Abstract

We propose a simple and flexible method to create identical multiple focal spots with three-dimensional arbitrary shifting without moving lenses or laser beams. The incident cylindrical vector (CV) beam superposed with predesigned phase and amplitude modulations is tightly focused by a single lens. The multiple focal spots with predetermined number and positions are generated and the identical intensity distribution as well as the polarization distribution for each individual focal spot is demonstrated. We also present a three-dimensional dynamic shifting with four identical focal spots along Pyramid-like trajectory by continuously regulating the phase and amplitude modulations on the incident CV beam. Furthermore, multiple focal spots with unique intensity profile can also be achieved when proper diffractive optical element (DOE) is associated in the focusing system. These engineered focal fields may find potential applications in 3D laser printing, moving multiple particles trapping and manipulations.

© 2017 Optical Society of America

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References

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  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
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  3. X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
  4. N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).
  5. H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
  6. T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).
  7. W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
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  11. N. Bokor and N. Davidson, “Toward a spherical spot distribution with 4π focusing of radially polarized light,” Opt. Lett. 29(17), 1968–1970 (2004).
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2017 (1)

2015 (3)

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).

2014 (2)

B. Gu, Y. Pan, J. L. Wu, and Y. Cui, “Manipulation of radial-variant polarization for creating tunable bifocusing spots,” J. Opt. Soc. Am. A 31(2), 253–257 (2014).

K. Lalithambigai, P. M. Anbarasan, and K. B. Rajesh, “Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask,” Optik (Stuttg.) 125(10), 2225–2228 (2014).

2013 (1)

T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).

2012 (2)

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

Q. Xu and J. Chen, “The creation of double tight focus by a concentric multi-belt pure phase fiter,” Opt. Commun. 285(7), 1642–1645 (2012).

2011 (2)

2010 (1)

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).

2008 (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

2006 (2)

Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).

2004 (2)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).

N. Bokor and N. Davidson, “Toward a spherical spot distribution with 4π focusing of radially polarized light,” Opt. Lett. 29(17), 1968–1970 (2004).

2000 (2)

1992 (1)

H. Fukuda and R. Yamanaka, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31(12B), 4126–4130 (1992).

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).

Anbarasan, P. M.

K. Lalithambigai, P. M. Anbarasan, and K. B. Rajesh, “Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask,” Optik (Stuttg.) 125(10), 2225–2228 (2014).

Arlt, J.

Bokor, N.

Brown, T.

Chen, J.

Q. Xu and J. Chen, “The creation of double tight focus by a concentric multi-belt pure phase fiter,” Opt. Commun. 285(7), 1642–1645 (2012).

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

Chen, K.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

Cui, Y.

Dan, D.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

Davidson, N.

DeSimone, J. M.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Ding, J.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

Du, L.

Ermoshkin, A.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Ermoshkin, N.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Fukuda, H.

H. Fukuda and R. Yamanaka, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31(12B), 4126–4130 (1992).

Gao, P.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

Gong, L.

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

Gu, B.

Guo, C. S.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).

Janusziewicz, R.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Johnson, A. R.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).

Kelly, D.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Kozawa, Y.

Lalithambigai, K.

K. Lalithambigai, P. M. Anbarasan, and K. B. Rajesh, “Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask,” Optik (Stuttg.) 125(10), 2225–2228 (2014).

Lei, M.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

Li, Y.

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

Li, Z.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

Lin, J.

T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).

Liu, J.

T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).

Liu, T.

T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

Ma, B.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

Nie, S.

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

Padgett, M. J.

Pan, Y.

Pinschmidt, R.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Pu, J.

Rajesh, K. B.

K. Lalithambigai, P. M. Anbarasan, and K. B. Rajesh, “Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask,” Optik (Stuttg.) 125(10), 2225–2228 (2014).

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).

Rolland, J. P.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Rupp, R.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

S. Yan, B. Yao, and R. Rupp, “Shifting the spherical focus of a 4Pi focusing system,” Opt. Express 19(2), 673–678 (2011).

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).

Samulski, E. T.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Sato, S.

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

Shi, P.

Shirvanyants, D.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Tan, J. B.

T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).

Tian, B.

Tumbleston, J. R.

J. R. Tumbleston, D. Shirvanyants, N. Ermoshkin, R. Janusziewicz, A. R. Johnson, D. Kelly, K. Chen, R. Pinschmidt, J. P. Rolland, A. Ermoshkin, E. T. Samulski, and J. M. DeSimone, “Additive manufacturing. Continuous liquid interface production of 3D objects,” Science 347(6228), 1349–1352 (2015).

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

Wang, H. T.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

Wang, M.

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

Wang, X.

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

Wang, X. L.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).

Weng, X.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).

Wu, J. L.

Xu, Q.

Q. Xu and J. Chen, “The creation of double tight focus by a concentric multi-belt pure phase fiter,” Opt. Commun. 285(7), 1642–1645 (2012).

Yamanaka, R.

H. Fukuda and R. Yamanaka, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31(12B), 4126–4130 (1992).

Yan, S.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

S. Yan, B. Yao, and R. Rupp, “Shifting the spherical focus of a 4Pi focusing system,” Opt. Express 19(2), 673–678 (2011).

Yao, B.

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

S. Yan, B. Yao, and R. Rupp, “Shifting the spherical focus of a 4Pi focusing system,” Opt. Express 19(2), 673–678 (2011).

Youngworth, K.

Yu, Y.

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).

Yuan, X.

Zhan, Q.

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).

Zhu, Z.

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).

Appl. Phys. Lett. (1)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239–6241 (2004).

