Abstract

Here a continuous axial-spiral phase microplate (CAsPP), based on combining a logarithmic axicon and a spiral phase plate, was proposed for generating high-quality higher-order Bessel vortex beams. The novel optical component implemented via femtosecond laser direct writing possesses compact geometry and unique optical properties. The CAsPP with a diameter of 80 µm possesses a controllable long focus ranging from 50 to 600 µm and exhibits a good self-healing ability after free transmission of about 45 µm. Unique optical properties were demonstrated in both experiments and simulations, which were well matched to each other. This Letter provides new opportunities for applications in integrated optics, optical trapping, laser machining, and information reconstruction.

© 2020 Optical Society of America

Full Article  |  PDF Article

Corrections

Zhi-Yong Hu, Zhen-Nan Tian, Hua Fan, Jian-Guan Hua, Meng-Dan Qian, Qi-Dai Chen, and Hong-Bo Sun, "Long focusing range and self-healing Bessel vortex beam generator: publisher’s note," Opt. Lett. 45, 3058-3058 (2020)
http://proxy.osapublishing.org/ol/abstract.cfm?uri=ol-45-11-3058

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References

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2019 (9)

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L. Gong, Q. Zhao, H. Zhang, X. Y. Hu, K. Huang, J. M. Yang, and Y. M. Li, Light Sci. Appl. 8, 27 (2019).
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Y. L. Zhang, Y. Tian, H. Wang, Z. C. Ma, D. D. Han, L. G. Niu, Q. D. Chen, and H. B. Sun, ACS Nano 13, 4041 (2019).
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2018 (4)

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2017 (4)

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W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, Light Sci. Appl. 6, e16259 (2017).
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2016 (2)

2015 (1)

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
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2013 (2)

A. Žukauskas, M. Malinauskas, and E. Brasselet, Appl. Phys. Lett. 103, 181122 (2013).
[Crossref]

L. Li and F. Li, Phys. Rev. E 88, 033205 (2013).
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2012 (1)

2011 (1)

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2010 (3)

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, Appl. Phys. Lett. 97, 211108 (2010).
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2009 (1)

K. Kuntz, B. Braverman, S. Youn, M. Lobino, E. Pessina, and A. Lvovsky, Phys. Rev. A 79, 043802 (2009).
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2000 (1)

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1992 (1)

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L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
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J. Arlt and K. J. O. C. Dholakia, Opt. Commun. 177, 297 (2000).
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X. Wang, A. A. Kuchmizhak, E. Brasselet, and S. Juodkazis, Appl. Phys. Lett. 110, 181101 (2017).
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A. Balcytis, D. Hakobyan, M. Gabalis, A. Žukauskas, D. Urbonas, M. Malinauskas, R. Petruskevicius, E. Brasselet, and S. Juodkazis, Opt. Express 24, 16988 (2016).
[Crossref]

A. Žukauskas, M. Malinauskas, and E. Brasselet, Appl. Phys. Lett. 103, 181122 (2013).
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E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, Appl. Phys. Lett. 97, 211108 (2010).
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K. Kuntz, B. Braverman, S. Youn, M. Lobino, E. Pessina, and A. Lvovsky, Phys. Rev. A 79, 043802 (2009).
[Crossref]

Cai, Z.

Cao, Y.

Capasso, F.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, Light Sci. Appl. 6, e16259 (2017).
[Crossref]

Chan, C.

J. Chen, J. Ng, Z. Lin, and C. Chan, Nat. Photonics 5, 531 (2011).
[Crossref]

Chebbi, B.

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. Chan, Nat. Photonics 5, 531 (2011).
[Crossref]

Chen, P.

Chen, Q. D.

Y. L. Zhang, Y. Tian, H. Wang, Z. C. Ma, D. D. Han, L. G. Niu, Q. D. Chen, and H. B. Sun, ACS Nano 13, 4041 (2019).
[Crossref]

Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
[Crossref]

Chen, W. T.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, Light Sci. Appl. 6, e16259 (2017).
[Crossref]

Chen, Z.

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
[Crossref]

Christodoulides, D. N.

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
[Crossref]

Chu, J.

