Abstract

We propose a technique for generating a sequence of co-axial zero axial irradiance with a so-called dual-type fractal spiral zone plate (DTFSZP). Based on the Fresnel diffraction theory, we simulated the focusing performance of this optical device. The results reveal that DTFSZP has the remarkable ability of generating a sequence of optical vortices with larger depth of focus and high lateral resolution. The central diffracted image rotates in the vicinity of the focal plane. Moreover, the focusing performance follows a modulo-4 transmutation rule. Such optics promises a complementary and versatile high-resolution non-destructive tool for particle manipulation and provides potential application in three-dimensional optical alignment systems.

© 2019 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  27. J. Ke and J. Y. Zhang, “Focusing properties of phase-only generalized Fibonacci photon sieves,” Opt. Commun. 368, 34–38 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (5)

C. Zheng, S. Su, H. Zang, Z. Ji, Y. Tian, S. Chen, K. Mu, L. Wei, Q. Fan, C. Wang, X. Zhu, C. Xie, L. Cao, and E. Liang, “Characterization of the focusing performance of axial line-focused spiral zone plates,” Appl. Opt. 57, 3802–3807 (2018).
[Crossref]

C. Zheng, H. Zang, Y. Du, Y. Tian, Z. Ji, J. Zhang, Q. Fan, C. Wang, L. Cao, and E. Liang, “Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates,” Opt. Commun. 414, 128–133 (2018).
[Crossref]

H. Zang, C. Zheng, Q. Fan, C. Wang, L. Wei, L. Cao, X. Wang, and E. Liang, “Generation of x-ray vortex with ultra-long depth of focus using axial line-focused spiral zone plates,” Chin. Opt. Lett. 16, 080501 (2018).
[Crossref]

Z. Ji, H. Zang, C. Fan, J. Wang, C. Zheng, L. Wei, C. Wang, and L. Cao, “Fractal spiral zone plates,” J. Opt. Soc. Am. A 35, 726–731 (2018).
[Crossref]

H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
[Crossref]

2017 (2)

2016 (2)

J. Ke and J. Y. Zhang, “Focusing properties of phase-only generalized Fibonacci photon sieves,” Opt. Commun. 368, 34–38 (2016).
[Crossref]

Q. Fan, S. Wang, Z. Yang, L. Wei, F. Hu, H. Zang, Q. Zhang, C. Wang, and G. Jiang, “The realization of long focal depth with a linear varied-area zone plate,” J. Mod. Opt. 64, 244–250 (2016).
[Crossref]

2013 (2)

A. Calatayud, V. Ferrando, F. Giménez, W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “Fractal square zone plates,” Opt. Commun. 286, 42–45 (2013).
[Crossref]

Y. Zhang and C. Xie, “Controlled interaction of the optical vortices generated by off-center spiral zone plates,” Opt. Commun. 311, 65–71 (2013).
[Crossref]

2012 (1)

A. Vijaykumar and S. Bhattacharya, “Design, fabrication, and evaluation of a multilevel spiral-phase Fresnel zone plate for optical rapping: Erratum,” Appl. Opt. 52, 6038–6044 (2012).
[Crossref]

2011 (1)

N. Gao, C. Xie, C. Li, C. Lin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[Crossref]

2010 (3)

2009 (1)

2008 (2)

H. H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. 47, 118001 (2008).
[Crossref]

B. Spektor, A. Normatov, and J. Shamir, “Singular beam microscopy,” Appl. Opt. 47, A78–A87 (2008).
[Crossref]

2007 (1)

2006 (1)

S. Tao, X. Yuan, and J. Lin, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89, 031105 (2006).
[Crossref]

2004 (2)

W. Cheong, W. Lee, X. Yuan, L. Zhang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

J. G. Francisco, A. Javier, I. Bojan, and D. B. Glenn, “Infrared antennas coupled to lithographic Fresnel zone plate lenses,” Appl. Opt. 43, 6067–6073 (2004).
[Crossref]

1999 (3)

M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[Crossref]

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[Crossref]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

1998 (1)

1996 (1)

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, 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)

1982 (1)

L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. 13, 199–206 (1982).
[Crossref]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Beijersbergen, M. W.

