Bortolozzo, M. G. Clerc, G. Assanto, E. Vidal-Henriquez, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Adv. Opt. Photon. 7, 635–683 (2015).
[Crossref]

R. Barboza, U. Bortolozzo, M. G. Clerc, S. Residori, and E. Vidal-Henriquez, “Optical vortex induction via light-matter interaction in liquid-crystal media,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

Coewinkel, R. P. C.

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Figures (5)

Fig. 1.
Fig. 1. Schematic overview of experimental setup to realize the optical vortex copier via type-II second-harmonic generation in the Fourier domain (see the text for details). Insets (a) and (b) show the initial array of Gaussian spots in Path 1 and the single vortex in Path 2, respectively.
Fig. 2.
Fig. 2. Experimental observations of the optical vortex copier. (a) and (d) Initial structured arrays of fundamental Gaussian spots. Single vortex with (b) l=1 and (c) l=2. Superposition of two vortices with (e) l=±1 and (f) l=±2.
Fig. 3.
Fig. 3. Schematic overview of the experimental setup to realize the optical regenerator (see the text for details). Insets (a), (b), and (c) show the initial array of two single vortices, the corresponding results of self-convolution, and the resultant array after the cylindrical lens, respectively.
Fig. 4.
Fig. 4. Experimental observations of the optical vortex regenerator with different arrays of single vortices. Top panel: Initial input arrays encoded in 1064 nm fundamental lights. Middle: Regenerated arrays encoded in 532 nm SHG light fields. Bottom: Measurements of topological charges with a cylindrical lens.
Fig. 5.
Fig. 5. Experimental observations of the optical vortex regenerator with an array of vortex superposition states. (a) Numerical simulation of input array. (b) Output array.

Equations (6)

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E1(r,ϕ)=iA1,i(ri)exp(iliϕi),
E2(r,ϕ)=jA2,j(rj)exp(iljϕj).
dE˜3(ρ,φ)dz=iω32deffk3c2E˜1(ρ,φ)E˜2(ρ,φ),
E3(r,ϕ)=αF[E˜1(ρ,ϕ)E˜2(ρ,ϕ)]=αij[A1,i(ri)exp(iliϕi)]*[A2,j(rj)exp(iljϕj)],
[A1,i(ri)exp(iliϕi)]*[A2,j(rj)exp(iljϕj)]=F1{F[A1,i(ri)exp(iliϕi)]×F[A2,j(rj)exp(iljϕj)]}=2πw2(|li+lj|)!(2rw)|li+lj|exp(r2w2)exp[i(li+lj)ϕ],
E3(r,ϕ)i[A1,i(ri)exp(iliϕi)]*[A1,i(ri)exp(iliϕi)]+ij[A1,i(ri)exp(iliϕi)]*[A1,j(rj)exp(iljϕj)].

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