Abstract

We study the propagation dynamics of Janus vortex wave under the action of a focusing lens based upon the formula of focused circular vortex Airy beams. Two dark foci would be generated under the action of a lens, and thus a perfect light hollow bottle could be formed. By controlling corresponding parameters, we could control the focal position and the relative intensity between the two focal intensities. The off-axis optical vortex (OV) would rotate rapidly in two focal regions, but keep still in the lens focus region. The angular displacement of OV in each focusing process is nearly π/2. (Note that the angular displacement for an off-axis OV in single focusing process of Gaussian beam is nearly π.) Two same OVs would repel to each other, but two opposite OVs would attract each other and annihilate at first focus plane in Janus vortex waves.

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

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References

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2019 (5)

2018 (3)

2017 (2)

Z. Zhao, C. Xie, D. Ni, Y. Zhang, Y. Li, F. Courvoisier, and M. Hu, “Scaling the abruptly autofocusing beams in the direct-space,” Opt. Express 25(24), 30598–30605 (2017).
[Crossref]

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[Crossref]

2016 (2)

D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref]

X. Xu, C. Cheng, Y. Zhang, H. Lei, and B. Li, “Dual focused coherent beams for three-dimensional optical trapping and continuous rotation of metallic nanostructures,” Sci. Rep. 6(1), 29449 (2016).
[Crossref]

2015 (4)

2014 (6)

2013 (5)

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref]

A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the perfect optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38(4), 534–536 (2013).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

2012 (2)

2011 (4)

2010 (2)

2004 (1)

2003 (2)

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

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

1998 (1)

1997 (2)

1996 (1)

1993 (1)

G. Indebetouw, “Optical Vortices and Their Propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

1991 (1)

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991).
[Crossref]

1970 (1)

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Arita, Y.

Arrizón, V.

Axner, O.

Cai, Y.

Chen, B.

Chen, C.

Chen, M.

Chen, W.

Chen, X.

Chen, Y.

Chen, Z.

Cheng, C.

X. Xu, C. Cheng, Y. Zhang, H. Lei, and B. Li, “Dual focused coherent beams for three-dimensional optical trapping and continuous rotation of metallic nanostructures,” Sci. Rep. 6(1), 29449 (2016).
[Crossref]

Christodoulides, D. N.

Collins, S. A.

Cottrell, D. M.

Couairon, A.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4(1), 2622 (2013).
[Crossref]

Courvoisier, F.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

Dai, H.

Davis, J. A.

Deng, D.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Chapter 5 Singular Optics: Optical Vortices and Polarization Singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009).

Desyatnikov, A.

Dholakia, K.

Efremidis, N. K.

Fällman, E.

Fang, Z.

Fedorov, V. Y.

Gahagan, K.

Gan, X.

Gong, L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Grier, D. G.

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

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

Guizar-Sicairos, M.

Gutiérrez-Vega, J. C.

Han, T.

Hashemi, M.

Hernandez, D.

Hu, F.

Hu, M.

Huang, K.

Huang, M.

Huang, S.

Huang, W.

Inaba, H.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991).
[Crossref]

Indebetouw, G.

G. Indebetouw, “Optical Vortices and Their Propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

Ishigure, M.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991).
[Crossref]

Izdebskaya, Y.

Jiang, Y.

Jin, W.

Kotlyar, V. V.

Koulouklidis, A. D.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref]

Kovalev, A. A.

Law, C. T.

Lei, H.

X. Xu, C. Cheng, Y. Zhang, H. Lei, and B. Li, “Dual focused coherent beams for three-dimensional optical trapping and continuous rotation of metallic nanostructures,” Sci. Rep. 6(1), 29449 (2016).
[Crossref]

Li, B.

X. Xu, C. Cheng, Y. Zhang, H. Lei, and B. Li, “Dual focused coherent beams for three-dimensional optical trapping and continuous rotation of metallic nanostructures,” Sci. Rep. 6(1), 29449 (2016).
[Crossref]

Li, N.

Li, P.

Li, Y.

Liu, H.

Liu, L.

Liu, S.

Liu, Y.

Lu, R.

Lu, T.

Lu, X.

