Abstract

The number of zero lines of the real and imaginary parts of the optical vortex (OV), both are the same as the topological charge (TC), and all of these lines intersect at one point where the phase singularity is. Furthermore, zero crossings distribute regularly on the transverse plane of the OV lattice. Zero lines of the real and imaginary parts of the non-diffracting fields without OV that generated by multi-waves interference are periodic but coincident. We stack two groups of these kind of zero lines which can be regarded as a set of zero lines of the real part and a set of zero lines of the imaginary part respectively, to satisfy the cross state of zero lines of an OV lattice. Then two groups of multi-waves corresponding to the two fields can be obtained. The expected OV lattice that generated by the two groups of engineered waves interference together is validated through both numerical simulations and experiments.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2016 (2)

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24(24), 28008–28013 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (1)

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[Crossref] [PubMed]

2011 (4)

Y. C. Lin, T. H. Lu, K. F. Huang, and Y. F. Chen, “Generation of optical vortex array with transformation of standing-wave Laguerre-Gaussian mode,” Opt. Express 19(11), 10293–10303 (2011).
[Crossref] [PubMed]

A. Kumar, P. Vaity, J. Banerji, and R. P. Singh, “Making an optical vortex and its copies using a single spatial light modulator,” Phys. Lett. A 375(41), 3634–3640 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A Gen. Phys. 84(1), 013832 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 06111 (2011).
[Crossref]

2010 (2)

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]

2006 (1)

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

2005 (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

2004 (3)

2003 (1)

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 (2)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1–3), 21–27 (2001).
[Crossref]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, “The Orbital Angular Momentum of Light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

1997 (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[Crossref]

1995 (1)

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5–6), 604–612 (1995).
[Crossref]

1994 (1)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

1993 (1)

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” P Roy Soc Lond a Mat 336(1605), 165–190 (1974).
[Crossref]

Ahmed, N.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The Orbital Angular Momentum of Light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Angelsky, O. V.

Arabaci, M.

Arias, A.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The Orbital Angular Momentum of Light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Banerji, J.

A. Kumar, P. Vaity, J. Banerji, and R. P. Singh, “Making an optical vortex and its copies using a single spatial light modulator,” Phys. Lett. A 375(41), 3634–3640 (2011).
[Crossref]

Bao, C.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5–6), 604–612 (1995).
[Crossref]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” P Roy Soc Lond a Mat 336(1605), 165–190 (1974).
[Crossref]

Boguslawski, M.

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A Gen. Phys. 84(1), 013832 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 06111 (2011).
[Crossref]

Brasselet, E.

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[Crossref] [PubMed]

Cao, Y.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Chen, X.

Chen, Y. F.

Cheng, C.

Cui, H.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[Crossref] [PubMed]

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

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

Denz, C.

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A Gen. Phys. 84(1), 013832 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 06111 (2011).
[Crossref]

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Ding, J. P.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Djordjevic, I. B.

Dubik, B.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1–3), 21–27 (2001).
[Crossref]

Etcheverry, S.

Feng, S.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Freund, I.

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Gallardo, M. J.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[Crossref]

Grier, D.

Grier, D. G.

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[Crossref] [PubMed]

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

Guo, C. S.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Han, Y. J.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Hanson, S. G.

He, J.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[Crossref]

Huang, H.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Huang, K. F.

Hui, W.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Jia, W.

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Koss, B. A.

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

Kumar, A.

A. Kumar, P. Vaity, J. Banerji, and R. P. Singh, “Making an optical vortex and its copies using a single spatial light modulator,” Phys. Lett. A 375(41), 3634–3640 (2011).
[Crossref]

Ladavac, K.

Lavery, M. P.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Li, L.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Li, X.

Li, Z.

Liang, G.

Lin, Y. C.

Lu, T. H.

Lu, Y.

Maksimyak, A. P.

Maksimyak, P. P.

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[Crossref]

Masajada, J.

J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4–6), 373–381 (2004).
[Crossref]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1–3), 21–27 (2001).
[Crossref]

Mitsui, T.

T. Mitsui, “A graphical technique for nonlinear algebraic equations,” Int. J. Comput. Math. 13(3–4), 245–261 (2010).
[Crossref]

Molisch, A. F.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” P Roy Soc Lond a Mat 336(1605), 165–190 (1974).
[Crossref]

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

Padgett, M. J.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

L. Allen, M. J. Padgett, and M. Babiker, “The Orbital Angular Momentum of Light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Pal, S. K.

Peng, H.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Ren, Y.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
[Crossref] [PubMed]

Rose, P.

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 06111 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A Gen. Phys. 84(1), 013832 (2011).
[Crossref]

Rubinsztein-Dunlop, H.

