Abstract

Optical cages attract considerable attentions recently owing to their potential applications in optical trapping, optical imaging and optical cloaking. However, the generation of tunable optical cage arrays in the transverse plane comes to a great challenge, which restricts the effectiveness of the above applications. In this work, we propose a full polarization-controlled method that optical cage arrays with tunable number and positions in the x-y plane can be generated by a so-called Dammann vector beam (DVB), both under the conditions of high- and low-NA focusing system. By adjusting the polarization state of the DVB with the phase of Dammann grating, the number and positions of optical cages can be adjusted flexibly. This work reveals the relationship between the complex polarization state of an incident vector beam and the output optical cage array in the focal region, and may find valuable applications in optical imaging, optical trapping, etc.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (3)

H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
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[Crossref] [PubMed]

M. M. Sánchez-López, J. A. Davis, N. Hashimoto, I. Moreno, E. Hurtado, K. Badham, A. Tanabe, and S. W. Delaney, “Performance of a q-plate tunable retarder in reflection for the switchable generation of both first- and second-order vector beams,” Opt. Lett. 41(1), 13–16 (2016).
[Crossref] [PubMed]

2015 (3)

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Y. Yu and Q. Zhan, “Generation of uniform three-dimensional optical chain with controllable characteristics,” J. Opt. 17(10), 105606 (2015).
[Crossref]

Y. Iketaki, H. Kumagai, K. Jahn, and N. Bokor, “Creation of a three-dimensional spherical fluorescence spot for super-resolution microscopy using a two-color annular hybrid wave plate,” Opt. Lett. 40(6), 1057–1060 (2015).
[Crossref] [PubMed]

2014 (4)

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
[PubMed]

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014).
[Crossref] [PubMed]

X. Weng, X. Gao, H. Guo, and S. Zhuang, “Creation of tunable multiple 3D dark spots with cylindrical vector beam,” Appl. Opt. 53(11), 2470–2476 (2014).
[Crossref] [PubMed]

2012 (5)

2011 (1)

2010 (2)

2009 (2)

2008 (3)

2007 (2)

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279(2), 229–234 (2007).
[Crossref]

N. Bokor and N. Davidson, “Tight parabolic dark spot with high numerical aperture focusing with a circular p phase plate,” Opt. Commun. 270(2), 145–150 (2007).
[Crossref]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

2005 (1)

2000 (1)

1996 (1)

1995 (1)

1994 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Badham, K.

Bingen, P.

Bokor, N.

Y. Iketaki, H. Kumagai, K. Jahn, and N. Bokor, “Creation of a three-dimensional spherical fluorescence spot for super-resolution microscopy using a two-color annular hybrid wave plate,” Opt. Lett. 40(6), 1057–1060 (2015).
[Crossref] [PubMed]

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279(2), 229–234 (2007).
[Crossref]

N. Bokor and N. Davidson, “Tight parabolic dark spot with high numerical aperture focusing with a circular p phase plate,” Opt. Commun. 270(2), 145–150 (2007).
[Crossref]

Brown, T.

Cao, W.

Cardano, F.

Chen, P.

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Chen, W.

J. Wang, W. Chen, and Q. Zhan, “Creation of uniform three-dimensional optical chain through tight focusing of space-variant polarized beams,” J. Opt. 14(5), 055004 (2012).
[Crossref]

Chen, Y.

Chigrinov, V.

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Chipman, R. A.

Dally, A.

Davidson, N.

N. Bokor and N. Davidson, “Tight parabolic dark spot with high numerical aperture focusing with a circular p phase plate,” Opt. Commun. 270(2), 145–150 (2007).
[Crossref]

N. Bokor and N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279(2), 229–234 (2007).
[Crossref]

Davis, J. A.

de Lisio, C.

Delaney, S. W.

Ding, W.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Egner, A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

Engelhardt, J.

P. Bingen, M. Reuss, J. Engelhardt, and S. W. Hell, “Parallelized STED fluorescence nanoscopy,” Opt. Express 19(24), 23716–23726 (2011).
[Crossref] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

Gahagan, K. T.

Gan, F.

H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
[Crossref] [PubMed]

Gao, X.

Gong, L.