Luo, D.

Martínez-Matos, Ó

Mazilu, M.

Miyamoto, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Morita, R.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Neshev, D.

Ni, D.

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Chapter 5 Singular Optics: Optical Vortices and Polarization Singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009).

Omatsu, T.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Ostrovsky, A. S.

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Chapter 5 Singular Optics: Optical Vortices and Polarization Singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009).

Panagiotopoulos, P.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4(1), 2622 (2013).
[Crossref]

Papazoglou, D. G.

V. Y. Fedorov, D. G. Papazoglou, and S. Tzortzakis, “Transformation of ring-Airy beams during efficient harmonic generation,” Opt. Lett. 44(12), 2974–2977 (2019).
[Crossref]

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref]

D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4(1), 2622 (2013).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref]

Peng, T.

Peng, X.

Peng, Y.

Ping, Y.

Popov, S.

Prakash, J.

Qian, Y.

Qiu, C.

Ren, Y.

Ren, Z.

Rickenstorff-Parrao, C.

Rozas, D.

Rusch, L.

Salazar, M.

Sand, D.

Sato, S.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991).
[Crossref]

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

Segev, M.

Senthilkumaran, P.

Shanei, M. M.

Shao, H.

Sharma, A. M.

Shi, Y.

Singh, R. K.

Soifer, V. A.

Sun, X.

Swartzlander, G. A.

Swartzlander, J. G. A.

Takahashi, F.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Takizawa, S.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Teng, J.

Tokizane, Y.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Toyoda, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref]

Tzortzakis, S.

V. Y. Fedorov, D. G. Papazoglou, and S. Tzortzakis, “Transformation of ring-Airy beams during efficient harmonic generation,” Opt. Lett. 44(12), 2974–2977 (2019).
[Crossref]

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref]

D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4(1), 2622 (2013).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref]

Vaity, P.

Vaveliuk, P.

Wan, C.

Wang, F.

Wang, G.

Wang, M.

Wang, P.

Wright, E. M.

Xie, C.

Xie, G.

Xu, X.

X. Xu, C. Cheng, Y. Zhang, H. Lei, and B. Li, “Dual focused coherent beams for three-dimensional optical trapping and continuous rotation of metallic nanostructures,” Sci. Rep. 6(1), 29449 (2016).
[Crossref]

Yang, X.

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Ye, H.

Yu, L.

Yu, W.

Zapata-Rodríguez, C. J.

Zhang, A.

Zhang, P.

Zhang, Y.

Z. Zhao, C. Xie, D. Ni, Y. Zhang, Y. Li, F. Courvoisier, and M. Hu, “Scaling the abruptly autofocusing beams in the direct-space,” Opt. Express 25(24), 30598–30605 (2017).
[Crossref]

X. Xu, C. Cheng, Y. Zhang, H. Lei, and B. Li, “Dual focused coherent beams for three-dimensional optical trapping and continuous rotation of metallic nanostructures,” Sci. Rep. 6(1), 29449 (2016).
[Crossref]

Zhang, Z.

Zhao, H.

Zhao, J.

Zhao, Z.

Zheng, W.

Zhou, M.

Zhu, S.

Zhu, X.

Zhu, Z.

Adv. Opt. Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (2)

Electron. Lett. (1)