Saavedra, C.

Senthilkumaran, P.

Shvartsman, N.

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Singh, R. P.

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I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5–6), 604–612 (1995).
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I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
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Staforelli, J. P.

Sun, W.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
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Torner, L.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
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Tur, M.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
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Ushenko, Y. A.

Vaity, P.

A. Kumar, P. Vaity, J. Banerji, and R. P. Singh, “Making an optical vortex and its copies using a single spatial light modulator,” Phys. Lett. A 375(41), 3634–3640 (2011).
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M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
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M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
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C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
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W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
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Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
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Xie, G.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
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W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
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Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
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W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
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Yu, J.

Zhang, M.

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
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Z. Li, M. Zhang, G. Liang, X. Li, X. Chen, and C. Cheng, “Generation of high-order optical vortices with asymmetrical pinhole plates under plane wave illumination,” Opt. Express 21(13), 15755–15764 (2013).
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Zhang, Y.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Zhao, Z.

Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
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Zhou, C.

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Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 06111 (2011).
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Y. Yan, G. Xie, M. P. 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(1), 4876 (2014).
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Opt. Commun. (6)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1–3), 21–27 (2001).
[Crossref]

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5–6), 604–612 (1995).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
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J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4–6), 373–381 (2004).
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Opt. Laser Technol. (1)

W. Hui, Z. Xie, M. Zhang, H. Cui, J. He, S. Feng, X. Wang, W. Sun, J. Ye, and H. Peng, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
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Phys. Lett. A (1)

A. Kumar, P. Vaity, J. Banerji, and R. P. Singh, “Making an optical vortex and its copies using a single spatial light modulator,” Phys. Lett. A 375(41), 3634–3640 (2011).
[Crossref]

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M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
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M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A Gen. Phys. 84(1), 013832 (2011).
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E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
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[Crossref]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Visualization the distribution of the real part zero lines (red dashed lines) and the imaginary part zero lines (green dashed lines) of the isolate OV on the transverse plane. The OV with TC l has l zero lines of the real part and l zero lines of the imaginary part: (a) l = 1, (b) l = 2, (c) l = 3. Zero lines intersect at one point where the phase singularity exist. Insets depict the corresponding phase map.
Fig. 2
Fig. 2 Sketch of the wave vectors distribution of the interfering plane waves. (a) A set of six plane waves on a cone. (b) Two sets of six plane waves on two cones with different opening angles. The arrowheads of those vectors locate on a sphere with a radius of wave number k0.
Fig. 3
Fig. 3 The discrete beams interference of E6, m and m = 0, 1, 2, 3 from left to right. The first row: numerical simulation of intensity in x-y plane. The middle row: numerical simulation of the phase map. The last row: zero lines distribution of the real (blue lines) and imaginary parts in the bottom right corner (black lines). Inserts in the bottom right corner of each simulation display the magnification of the area (red circle) in the host graph. Red points are OVs.
Fig. 4
Fig. 4 (a) Zero lines of the imaginary part plot of the original group waves interference field (blue lines) and the introduced group waves (δ = π/6) interference field (black lines). (b) The transverse intensity map of the field that formed by the two groups of waves interference directly. (c) The real (green) and imaginary (black) parts zero lines crossing diagram of the wave field (b). (d) Phase pattern of (b). TC of the OV at the center is 3. The vortex with TC 1 is marked by a red circle and insert is the magnification of the circular domain.
Fig. 5
Fig. 5 (a) Zero lines map of combination mode 1 that consisted by two sets of wave groups. (blue lines: Re(Eog 6,3) = Im(Eog 6,3) = 0, black lines: Re(Eig 6,3) = Im(Eig 6,3) = 0). The distance between adjacent zeros are d1 and d2 respectively. (b) The intensity field generated by the interference of whole waves of combination mode 1. (c) Zero crossing map of (b) (the real part: green, the imaginary part: black).(d) The phase distribution of (b). (e) Zero crossing map of combination mode 2. (blue lines: Re(Eog 6,3) = Im(Eog 6,3) = 0, black lines: Re(Eig 6,3′) = Im(Eig 6,3′) = 0). The distances between adjacent zeros are d1 and d3 respectively. (f) The intensity field generated by the interference of whole waves of combination mode 2. (g) Zero crossing map of (f) (the real part: green, the imaginary part: black). (h) The phase distribution of (f).
Fig. 6
Fig. 6 (a) Fringe pattern of a cell of the mode 1. (b) Phase map of (a). (c) Fringe pattern of a cell of the mode 2. (d) Phase map of (c). The circles mark the position of the singularities. The sign of TC can be confirmed by observing the fringe bifurcation direction.
Fig. 7
Fig. 7 (a) The shuttle shape interference region. (b) First row: transverse intensity maps of a cell; middle row: intensity maps of a cell interference with a reference plane wave (fringe pattern); last row: the phase distribution of the cell corresponding to the same column.
Fig. 8
Fig. 8 (a) Simulated intensity modulations of E4,2. (b) Phase profile of (a). (c) Zero lines map of combination mode that consisted by two sets of wave groups interference fields. (blue lines: Re(Eog 4,2) = Im(Eog 4,2) = 0, black lines: Re(Eig 4,2) = Im(Eig 4,2) = 0). Zero lines of the real and imaginary parts are both coincident in each field. (d) The intensity field generated by the interference of whole waves of combination mode. (e) Phase profile of (d). (f) Zero lines (the real part: green, the imaginary part: black) crossing map of (d). The cross state of zero lines of the red circle region in (c) and (f) both perform in the similar way.
Fig. 9
Fig. 9 (a) Experimental configuration for induction of compound OV lattice. SF: Spatial filter; BE: Beam expander; BS: Beam splitter; M: Mirror; S: shutter; LP: Linear polarizer; SLM: Spatial light modulator; FF: Fourier filter; NA: Neutral attenuator; TS: Translation stage. (b)-(e) Phase maps that will be loaded on the SLM in turn.
Fig. 10
Fig. 10 Experimental records of transverse intensity profile (top row) and interferogram (last row). (a) and (b) OV lattice with TC 2; (c) and (d) OV lattice with TC 3; Insets show the according simulation. The sequence from left to right corresponds to the experimental results when the SLM is loaded phase maps of Figs. 9 (b)-9(e) respectively.
Fig. 11
Fig. 11 (a) and (b) Experimental records of intensity patterns in the x-z plane and y-z plane. (c), (e) and (g) Transverse intensity profile at the position of z = 265mm < T/4, z = 267mm > T/4 and z = 531mm ≈T/2, respectively. (d), (f) and (h) are the corresponding interferogram patterns. The sign of TC can be confirmed by observing the fringe bifurcation direction (red arrow) from the interferogram.