L. Gong, W. Liu, Q. Zhao, Y. Ren, X. Qiu, M. Zhong, and Y. Li, “Controllable light capsules employing modified Bessel-Gauss beams,” Sci. Rep. 6(1), 29001 (2016).
[Crossref] [PubMed]

Gu, M.

H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
[Crossref] [PubMed]

Gu, Z.

Guo, H.

Han, T.

H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014).
[Crossref] [PubMed]

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Hashimoto, N.

He, X.

Hell, S. W.

Hu, A.

Hu, W.

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Huang, K.

H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014).
[Crossref] [PubMed]

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Hurtado, E.

Iketaki, Y.

Isenhower, L.

Jahn, K.

Jakobs, S.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

Ji, W.

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Jia, W.

Karimi, E.

Kozawa, Y.

Kuang, C.

Kumagai, H.

Lei, D.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Lei, M.

Leong, E. S. P.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Li, S.

Li, T.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
[PubMed]

Li, Y.

L. Gong, W. Liu, Q. Zhao, Y. Ren, X. Qiu, M. Zhong, and Y. Li, “Controllable light capsules employing modified Bessel-Gauss beams,” Sci. Rep. 6(1), 29001 (2016).
[Crossref] [PubMed]

Li, Y. P.

Lin, J.

H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
[Crossref] [PubMed]

Liu, L.

Liu, W.

L. Gong, W. Liu, Q. Zhao, Y. Ren, X. Qiu, M. Zhong, and Y. Li, “Controllable light capsules employing modified Bessel-Gauss beams,” Sci. Rep. 6(1), 29001 (2016).
[Crossref] [PubMed]

Liu, X.

Lu, Y.

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Luk’yanchuk, B.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Maier, S. A.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Marrucci, L.

McEldowney, S. C.

Moreno, I.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Peng, F.

Ping, Y. S.

Qiu, C.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

Qiu, C. W.

Qiu, X.

L. Gong, W. Liu, Q. Zhao, Y. Ren, X. Qiu, M. Zhong, and Y. Li, “Controllable light capsules employing modified Bessel-Gauss beams,” Sci. Rep. 6(1), 29001 (2016).
[Crossref] [PubMed]

Ramachandran, S.

Ren, Y.

L. Gong, W. Liu, Q. Zhao, Y. Ren, X. Qiu, M. Zhong, and Y. Li, “Controllable light capsules employing modified Bessel-Gauss beams,” Sci. Rep. 6(1), 29001 (2016).
[Crossref] [PubMed]

Reuss, M.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Rishøj, L.

Saffman, M.

Sánchez-López, M. M.

Santamato, E.

Sato, S.

Schmidt, R.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

Shemo, D. M.

Slussarenko, S.

Smith, P. K.

Steinvurzel, P.

Swartzlander, G. A.

Tanabe, A.

Teng, J.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014).
[Crossref] [PubMed]

Urbach, H. P.

H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
[Crossref] [PubMed]

Wan, C.

C. Wan, K. Huang, T. Han, E. S. P. Leong, W. Ding, L. Zhang, T. Yeo, X. Yu, J. Teng, D. Lei, S. A. Maier, B. Luk’yanchuk, S. Zhang, and C. Qiu, “Three-dimensional visible-light capsule enclosing perfect supersized darkness via antiresolution,” Laser Photonics Rev. 8(5), 743–749 (2014).
[Crossref]

H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014).
[Crossref] [PubMed]

Wang, H.

H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
[Crossref] [PubMed]

Wang, J.

J. Wang, W. Chen, and Q. Zhan, “Creation of uniform three-dimensional optical chain through tight focusing of space-variant polarized beams,” J. Opt. 14(5), 055004 (2012).
[Crossref]

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Appl. Opt. (5)

Appl. Phys. Lett. (1)

P. Chen, W. Ji, B. Wei, W. Hu, V. Chigrinov, and Y. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
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J. Opt. (2)

J. Wang, W. Chen, and Q. Zhan, “Creation of uniform three-dimensional optical chain through tight focusing of space-variant polarized beams,” J. Opt. 14(5), 055004 (2012).
[Crossref]

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J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

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[Crossref]

Nat. Commun. (1)

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Nat. Methods (1)