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. The CAVB with + 1 OV in the input plane (a) and the lens system (b). The focus of the lens is f, f1 and f2 denote the two foci of focused CAVB.
Fig. 2.
Fig. 2. Propagation dynamics of focused CAVB (the first column), the intensity pattern at the first focus (the second column) and the second focus (the third column). (a)–(c) n = 0; (d)–(f) n = 1; (g)–(i) n = 2.
Fig. 3.
Fig. 3. Changes of the maximum intensity along z axis with different parameters: (a) with different n, when r0=1 mm, s = 0; (b) with different r0, when n = 1, s = 0; (c) with different s, when n = 1, r0=1 mm.
Fig. 4.
Fig. 4. Intensity patterns [(a)–(h)] and phase patterns [(a1)–(h1)] of focused CAVB at different z position. (a) z = 0; (b) z = 0.24 m; (c) first focus plane, z = 0.26 m; (d) z = 0.28 m; (e) lens focus plane, z = 0.3 m; (f) z = 0.32 m; (g) second focus plane, z = 0.35 m; (h) z = 0.4 m. The inset arrows in the third column denote the rotation direction of OV.
Fig. 5.
Fig. 5. Changes of maximum intensity along z axis for the focused CAVB with an off-axis OV.
Fig. 6.
Fig. 6. Comparison of angle position of OV in dual focus light beams (i.e., focused CAVB) and in single focus light beams (i.e., focused GB).
Fig. 7.
Fig. 7. Intensity profiles [(a)–(f)] and phase patterns [(a1)–(f1)] when two same OVs (+1, +1) are imposed in focused CAVB. (a) z = 0; (b) z = 0.2 m; (c) first focus plane, z = 0.26 m; (d) lens focus plane, z = 0.3 m; (e) second focus plane, z = 0.35 m; (f) z = 0.4 m.
Fig. 8.
Fig. 8. Changes of the distance between OV and beam axis rOV with z in dual focusing process, rk=0.5 mm for both cases.
Fig. 9.
Fig. 9. Intensity profiles [(a)–(f)] and phase patterns [(a1)–(f1)] when two opposite OVs (−1, +1) are imposed in focused CAVB. (a) z = 0; (b) z = 0.2 m; (c) first focus plane, z = 0.26 m; (d) lens focus plane, z = 0.3 m; (e) second focus plane z = 0.35 m; (f) z = 0.4 m.
Fig. 10.
Fig. 10. Propagation dynamics of focused CAVB with (+1, −1) OVs in y-z plane (a) and the comparison of intensity distribution along beam axis with focused CAB without OV (b).

Equations (14)

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u 0 ( r , φ , z = 0 ) = G A i ( r 0 r w ) exp ( a r 0 r w ) ( r e i φ r k e i φ k ) n ,
u ( x , y , z ) = e i k z i λ B u 0 ( x 0 , y 0 ) exp { i k A 2 B [ ( x 0 2 + y 0 2 ) + D A ( x 2 + y 2 ) 2 A ( x x 0 + y y 0 ) ] } d x 0 d y 0
 =  e i k z i λ B exp [ i k 2 B ( D 1 A ) ( x 2 + y 2 ) ]   × u 0 ( x 0 , y 0 ) exp { i k 2 A B [ ( A x 0 x ) 2 + ( A y 0 y ) 2 ] } d x 0 d y 0
 =  e i k z i λ B exp [ i k 2 B ( D 1 A ) ( x 2 + y 2 ) ]   × 1 A 2 u 0 ( x t A , y t A ) exp { i k 2 A B [ ( x t x ) 2 + ( y t y ) 2 ] } d x t d y t ,
u ( x , y , z ) = exp [ i k C 2 A ( x 2 + y 2 ) ] × F T 1 [ u ~ 0 ( A f x , A f y ) p r o p ] ,
p r o p = F T ( e i k z i λ B exp [ i k 2 A B ( x 2 + y 2 ) ] ) = e i k z A exp [ i B A λ π f r 2 ] ,
P l = G ( 1 ) n l ( n l ) r k n l e i ( n l ) φ k ,
u 0 l ( r , φ ) = A i ( r 0 r w ) exp ( a r 0 r w ) r l e i l φ .
g ~ ( f r ) = 2 π 0 g ( r | A | ) J l ( i 2 π f r r ) r d r ,
u ~ 0 l ( A f x , A f y ) = g ~ ( f r ) exp [ i l ( φ + 1 s i g n ( A ) 2 π ) ] ,
u l ( r , φ , z ) = 2 π exp [ i l ( φ + 1 s i g n ( A ) 2 π ) ] 0 g ~ ( f r ) J l ( i 2 π f r r ) p r o p d f r .
u ( r , φ , z ) = l = 0 n P l u l ( r , φ , z ) .
[ A B C D ] = [ 1 z f z s f + s + z 1 f 1 s f ] ,
u 0 ( r , φ , z = 0 ) = G A i ( r 0 r w ) exp ( a r 0 r w ) ( r e i φ r k ) ( r e ± i φ  +  r k ) .