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).

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).

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).

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).

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).

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

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).

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

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).

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).

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).

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).

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

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).

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. 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).

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).

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).

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).

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

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).

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).

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. 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).

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).

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. 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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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. 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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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

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).

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).

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

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).

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).

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

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).

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).

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

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).

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).

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).

K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).

X. Weng, L. Du, P. Shi, and X. Yuan, “Tunable optical cage array generated by Dammann vector beam,” Opt. Express 25(8), 9039–9048 (2017).

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

B. Tian and J. Pu, “Tight focusing of a double-ring-shaped, azimuthally polarized beam,” Opt. Lett. 36(11), 2014–2016 (2011).

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

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

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000).

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).

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).

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).

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

G. D. Villiers and E. R. Pike, The Limits of Resolution, (CRC Press, 2016), Chap. 1.