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H. Wang, J. Lin, D. Zhang, Y. Wang, M. Gu, H. P. Urbach, F. Gan, and S. Zhuang, “Creation of an anti-imaging system using binary optics,” Sci. Rep. 6(1), 33064 (2016).
[Crossref] [PubMed]

L. Gong, W. Liu, Q. Zhao, Y. Ren, X. Qiu, M. Zhong, and Y. Li, “Controllable light capsules employing modified Bessel-Gauss beams,” Sci. Rep. 6(1), 29001 (2016).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

The schematic of optical system used for generating the optical cage arrays in the transverse plane with pure polarization modulation. (a) DG for 4 × 4 focus array; (b) DG for 1 × 2 focuses with topological charge of 1.

Fig. 2
Fig. 2

The generation of an optical cage (f) under a high-NA focusing condition with a DVB (c) composed of a pair of Dammann grating modulated RP (a) and AP (b) beams. (d) and (e) the field intensity distributions in the focal region from the individual RP and AP beams, respectively.

Fig. 3
Fig. 3

The generation of optical cage arrays with DVBs under a high-NA focusing condition. Top panels: 2 × 2 and bottom ones: 3 × 3 optical cage array, respectively. The figures show the field intensity distributions in the focal region at different z-planes; (a,d) z = −2λ; (b,e) z = 0; (c,f) z = 2λ.

Fig. 4
Fig. 4

The field intensity distributions in the y-z plane for the optical cages as shown in Fig. 3, where (b) x = 2λ and (e) x = 0 plane. (a) and (d) are the polarization state of DVBs for generating the 2 × 2 and 3 × 3 optical cage arrays, respectively. (c, f) are the light intensity along y (red dash line) and z axis (blue line), respectively. The FWHMs of optical cage along y and z axis are about 0.455λ and 2.434λ for all optical cages.

Fig. 5
Fig. 5

The generation of a 1 × 2 optical cage (f) under a low-NA focusing condition generated by a DVB (c) composed of a pair of Dammann grating modulation x- (a) and y-polarized (b) beams. (d) and (e) the field intensity distributions in the focal region from the individual x- and y-polarized beams, respectively.

Fig. 6
Fig. 6

The generation of optical cage arrays with DVBs under a low-NA focusing condition. Top panels: 2 × 2 and bottom ones: 4 × 4 optical cage array, respectively. The figures show the field intensity distributions in the focal region at different z-planes; (a,d) z = −34λ; (b,e) z = 0; (c,f) z = 34λ.

Fig. 7
Fig. 7

The field intensity distributions in the y-z plane for the optical cages as shown in Fig. 6, where (b) x = 15λ and (e) x = 12λ plane. (a) and (d) are the polarization state of DVBs for generating the 2 × 2 and 4 × 4 optical cage arrays, respectively. (c, f) are the light intensity along y (red dash line) and z axis (blue line), respectively. The FWHMs of optical cage along y and z axis are about 1.90λ and 40.14λ for all optical cages.

Equations (11)

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

E DVBH = η H D G 1 e r +D G 2 e φ
D G j =D G xj ( N xj , d xj , t pj )×D G yj ( N yj , d yj )×D G zj ( N zj , d zj ) j=1,2
D G 2 =D G x2 ( N x2 , d x2 )×D G y2 (2, d y2 ,1)×D G y2 ( N y2 , d y2 ' )×D G z2 ( N z2 , d z2 )
D G 1 =D G x1 ( N x1 , d x1 , t p1 )×D G y1 ( N y1 , d y1 )×D G z1 ( N z1 , d z1 )
E DVBL = η L D G 1 e x +D G 2 e y
E(r,ϕ,z)= iA π 0 2π 0 α sinθ cos 1/2 θ l 0 (θ)V exp[ik(rsinθcos(φϕ)+zcosθ)]dθdφ
l 0 (θ)= J 1 (2 β 0 sinθ sinα )exp[ ( β 0 sinθ sinα ) 2 ]
V high = η H D G 1 V r +D G 2 V φ
V low = η L D G 1 V x +D G 2 V y
V r = [ cosθcosφ cosθsinφ sinθ ] T
V φ = [ sinφ cosφ 0 ] T

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