Devlin, R. C.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, Light Sci. Appl. 6, e16259 (2017).
[Crossref]

Dharmavarapu, R.

R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, J. Opt. 20, 085606 (2018).
[Crossref]

Dholakia, K. J. O. C.

J. Arlt and K. J. O. C. Dholakia, Opt. Commun. 177, 297 (2000).
[Crossref]

Ding, H.

H. Wang, Y. L. Zhang, W. Wang, H. Ding, and H. B. Sun, Laser Photonics Rev. 11, 1600116 (2017).
[Crossref]

Dorrah, A. H.

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, Light Sci. Appl. 7, 40 (2018).
[Crossref]

Efremidis, N. K.

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
[Crossref]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
[Crossref]

Fang, X.

Fonseca, E. J.

J. M. Oliveira, A. J. Jesus Silva, and E. J. Fonseca, Opt. Laser Technol. 119, 105632 (2019).
[Crossref]

Fu, X.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Gabalis, M.

Gailevicius, D.

D. Gailevičius, V. Padolskytė, L. Mikoliūnaitė, S. Šakirzanovas, S. Juodkazis, and M. Malinauskas, Nanoscale Horiz. 4, 647 (2019).
[Crossref]

Golub, I.

Gong, L.

L. Gong, Q. Zhao, H. Zhang, X. Y. Hu, K. Huang, J. M. Yang, and Y. M. Li, Light Sci. Appl. 8, 27 (2019).
[Crossref]

Gong, M.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Goutsoulas, M.

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
[Crossref]

Gross, H.

C. Vetter, R. Steinkopf, K. Bergner, M. Ornigotti, S. Nolte, H. Gross, and A. Szameit, Laser Photoicsn Rev. 13, 1900103 (2019).
[Crossref]

Hakobyan, D.

Han, B.

Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
[Crossref]

Han, D. D.

Y. L. Zhang, Y. Tian, H. Wang, Z. C. Ma, D. D. Han, L. G. Niu, Q. D. Chen, and H. B. Sun, ACS Nano 13, 4041 (2019).
[Crossref]

Hou, C.

Hou, Z. S.

Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
[Crossref]

Hu, W.

Hu, X. Y.

L. Gong, Q. Zhao, H. Zhang, X. Y. Hu, K. Huang, J. M. Yang, and Y. M. Li, Light Sci. Appl. 8, 27 (2019).
[Crossref]

Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
[Crossref]

Hu, Y.

Huang, K.

L. Gong, Q. Zhao, H. Zhang, X. Y. Hu, K. Huang, J. M. Yang, and Y. M. Li, Light Sci. Appl. 8, 27 (2019).
[Crossref]

Huang, T.

T. Lu, T. Huang, J. Wang, L. Wang, and R. R. Alfano, Sci. Rep. 6, 39657 (2016).
[Crossref]

Jesus Silva, A. J.

J. M. Oliveira, A. J. Jesus Silva, and E. J. Fonseca, Opt. Laser Technol. 119, 105632 (2019).
[Crossref]

Ji, R.

Ji, S.

Jia, P.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

Juodkazis, S.

D. Gailevičius, V. Padolskytė, L. Mikoliūnaitė, S. Šakirzanovas, S. Juodkazis, and M. Malinauskas, Nanoscale Horiz. 4, 647 (2019).
[Crossref]

R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, J. Opt. 20, 085606 (2018).
[Crossref]

X. Wang, A. A. Kuchmizhak, E. Brasselet, and S. Juodkazis, Appl. Phys. Lett. 110, 181101 (2017).
[Crossref]

A. Balcytis, D. Hakobyan, M. Gabalis, A. Žukauskas, D. Urbonas, M. Malinauskas, R. Petruskevicius, E. Brasselet, and S. Juodkazis, Opt. Express 24, 16988 (2016).
[Crossref]

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, Appl. Phys. Lett. 97, 211108 (2010).
[Crossref]

Kärtner, F.

Khorasaninejad, M.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, Light Sci. Appl. 6, e16259 (2017).
[Crossref]

Kuang, Z.

Kuchmizhak, A. A.

X. Wang, A. A. Kuchmizhak, E. Brasselet, and S. Juodkazis, Appl. Phys. Lett. 110, 181101 (2017).
[Crossref]

Kuntz, K.