J. Opt. (1)

Z. Li, S. Yan, B. Yao, M. Lei, B. Ma, P. Gao, D. Dan, and R. Rupp, “Theoretical prediction of three- dimensional shifting of a spherical focal spot in a 4Pi focusing system,” J. Opt. 14(5), 055706 (2012).

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

Jpn. J. Appl. Phys. (1)

H. Fukuda and R. Yamanaka, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31(12B), 4126–4130 (1992).

Nat. Photonics (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).

Opt. Commun. (3)

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).

Q. Xu and J. Chen, “The creation of double tight focus by a concentric multi-belt pure phase fiter,” Opt. Commun. 285(7), 1642–1645 (2012).

L. Gong, Z. Zhu, X. Wang, Y. Li, M. Wang, and S. Nie, “Changeable focused field distribution of double- ring-shaped cylindrical vector beams,” Opt. Commun. 342, 204–213 (2015).

Opt. Eng. (1)

T. Liu, J. B. Tan, J. Lin, and J. Liu, “Generating super-Gaussian light needle of 0.36λ beam size and pure longitudinal polarization,” Opt. Eng. 52(7), 074104 (2013).

Opt. Express (3)

Opt. Lett. (4)

Optik (Stuttg.) (1)

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Phys. Rev. Lett. (1)

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Sci. Rep. (1)

Y. Yu and Q. Zhan, “Creation of identical multiple focal spots with prescribed axial distribution,” Sci. Rep. 5, 14673 (2015).

Science (1)

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Other (1)

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Supplementary Material (1)

NameDescription
» Visualization 1       The movie presents four focal spots continuous shifting along a Pyramid-like trajectory in three-dimensional space.

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of single focal spot shifting system under the illumination of a generalized CV beam. V(r,ϕ, z)/ V'(r',ϕ', z') is an observational point in the focal plane before /after focal shifting.
Fig. 2
Fig. 2 Schematic of one focal spot shifting with (a) phase modulation, (b) amplitude modulation and (c) the position of the shifted one focal spot. The insert of (c) shows the distributions of both normalized intensity and polarization in the cross-section of the focal plane.
Fig. 3
Fig. 3 Schematic of multiple focal spots shifting. (a)-(c) phase modulation, amplitude modulation and positions as well as normalized intensity distribution in the cross-section of the focal plane of two focal spots and (d)-(f) of three focal spots.
Fig. 4
Fig. 4 One frame of four focal spots shifting along a Pyramid-like trajectory in three-dimensional space. Under continuous phase and amplitude modulations, four focal spots are moved in real time (see Visualization 1).
Fig. 5
Fig. 5 Schematic of three focal spots shifting with the same flattop profile. (a) phase modulation, (b) amplitude modulation and (c) normalized total intensity distributions at focus and through focus. Τhe focal spot is located at (10λ, 0, −10λ), (0, 0, 0) and (−10λ, 0, 10λ), respectively.

Equations (21)

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E 0 (θ,ϕ)= l 0 circ(sinθ/sinα)(cos ϕ 0 e ρ +sin ϕ 0 e ϕ ),
e ρ =cosϕ e x +sinϕ e y ,
e ϕ =sinϕ e x +cosϕ e y .
e r ' =cosθ(cosϕ e x +sinϕ e y )+sinθ e z ,
e ϕ ' =sinϕ e x +cosϕ e y .
E ( r,φ,z )= ik 2π 0 α dθ 0 2π E 1 ( θ,ϕ ) e ik( s r ) sinθdϕ,
E 1 (θ,ϕ)= l 0 circ(sinθ/sinα)A(θ)(cos ϕ 0 e r ' +sin ϕ 0 e ϕ ' ).
s r =zcosθ+rsinθcos( ϕφ ).
s ( r r 0 )=( z z 0 )cosθ+rsinθcos( φϕ )sinθ( cosϕ x 0 +sinϕ y 0 )
P( θ,ϕ )= e ik( s r 0 ) = e ik( sinθcosϕ x 0 +sinθsinϕ y 0 +cosθ z 0 ) .
E r ( r,φ,z )=2 0 α l 0 cosθ e ik z cosθ sinθ [ cosθcos ϕ 0 cos( φ φ ) J 1 ( k r sinθ ) sin ϕ 0 sin( φ φ ) J 1 ( k r sinθ ) ]dθ ,
E φ ( r,φ,z )=2 0 α l 0 cosθ e ik z cosθ sinθ [ cosθcos ϕ 0 sin( φ φ ) J 1 ( k r sinθ ) +sin ϕ 0 cos( φ φ ) J 1 ( k r sinθ ) ]dθ ,
E z ( r,φ,z )=2i 0 α l 0 cosθ e ik z cosθ cos ϕ 0 sin 2 θ J 0 ( k r sinθ )dθ ,
r = ( rcosφ x 0 ) 2 + ( rsinφ y 0 ) 2 ,
cos φ =( rcosφ x 0 )/ r ,
sin φ =( rsinφ y 0 )/ r ,
z =z z 0 ,
f i ( θ,ϕ )= e ik( s r i ) = e ik( sinθcosϕ x i +sinθsinϕ y i +cosθ z i ) ,( i=1m ).
T( θ,ϕ )S( θ,ϕ ) E 0 ( θ,ϕ ) = 1 m E 0 ( θ,ϕ ) i=1 m f i (θ,ϕ) ,
T( θ,ϕ )= m+2 j,i=1,ji m cos[k( s r j s r i )] m ,
S( θ,ϕ )=exp{iarctan j=1 m sin[k( s r j )] j=1 m cos[k( s r j )] }.

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