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

Bhattacharya, S.

A. Vijaykumar and S. Bhattacharya, “Design, fabrication, and evaluation of a multilevel spiral-phase Fresnel zone plate for optical rapping: Erratum,” Appl. Opt. 52, 6038–6044 (2012).
[Crossref]

Bojan, I.

Bradman, N. M.

H. H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. 47, 118001 (2008).
[Crossref]

Calatayud, A.

A. Calatayud, V. Ferrando, F. Giménez, W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “Fractal square zone plates,” Opt. Commun. 286, 42–45 (2013).
[Crossref]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896 (2009).
[Crossref]

Cao, L.

H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
[Crossref]

H. Zang, C. Zheng, Q. Fan, C. Wang, L. Wei, L. Cao, X. Wang, and E. Liang, “Generation of x-ray vortex with ultra-long depth of focus using axial line-focused spiral zone plates,” Chin. Opt. Lett. 16, 080501 (2018).
[Crossref]

Z. Ji, H. Zang, C. Fan, J. Wang, C. Zheng, L. Wei, C. Wang, and L. Cao, “Fractal spiral zone plates,” J. Opt. Soc. Am. A 35, 726–731 (2018).
[Crossref]

C. Zheng, S. Su, H. Zang, Z. Ji, Y. Tian, S. Chen, K. Mu, L. Wei, Q. Fan, C. Wang, X. Zhu, C. Xie, L. Cao, and E. Liang, “Characterization of the focusing performance of axial line-focused spiral zone plates,” Appl. Opt. 57, 3802–3807 (2018).
[Crossref]

C. Zheng, H. Zang, Y. Du, Y. Tian, Z. Ji, J. Zhang, Q. Fan, C. Wang, L. Cao, and E. Liang, “Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates,” Opt. Commun. 414, 128–133 (2018).
[Crossref]

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

Chen, S.

Cheong, W.

W. Cheong, W. Lee, X. Yuan, L. Zhang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Chung, H. H.

H. H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. 47, 118001 (2008).
[Crossref]

Coerwinkel, R. P. C.

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

Davidson, M. R.

H. H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. 47, 118001 (2008).
[Crossref]

Dholakia, K.

W. Cheong, W. Lee, X. Yuan, L. Zhang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Du, Y.

C. Zheng, H. Zang, Y. Du, Y. Tian, Z. Ji, J. Zhang, Q. Fan, C. Wang, L. Cao, and E. Liang, “Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates,” Opt. Commun. 414, 128–133 (2018).
[Crossref]

Fan, C.

Fan, Q.

C. Zheng, H. Zang, Y. Du, Y. Tian, Z. Ji, J. Zhang, Q. Fan, C. Wang, L. Cao, and E. Liang, “Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates,” Opt. Commun. 414, 128–133 (2018).
[Crossref]

H. Zang, C. Zheng, Q. Fan, C. Wang, L. Wei, L. Cao, X. Wang, and E. Liang, “Generation of x-ray vortex with ultra-long depth of focus using axial line-focused spiral zone plates,” Chin. Opt. Lett. 16, 080501 (2018).
[Crossref]

H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
[Crossref]

C. Zheng, S. Su, H. Zang, Z. Ji, Y. Tian, S. Chen, K. Mu, L. Wei, Q. Fan, C. Wang, X. Zhu, C. Xie, L. Cao, and E. Liang, “Characterization of the focusing performance of axial line-focused spiral zone plates,” Appl. Opt. 57, 3802–3807 (2018).
[Crossref]

Q. Fan, S. Wang, Z. Yang, L. Wei, F. Hu, H. Zang, Q. Zhang, C. Wang, and G. Jiang, “The realization of long focal depth with a linear varied-area zone plate,” J. Mod. Opt. 64, 244–250 (2016).
[Crossref]

Ferrando, V.