K. Kuntz, B. Braverman, S. Youn, M. Lobino, E. Pessina, and A. Lvovsky, Phys. Rev. A 79, 043802 (2009).
[Crossref]

Lao, Z.

Lei, T.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

Li, D.

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
[Crossref]

Li, F.

L. Li and F. Li, Phys. Rev. E 88, 033205 (2013).
[Crossref]

Li, J.

Li, L.

L. Li and F. Li, Phys. Rev. E 88, 033205 (2013).
[Crossref]

Li, Q.

Li, R.

Li, Y.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

Li, Y. M.

L. Gong, Q. Zhao, H. Zhang, X. Y. Hu, K. Huang, J. M. Yang, and Y. M. Li, Light Sci. Appl. 8, 27 (2019).
[Crossref]

Li, Z.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

Liang, X.

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
[Crossref]

Lin, G.

Lin, J.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. Chan, Nat. Photonics 5, 531 (2011).
[Crossref]

Liu, G. N.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

Liu, Q.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Liu, X. Q.

Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
[Crossref]

Liu, Y.

Lobino, M.

K. Kuntz, B. Braverman, S. Youn, M. Lobino, E. Pessina, and A. Lvovsky, Phys. Rev. A 79, 043802 (2009).
[Crossref]

Lu, T.

T. Lu, T. Huang, J. Wang, L. Wang, and R. R. Alfano, Sci. Rep. 6, 39657 (2016).
[Crossref]

Lu, Y.

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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
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Zhu, A. Y.

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Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
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Žukauskas, A.

A. Balcytis, D. Hakobyan, M. Gabalis, A. Žukauskas, D. Urbonas, M. Malinauskas, R. Petruskevicius, E. Brasselet, and S. Juodkazis, Opt. Express 24, 16988 (2016).
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A. Žukauskas, M. Malinauskas, and E. Brasselet, Appl. Phys. Lett. 103, 181122 (2013).
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E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, Appl. Phys. Lett. 97, 211108 (2010).
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ACS Nano (1)

Y. L. Zhang, Y. Tian, H. Wang, Z. C. Ma, D. D. Han, L. G. Niu, Q. D. Chen, and H. B. Sun, ACS Nano 13, 4041 (2019).
[Crossref]

Adv. Funct. Mater. (1)

Z. C. Ma, X. Y. Hu, Y. L. Zhang, X. Q. Liu, Z. S. Hou, L. G. Niu, L. Zhu, B. Han, Q. D. Chen, and H. B. Sun, Adv. Funct. Mater. 29, 1903340 (2019).
[Crossref]

APL Photonics (1)

Z. Zhang, X. Liang, M. Goutsoulas, D. Li, X. Yang, S. Yin, J. Xu, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, APL Photonics 4, 076103 (2019).
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Appl. Phys. Lett. (3)

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, Appl. Phys. Lett. 97, 211108 (2010).
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A. Žukauskas, M. Malinauskas, and E. Brasselet, Appl. Phys. Lett. 103, 181122 (2013).
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X. Wang, A. A. Kuchmizhak, E. Brasselet, and S. Juodkazis, Appl. Phys. Lett. 110, 181101 (2017).
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R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, J. Opt. 20, 085606 (2018).
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Laser Photoicsn Rev. (1)

C. Vetter, R. Steinkopf, K. Bergner, M. Ornigotti, S. Nolte, H. Gross, and A. Szameit, Laser Photoicsn Rev. 13, 1900103 (2019).
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Laser Photonics Rev. (1)

H. Wang, Y. L. Zhang, W. Wang, H. Ding, and H. B. Sun, Laser Photonics Rev. 11, 1600116 (2017).
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Light Sci. Appl. (5)

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

L. Gong, Q. Zhao, H. Zhang, X. Y. Hu, K. Huang, J. M. Yang, and Y. M. Li, Light Sci. Appl. 8, 27 (2019).
[Crossref]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, Light Sci. Appl. 4, e257 (2015).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, Light Sci. Appl. 7, 40 (2018).
[Crossref]

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, Light Sci. Appl. 6, e16259 (2017).
[Crossref]

