Z. Mei, Y. Mao, and Y. Wang, “Electromagnetic multi-Gaussian Schell-model vortex light sources and their radiation field properties,” Opt. Express 26(17), 21992–22000 (2018).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

J. Zeng, X. Liu, F. Wang, C. Zhao, and Y. Cai, “Partially coherent fractional vortex beam,” Opt. Express 26(21), 26830–26844 (2018).

[Crossref]

H. Xu, Y. Zhou, H. Wu, H. Chen, Z. Sheng, and J. Qu, “Focus shaping of the radially polarized Laguerre- Gaussian-correlated Schell-model vortex beams,” Opt. Express 26(16), 20076–20088 (2018).

[Crossref]

C. Ping, C. Liang, F. Wang, and Y. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).

[Crossref]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

X. Wang, L. Gong, Z. Zhu, B. Gu, and Q. Zhan, “Creation of identical multiple focal spots with three-dimensional arbitrary shifting,” Opt. Express 25(15), 17737–17745 (2017).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).

[Crossref]

L. Huang, H. Guo, J. Li, L. Ling, B. Feng, and Z. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012).

[Crossref]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86(1), 013840 (2012).

[Crossref]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).

[Crossref]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).

[Crossref]

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

[Crossref]

L. Hua, B. Chen, Z. Chen, and J. Pu, “Tight focusing of partially coherent, partially polarized vortex beams,” J. Opt. 13(7), 075702 (2011).

[Crossref]

L. Guo, Z. Tang, C. Liang, and Z. Tan, “Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams,” Opt. Laser Technol. 43(4), 895–898 (2011).

[Crossref]

K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).

[Crossref]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010).

[Crossref]

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

[Crossref]

L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical aperture lens,” Opt. Laser Technol. 41(3), 241–246 (2009).

[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).

[Crossref]

T. G. Jabbour and S. M. Kuebler, “Vectorial beam shaping,” Opt. Express 16(10), 7203–7213 (2008).

[Crossref]

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

[Crossref]

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

[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).

[Crossref]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).

[Crossref]

I. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).

[Crossref]

I. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).

[Crossref]

J. Zeng, X. Liu, F. Wang, C. Zhao, and Y. Cai, “Partially coherent fractional vortex beam,” Opt. Express 26(21), 26830–26844 (2018).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

C. Ping, C. Liang, F. Wang, and Y. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).

[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).

[Crossref]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86(1), 013840 (2012).

[Crossref]

L. Hua, B. Chen, Z. Chen, and J. Pu, “Tight focusing of partially coherent, partially polarized vortex beams,” J. Opt. 13(7), 075702 (2011).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

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

[Crossref]

Z. Chen, T. Zeng, and J. Ding, “Reverse engineering approach to focus shaping,” Opt. Lett. 41(9), 1929–1932 (2016).

[Crossref]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).

[Crossref]

L. Hua, B. Chen, Z. Chen, and J. Pu, “Tight focusing of partially coherent, partially polarized vortex beams,” J. Opt. 13(7), 075702 (2011).

[Crossref]

L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical aperture lens,” Opt. Laser Technol. 41(3), 241–246 (2009).

[Crossref]

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

[Crossref]

Z. Chen, T. Zeng, and J. Ding, “Reverse engineering approach to focus shaping,” Opt. Lett. 41(9), 1929–1932 (2016).

[Crossref]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).

[Crossref]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).

[Crossref]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86(1), 013840 (2012).

[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).

[Crossref]

L. Guo, Z. Tang, C. Liang, and Z. Tan, “Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams,” Opt. Laser Technol. 43(4), 895–898 (2011).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

L. Hua, B. Chen, Z. Chen, and J. Pu, “Tight focusing of partially coherent, partially polarized vortex beams,” J. Opt. 13(7), 075702 (2011).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).

[Crossref]

C. Ping, C. Liang, F. Wang, and Y. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).

[Crossref]

L. Guo, Z. Tang, C. Liang, and Z. Tan, “Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams,” Opt. Laser Technol. 43(4), 895–898 (2011).

[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

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

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

L. Hua, B. Chen, Z. Chen, and J. Pu, “Tight focusing of partially coherent, partially polarized vortex beams,” J. Opt. 13(7), 075702 (2011).

[Crossref]

L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical aperture lens,” Opt. Laser Technol. 41(3), 241–246 (2009).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

H. Xu, Y. Zhou, H. Wu, H. Chen, Z. Sheng, and J. Qu, “Focus shaping of the radially polarized Laguerre- Gaussian-correlated Schell-model vortex beams,” Opt. Express 26(16), 20076–20088 (2018).

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).

[Crossref]

L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical aperture lens,” Opt. Laser Technol. 41(3), 241–246 (2009).

[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).

[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).

[Crossref]

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

[Crossref]

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

[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).

[Crossref]

I. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).

[Crossref]

L. Guo, Z. Tang, C. Liang, and Z. Tan, “Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams,” Opt. Laser Technol. 43(4), 895–898 (2011).

[Crossref]

L. Guo, Z. Tang, C. Liang, and Z. Tan, “Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams,” Opt. Laser Technol. 43(4), 895–898 (2011).

[Crossref]

L. Wei and H. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).

[Crossref]

I. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).

[Crossref]

J. Zeng, X. Liu, F. Wang, C. Zhao, and Y. Cai, “Partially coherent fractional vortex beam,” Opt. Express 26(21), 26830–26844 (2018).