A. Calatayud, V. Ferrando, F. Giménez, W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “Fractal square zone plates,” Opt. Commun. 286, 42–45 (2013).
[Crossref]

Francisco, J. G.

Freund, I.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[Crossref]

Fu, S.

Furlan, W. D.

Gahagan, K. T.

Gao, C.

Gao, N.

N. Gao, C. Xie, C. Li, C. Lin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[Crossref]

Giménez, F.

A. Calatayud, V. Ferrando, F. Giménez, W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “Fractal square zone plates,” Opt. Commun. 286, 42–45 (2013).
[Crossref]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896 (2009).
[Crossref]

Glenn, D. B.

Haist, T.

Heckenberg, N. R.

Holloway, P. H.

H. H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. 47, 118001 (2008).
[Crossref]

Hu, F.

Q. Fan, S. Wang, Z. Yang, L. Wei, F. Hu, H. Zang, Q. Zhang, C. Wang, and G. Jiang, “The realization of long focal depth with a linear varied-area zone plate,” J. Mod. Opt. 64, 244–250 (2016).
[Crossref]

Janicijevic, L. J.

L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. 13, 199–206 (1982).
[Crossref]

Javier, A.

Ji, Z.

H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
[Crossref]

Z. Ji, H. Zang, C. Fan, J. Wang, C. Zheng, L. Wei, C. Wang, and L. Cao, “Fractal spiral zone plates,” J. Opt. Soc. Am. A 35, 726–731 (2018).
[Crossref]

C. Zheng, S. Su, H. Zang, Z. Ji, Y. Tian, S. Chen, K. Mu, L. Wei, Q. Fan, C. Wang, X. Zhu, C. Xie, L. Cao, and E. Liang, “Characterization of the focusing performance of axial line-focused spiral zone plates,” Appl. Opt. 57, 3802–3807 (2018).
[Crossref]

C. Zheng, H. Zang, Y. Du, Y. Tian, Z. Ji, J. Zhang, Q. Fan, C. Wang, L. Cao, and E. Liang, “Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates,” Opt. Commun. 414, 128–133 (2018).
[Crossref]

Jiang, G.

Q. Fan, S. Wang, Z. Yang, L. Wei, F. Hu, H. Zang, Q. Zhang, C. Wang, and G. Jiang, “The realization of long focal depth with a linear varied-area zone plate,” J. Mod. Opt. 64, 244–250 (2016).
[Crossref]

Ke, J.

J. Ke and J. Y. Zhang, “Focusing properties of phase-only generalized Fibonacci photon sieves,” Opt. Commun. 368, 34–38 (2016).
[Crossref]

Kristensen, M.

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

Lee, W.

W. Cheong, W. Lee, X. Yuan, L. Zhang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Li, C.

N. Gao, C. Xie, C. Li, C. Lin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[Crossref]

Liang, E.

H. Zang, C. Zheng, Q. Fan, C. Wang, L. Wei, L. Cao, X. Wang, and E. Liang, “Generation of x-ray vortex with ultra-long depth of focus using axial line-focused spiral zone plates,” Chin. Opt. Lett. 16, 080501 (2018).
[Crossref]

H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
[Crossref]

C. Zheng, H. Zang, Y. Du, Y. Tian, Z. Ji, J. Zhang, Q. Fan, C. Wang, L. Cao, and E. Liang, “Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates,” Opt. Commun. 414, 128–133 (2018).
[Crossref]

C. Zheng, S. Su, H. Zang, Z. Ji, Y. Tian, S. Chen, K. Mu, L. Wei, Q. Fan, C. Wang, X. Zhu, C. Xie, L. Cao, and E. Liang, “Characterization of the focusing performance of axial line-focused spiral zone plates,” Appl. Opt. 57, 3802–3807 (2018).
[Crossref]

Lin, C.

N. Gao, C. Xie, C. Li, C. Lin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[Crossref]

Lin, J.

S. Tao, X. Yuan, and J. Lin, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89, 031105 (2006).
[Crossref]

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

Liu, M.