Nanoscale Horiz. (1)

D. Gailevičius, V. Padolskytė, L. Mikoliūnaitė, S. Šakirzanovas, S. Juodkazis, and M. Malinauskas, Nanoscale Horiz. 4, 647 (2019).
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Nat. Photonics (2)

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
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J. Chen, J. Ng, Z. Lin, and C. Chan, Nat. Photonics 5, 531 (2011).
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Opt. Commun. (1)

J. Arlt and K. J. O. C. Dholakia, Opt. Commun. 177, 297 (2000).
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Opt. Express (2)

Opt. Laser Technol. (1)

J. M. Oliveira, A. J. Jesus Silva, and E. J. Fonseca, Opt. Laser Technol. 119, 105632 (2019).
[Crossref]

Opt. Lett. (5)

Phys. Rev. A (2)

K. Kuntz, B. Braverman, S. Youn, M. Lobino, E. Pessina, and A. Lvovsky, Phys. Rev. A 79, 043802 (2009).
[Crossref]

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
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Phys. Rev. E (1)

L. Li and F. Li, Phys. Rev. E 88, 033205 (2013).
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Sci. Rep. (1)

T. Lu, T. Huang, J. Wang, L. Wang, and R. R. Alfano, Sci. Rep. 6, 39657 (2016).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Galvanometer-based femtosecond laser processing system and calculation process of CAsPP phase distribution. (a) Phase distribution. i, SPP; ii, logarithmic axicon; iii, micro-vortex beam generator. (b) Schematic of processing system. AOM, acousto-optic modulator; BE, beam expander; M, mirror; L, lens; CCD, charge-coupled device.
Fig. 2.
Fig. 2. Fabrication results of CAsPPs (focusing range of 50–600 µm) with various topological charges. (a) SEM images. i, $l = 1$; ii, $l = 2$; iii, $l = 3$. (b) Laser confocal microscopy 3D images. (c) Surface profile of (b)-iii. The blue and red lines separately correspond to the theoretical and experimental results, respectively. The illustration displays the corresponding extraction position of the section profile. i, horizontal; ii, vertical.
Fig. 3.
Fig. 3. Numerical simulations and experimental results of CAsPPs (50–600 µm) in the X–Y plane. (a) Simulated and (b) measured intensity distributions; (c) simulated and (d) measured interferograms in the X–Y plane (${\rm Z} = 360 \;{\unicode{x00B5} \rm m}$). i, $l = 1$; ii, $l = 2$; iii, $l = 3$. (e) Normalized energy distributions along horizontal and vertical directions of foci. i, ii, and iii correspond to (b)-i, ii, and iii. iv shows theoretical and experimental focus diameters at different topological charges.
Fig. 4.
Fig. 4. Simulated and experimental axial intensities of CAsPPs. Intensity distribution in the X–Z plane: focal length range (a) 100–300, (b) 300–500, and (c) 50–600 µm. i, phase information; ii, SEM images; iii, simulated and iv, measured energy distribution in the X–Z plane. (d) Corresponding uniform axial intensity curves (50–600 µm) of the simulation and the experiment in the Y–Z plane.
Fig. 5.
Fig. 5. Characterization of self-healing properties. (a) Schematic of exploring the self-healing ability of OVs and Bessel letters. (b) Demonstration of focusing OVs self-healing process under the obstruction of different light barriers. (c) Reconstruction of Bessel letter F after being destroyed. i, detecting results before obstruction; ii–vi, detecting results after obstruction.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ψ S P P ( r , θ ) = e x p ( i l θ ) .
a = ( d 2 d 1 ) R 2 ,
ψ L A ( r , θ ) = 1 2 a ln { 2 a [ a 2 r 4 + ( 1 2 a d 2 ) r 2 + d 2 2 ] 1 2 + 2 a 2 r 2 + 1 2 a d 2 { 2 a [ a 2 r 4 + ( 1 2 a d 2 ) r 2 + d 2 2 ] 1 2 } ,
ψ C A s P P ( r , θ ) = ψ S P P ( r , θ ) × ψ L A ( r , θ ) .
Δ φ = Δ n h 2 π λ .

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