[Crossref]

C. Ping, C. Liang, F. Wang, and Y. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).

[Crossref]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86(1), 013840 (2012).

[Crossref]

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

[Crossref]

X. Wang, L. Gong, Z. Zhu, B. Gu, and Q. Zhan, “Creation of identical multiple focal spots with three-dimensional arbitrary shifting,” Opt. Express 25(15), 17737–17745 (2017).

[Crossref]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

L. Wei and H. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).

[Crossref]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).

[Crossref]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University).

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

H. Xu, Y. Zhou, H. Wu, H. Chen, Z. Sheng, and J. Qu, “Focus shaping of the radially polarized Laguerre- Gaussian-correlated Schell-model vortex beams,” Opt. Express 26(16), 20076–20088 (2018).

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical aperture lens,” Opt. Laser Technol. 41(3), 241–246 (2009).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

J. Zeng, X. Liu, F. Wang, C. Zhao, and Y. Cai, “Partially coherent fractional vortex beam,” Opt. Express 26(21), 26830–26844 (2018).

[Crossref]

Z. Chen, T. Zeng, and J. Ding, “Reverse engineering approach to focus shaping,” Opt. Lett. 41(9), 1929–1932 (2016).

[Crossref]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).

[Crossref]

X. Wang, L. Gong, Z. Zhu, B. Gu, and Q. Zhan, “Creation of identical multiple focal spots with three-dimensional arbitrary shifting,” Opt. Express 25(15), 17737–17745 (2017).

[Crossref]

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

[Crossref]

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

[Crossref]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).

[Crossref]

Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

J. Zeng, X. Liu, F. Wang, C. Zhao, and Y. Cai, “Partially coherent fractional vortex beam,” Opt. Express 26(21), 26830–26844 (2018).

[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).

[Crossref]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86(1), 013840 (2012).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

X. Wang, L. Gong, Z. Zhu, B. Gu, and Q. Zhan, “Creation of identical multiple focal spots with three-dimensional arbitrary shifting,” Opt. Express 25(15), 17737–17745 (2017).

[Crossref]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).

[Crossref]

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

[Crossref]

Z. Zhang, H. Fan, H. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).

[Crossref]

L. Hua, B. Chen, Z. Chen, and J. Pu, “Tight focusing of partially coherent, partially polarized vortex beams,” J. Opt. 13(7), 075702 (2011).

[Crossref]

L. Wei and H. Urbach, “Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials,” J. Opt. 18(6), 065608 (2016).

[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).

[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).

[Crossref]

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

[Crossref]

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

[Crossref]

I. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).

[Crossref]

X. Wang, L. Gong, Z. Zhu, B. Gu, and Q. Zhan, “Creation of identical multiple focal spots with three-dimensional arbitrary shifting,” Opt. Express 25(15), 17737–17745 (2017).

[Crossref]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).

[Crossref]

S. Tao, X. C. Yuan, J. Lin, X. Peng, and H. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005).

[Crossref]

J. Zeng, X. Liu, F. Wang, C. Zhao, and Y. Cai, “Partially coherent fractional vortex beam,” Opt. Express 26(21), 26830–26844 (2018).

[Crossref]

J. Wen, L. Wang, X. Yang, J. Zhang, and S. Zhu, “Vortex strength and beam propagation factor of fractional vortex beams,” Opt. Express 27(4), 5893–5904 (2019).

[Crossref]

Z. Mei, Y. Mao, and Y. Wang, “Electromagnetic multi-Gaussian Schell-model vortex light sources and their radiation field properties,” Opt. Express 26(17), 21992–22000 (2018).

[Crossref]

T. G. Jabbour and S. M. Kuebler, “Vectorial beam shaping,” Opt. Express 16(10), 7203–7213 (2008).

[Crossref]

Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).

[Crossref]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).

[Crossref]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010).

[Crossref]

C. Ping, C. Liang, F. Wang, and Y. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).

[Crossref]

H. Xu, Y. Zhou, H. Wu, H. Chen, Z. Sheng, and J. Qu, “Focus shaping of the radially polarized Laguerre- Gaussian-correlated Schell-model vortex beams,” Opt. Express 26(16), 20076–20088 (2018).

[Crossref]

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

[Crossref]

Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).

[Crossref]

L. Rao, J. Pu, Z. Chen, and P. Yei, “Focus shaping of cylindrically polarized vortex beams by a high numerical aperture lens,” Opt. Laser Technol. 41(3), 241–246 (2009).

[Crossref]

L. Guo, Z. Tang, C. Liang, and Z. Tan, “Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams,” Opt. Laser Technol. 43(4), 895–898 (2011).

[Crossref]

Z. Chen, T. Zeng, and J. Ding, “Reverse engineering approach to focus shaping,” Opt. Lett. 41(9), 1929–1932 (2016).

[Crossref]

L. Huang, H. Guo, J. Li, L. Ling, B. Feng, and Z. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012).

[Crossref]

K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).

[Crossref]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).

[Crossref]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).

[Crossref]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378(9), 750–754 (2014).

[Crossref]

Y. Fang, Q. Lu, X. Wang, W. Zhang, and L. Chen, “Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale,” Phys. Rev. A 95(2), 023821 (2017).

[Crossref]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing, and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86(1), 013840 (2012).

[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).

[Crossref]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).

[Crossref]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University).