Abstract

We propose a new diffractive optical element, called a spiral Dammann zone plate (SDZP), to generate a series of dipole vortices along the optical axis in the focal region of a focusing objective. By combining this SDZP and another Dammann grating, we describe the generation of three-dimensional dipole vortex arrays in the focal volume of an objective. For experimental demonstration, a 1×5 SDZP with base charge of l=1 is fabricated by using lithography and wet-etching techniques, and a 1×5 coaxial dipole vortex array is achieved for an objective of NA=0.127. Furthermore, by combining the 1×5 SDZP and another 5×5 Dammann grating, a 5×5×5 dipole vortex array is also experimentally demonstrated. The results show that topological charges of these 5×5 vortex arrays on five coaxial planes could be tunable by selecting a vortex beam carrying different charge as the incident field.

© 2012 Optical Society of America

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References

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2012

2011

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, 3634–3640 (2011).
[CrossRef]

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

Z. Wang, N. Zhang, and X. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19, 482–492 (2011).
[CrossRef]

J. Xavier, S. Vyas, P. Senthilkumaran, C. Denz, and J. Joseph, “Sculptured 3D twister superlattices embedded with tunable vortex spirals,” Opt. Lett. 36, 3512–3514(2011).
[CrossRef]

2010

2009

2008

2007

2006

2004

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

2003

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

1995

1992

Alda, J.

J. Alda and F. J. Gonzalez, “Polygonal Fresnel zone plates,” J. Opt. A: Pure Appl. Opt. 11, 085707 (2009).
[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, 3634–3640 (2011).
[CrossRef]

Brasselet, E.

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

Burge, R. E.

N. Zhang, X. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35, 3495–3497 (2010).
[CrossRef]

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

Cao, H.

Cao, W.

Chen, Y.-T.

Chu, S.-C.

Cottrell, D. M.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Daria, V. R.

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

Davis, J. A.

Denz, C.

Di, C.

Gao, N.

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

Gluckstad, J.

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

Gonzalez, F. J.

J. Alda and F. J. Gonzalez, “Polygonal Fresnel zone plates,” J. Opt. A: Pure Appl. Opt. 11, 085707 (2009).
[CrossRef]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Heckenberg, N. R.

Hu, A.

Janicijevic, L.

Jia, W.

Jin, C.

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

Joseph, J.

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, 3634–3640 (2011).
[CrossRef]

Lasser, T.

Leitgeb, R. A.

Leutenegger, M.

Li, C.

N. Gao, C. Xie, C. Li, C. Jin, 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, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Liu, L.

Liu, M.

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

Ma, J.

McDuff, R.

Mitry, M. J.

Moreno, I.

Otsuka, K.

Pascoguin, B. M. L.

Rao, R.

Rodrigo, P. J.

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

Senthilkumaran, P.

Singh, R. 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, 3634–3640 (2011).
[CrossRef]

Smith, C. P.

Tao, S.

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

Topuzoski, S.

Tsai, K.-F.

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, 3634–3640 (2011).
[CrossRef]

Vyas, S.

Wang, S.

Wang, Z.

White, A. G.

Wu, J.

Xavier, J.

Xie, C.

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

Yu, J.

Yuan, X.

Zhang, N.

Zhou, C.

Appl. Opt.

Appl. Phys. Lett.

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

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

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

J. Opt. A: Pure Appl. Opt.

J. Alda and F. J. Gonzalez, “Polygonal Fresnel zone plates,” J. Opt. A: Pure Appl. Opt. 11, 085707 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Lett. 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, 3634–3640 (2011).
[CrossRef]

Phys. Rev. Lett.

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

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Supplementary Material (6)

» Media 1: MOV (2026 KB)     
» Media 2: MOV (4335 KB)     
» Media 3: MOV (3712 KB)     
» Media 4: MOV (4279 KB)     
» Media 5: MOV (2350 KB)     
» Media 6: MOV (3038 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Phase distributions of the binary pure-phase 1×5 SDZPs with different base charges under condition of NA=0.1. (a) Charge 0; (b) charge 1/2, (c) charge 1, (d) charge 2.

Fig. 2.
Fig. 2.

Geometry of the focusing system with a SDZP for generation of a coaxial dipole vortex array along the optical axis, where the SDZP is located in contact with a focusing objective. The geometrical focus is set as the origin of the coordinate and the optical axis is along the z axis.

Fig. 3.
Fig. 3.

Experimental results of a 1×5 SDZP embedded with base charge of 1 under focusing of a focusing objective (NA=0.127). (a) Microscopic images of the fabricated SDZP sample in two local areas (the scale bar is 100 μm); (b) transverse intensity distributions on five focal planes (the scale bar is 5 μm); (c) longitudinal intensity distribution on a meridian plane. Here (b) and (c) illustrate the 3D intensity distribution of the 1×5 coaxial dipole vortex array generated by the SDZP in the focal volume of the objective (Media 1).

Fig. 4.
Fig. 4.

Experimental setup for generation of 5×5×5 dipole vortex array in the focal volume of a focusing objective with a 1×5 SDZP embedded with base charge of l=1. DVG, Dammann vortex grating; SDZP, 1×5 spiral Dammann zone plate; MO1, objective for focusing; MO2, objective for magnifying; DG, 5×5 Dammann grating; L1 and L2, lens pair for expanding; L3 and L4, lens pair for projecting of the diffractive field of the DG onto the entrance aperture of MO1; γ, angle between the incident light and the reflective plane of the mirror; d1, distance from the center of the mirror when it is located at the z axis to the DVG; d2, distance between the DVG and the pupil stop.

Fig. 5.
Fig. 5.

Experimental results of the 3D intensity distribution of a 5×5×5 dipole vortex array when the topological charge of the incident beam is changing from 2 to 2: (a) charge 2 (Media 2); (b) charge 1 (Media 3); (c) charge 0 (Media 4); (d) charge 1 (Media 5); (e) charge 2 (Media 6). The left plot illustrates the 2D intensity distribution on one meridian plane, and the right one is the transverse intensity on the geometrical focal plane (the scale bar is 50 μm). The inset at the top-right corner shows the enlarged plot of the intensity distribution near the geometrical focus.

Tables (1)

Tables Icon

Table 1. Radius Size in FWHM of the Focused Vortex Embedded with Different Topological Charge at the Corresponding Focal Plane along the Axial Direction (NA=0.127)

Equations (4)

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TSDZP(ρ,φ)=m=Cmexp{im[2π1(ρsinα)2/Λξ+lφ]},
Cm={i2mπ[1+2n=1N1(1)nei2πmxn+(1)Nei2πmxN]m02n=1N1(1)nxn+(1)NxNm=0,
Eo(x,y,z)=00{TSDZP(kx,ky)Et(kx,ky)eikzz/cosθ}ei(kxx+kyy)dkxdky=mδ(zmΔz)Em(x,y,z),
Em(x,y,z)=0α02πA(θ)eimlφEt(θ,φ)×exp[ik(xsinθcosφ+ysinθsinφzcosθ)]sinθdφdθ,

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