Equations (17)

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E(r,τ,z)=u(r,z)exp(ilτ)exp(ikz),
E(x,y)=u(x,y)exp[iϕ(x,y)].
E(x,y)=u(x,y)exp[il tan 1 (y/x)].
{ Re[u(x,y)]=u(x,y)cos[l tan 1 (y/x)]=0 Im[u(x,y)]=u(x,y)sin[l tan 1 (y/x)]=0 ,
L ϕ dL=±2lπ.
E n,m =A j=1 n exp[i k 0 (xsinθcos φ j +ysinθsin φ j +zcosθ)+im φ j ],
Re=A j=1 n cos[ k 0 (xsinθcos φ j +ysinθsin φ j +zcosθ)+m φ j ) ],
Im=A j=1 n sin[ k 0 (xsinθcos φ j +ysinθsin φ j +zcosθ)+m φ j ) ],
Ψ sum = E n,m og + E n,m ig =A j=1 n exp[i k 0 (xsin θ og cos φ j +ysin θ og sin φ j +zcos θ og )+im φ j ] +A j=1 n exp[i k 0 (xsin θ ig cos φ j +ysin θ ig sin φ j +zcos θ ig )+im φ j ] ,
Re(x,y)= j=1 6 cos[ k 0 (xsinθcos φ j +ysinθsin φ j )+ς)+m φ j ] = j=1 6 cos[κ(xcos φ j +ysin φ j )+ς+ m φ j ],
Re(x,y)=cos[κx+ς]cos[κx+ς]+cos[κ( 1 2 x+ 3 2 y)ς] cos[κ( 1 2 x+ 3 2 y)ς]+cos[κ( 1 2 x 3 2 y)ς]cos[κ( 1 2 x 3 2 y)ς].
Im(x,y)=sin[κx+ς]sin[κx+ς]+sin[κ( 1 2 x+ 3 2 y)+ς] sin[κ( 1 2 x 3 2 y)+ς]+sin[κ( 1 2 x 3 2 y)+ς]sin[κ( 1 2 x+ 3 2 y)+ς].
{ κx+ς=κx+ς+2pπ κ( 1 2 x+ 3 2 y)+ς=κ( 1 2 x+ 3 2 y)+ς+2pπ κ( 1 2 x 3 2 y)+ς=κ( 1 2 x 3 2 y)+ς+2pπ ,p.
{ x=pπ/κ x+ 3 y=2pπ/κ,p x 3 y=2pπ/κ .
d= 2π 3 κ 1 sinθ .
sin θ 1 :sin θ 2 = d 2 : d 1 .
T=| 2π k 0 (cos θ og cos θ ig ) |.

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