N. Gao, C. Xie, C. Li, C. Lin, and M. Liu, “Square optical vortices generated by binary spiral zone plates,” Appl. Phys. Lett. 98, 151106 (2011).
[Crossref]

C. Xie, X. Zhu, L. Shi, and M. Liu, “Spiral photon sieves apodized by digital prolate spheroidal window for the generation of hard-x-ray vortex,” Opt. Lett. 35, 1765–1767 (2010).
[Crossref]

Liu, X.

H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
[Crossref]

McDuff, R.

Minin, I. V.

Minin, O. V.

Monsoriu, J. A.

Mu, K.

Ng, J.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

Normatov, A.

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Reicherter, M.

Rosen, J.

Saavedra, G.

A. Calatayud, V. Ferrando, F. Giménez, W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “Fractal square zone plates,” Opt. Commun. 286, 42–45 (2013).
[Crossref]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32, 2109–2111 (2007).
[Crossref]

Shamir, J.

Shi, L.

Smith, C. P.

Spektor, B.

Su, S.

Swartzlander, G. A.

Tao, S.

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H. Zang, C. Zheng, Z. Ji, X. Liu, Y. Tian, L. Wei, Q. Fan, X. Wang, L. Cao, and E. Liang, “Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator,” Optik 175, 344–350 (2018).
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Figures (6)

Fig. 1.
Fig. 1. Schematic views. (a) Negative SZP; (b) negative FSZP; (c) SZPWSP with p = 1 , S = 3 , N = 2 ; (d) DTFSZP with p = 1 , S = 3 , N = 2 ; (e) the representation of phase type zones; (f) the representation of opaque zones.
Fig. 2.
Fig. 2. Axial irradiance. (a) The negative FSZP with S = 3 , N = 2 ; (b) FZPWSP with p = 1 ; (c) DTFSZP with p = 1 , S = 3 , N = 2 . The horizontal line displays the axial sampling lines through the maximum intensity points.
Fig. 3.
Fig. 3. Calculated transverse intensity profiles for (a) negative FSZP, (b) SZPWSP, and (c) DTFSZP at different axial distances. The total simulation area is 0.1 mm × 0.1 mm .
Fig. 4.
Fig. 4. Axial intensity profiles of DTFSZP with different fractal stages. (a)  S = 2 , (b)  S = 3 , (c)  S = 4 . Parameters: λ = 632.8 nm , f = 0.8 m , N = 2 , p = 1 .
Fig. 5.
Fig. 5. Calculation of DTFSZP with different TCs. (a) The transmittance, (b) the transverse intensity profiles, (c) the phase distribution profiles. The fractal parameters: S = 3 , N = 2 .
Fig. 6.
Fig. 6. Central phase profiles of DTFSZP ( f = 0.8 m , S = 3 , N = 2 ) with different TCs. (a)  p = 1 , 3, 5, and 7; (b)  p = 9 , 11, 13, and 15.

Equations (7)

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t j = { 1 , j = 2 i 1 0 , j = 2 i , i = 1 , 2 , 3 , ,
P ( x 0 , y 0 ) = j = 1 N t j [ rect ( x 0 L j / M ) rect ( y 0 L j / M ) rect ( x 0 L ( j 1 ) / M ) rect ( y 0 L ( j 1 ) / M ) ] ,
t j = { 0 , j = 2 i 1 1 , j = 2 i , i = 1 , 2 , 3 , .
t j = { 1 , j = a S ( k ) + 1 0 , else ,
a S ( k ) = { 0 , k = 1 2 , k = 2 a S 1 ( k ) k 2 S 1 a S ( k 2 S 1 ) + 2 ( a S ( 2 S 1 ) + 1 ) k > 2 S 1 k = 1 , 2 , N S .
t j = { 0 , j = a S ( k ) + 1 1 , else .
I ( x , y , z ) = 1 λ 2 z 2 | P ( x 0 , y 0 ) e i π λ z ( x 2 + y 2 ) e i 2 π λ z ( x x 0 + y y 0 ) d x 0 d y 0 | 2 ,

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