Abstract

In this paper, we introduce a new kind of vector multi-Gaussian Schell-model (MGSM) beam named radially polarized MGSM beam as an extension of recently introduced scalar MGSM beam [Opt. Lett. 37, 2970 (2012)], and we obtain the realizability conditions of such beam. The tight focusing properties of a radially polarized MGSM beam passing through a high numerical aperture objective lens are investigated numerically based on the vectorial diffraction theory. It is interesting to find that the intensity distributions of both transverse and longitudinal fields near the focus display flat-top beam profiles due to the special correlation functions of the incident beam. Our results clearly show that engineering the structures of the correlation functions of a radially polarized partially coherent beam provides a novel way for shaping both transverse and longitudinal fields distributions, which have potential applications in particle acceleration and laser machining. Finally, we report experimental generation of a radially polarized MGSM beam with the help of a spatial light modulator and a radial polarization converter.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [Crossref] [PubMed]
  2. Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
    [Crossref] [PubMed]
  3. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [Crossref] [PubMed]
  4. Q. Zhan, “Cylindrical vector beams from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
    [Crossref]
  5. B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
    [Crossref] [PubMed]
  6. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
    [Crossref] [PubMed]
  7. M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210–1215 (2004).
    [Crossref]
  8. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
    [Crossref] [PubMed]
  9. J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
    [Crossref]
  10. Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
    [Crossref]
  11. S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
    [Crossref]
  12. H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
    [Crossref]
  13. Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
    [Crossref] [PubMed]
  14. W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
    [Crossref] [PubMed]
  15. P. Woźniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photonics Rev. 9(2), 231–240 (2015).
    [Crossref]
  16. M. Cai, C. Tu, H. Zhang, S. Qian, K. Lou, Y. Li, and H. T. Wang, “Subwavelength multiple focal spots produced by tight focusing the patterned vector optical fields,” Opt. Express 21(25), 31469–31482 (2013).
    [Crossref] [PubMed]
  17. B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
    [Crossref] [PubMed]
  18. Y. Yu and Q. Zhan, “Generation of uniform three-dimensional optical chain with controllable characteristics,” J. Opt. 17(10), 105606 (2015).
    [Crossref]
  19. 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]
  20. G. H. Yuan, S. B. Wei, and X. C. Yuan, “Non-diffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
    [Crossref] [PubMed]
  21. 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] [PubMed]
  22. Z. Man, C. Min, L. Du, Y. Zhang, S. Zhu, and X. Yuan, “Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes,” Opt. Express 24(2), 874–882 (2016).
    [Crossref] [PubMed]
  23. P. Suresh, C. Mariyal, K. B. Rajesh, T. V. Pillai, and Z. Jaroszewicz, “Generation of a strong uniform transversely polarized nondiffracting beam using a high-numerical-aperture lens axicon with a binary phase mask,” Appl. Opt. 52(4), 849–853 (2013).
    [Crossref] [PubMed]
  24. J. W. Goodman, Statistical optics (Wiley, 1995).
  25. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  26. 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]
  27. Y. Dong, Y. Cai, and C. Zhao, “Degree of polarization of a tightly focused partially coherent dark hollow beam,” Appl. Phys. B 105(2), 405–414 (2011).
    [Crossref]
  28. C. Liang, C. Zhao, C. Zhao, K. Wang, and Y. Cai, “Degree of polarization of a tightly focused, partially coherent anomalous hollow beam,” J. Opt. Soc. Am. A 31(12), 2753–2758 (2014).
    [Crossref] [PubMed]
  29. 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]
  30. 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]
  31. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
    [Crossref] [PubMed]
  32. F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. 11(8), 085706 (2009).
  33. R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34(9), 1399–1401 (2009).
    [Crossref] [PubMed]
  34. Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
    [Crossref]
  35. Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
    [Crossref] [PubMed]
  36. D. P. Brown and T. G. Brown, “Partially correlated azimuthal vortex illumination: coherence and correlation measurements and effects in imaging,” Opt. Express 16(25), 20418–20426 (2008).
    [Crossref] [PubMed]
  37. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
    [Crossref] [PubMed]
  38. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
    [Crossref] [PubMed]
  39. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
    [Crossref] [PubMed]
  40. L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
    [Crossref] [PubMed]
  41. L. Ma and S. A. Ponomarenko, “Free-space propagation of optical coherence lattices and periodicity reciprocity,” Opt. Express 23(2), 1848–1856 (2015).
    [Crossref] [PubMed]
  42. Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
    [Crossref]
  43. F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
    [Crossref] [PubMed]
  44. S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, “Experimental generation of ring-shaped beams with random sources,” Opt. Lett. 38(21), 4441–4444 (2013).
    [Crossref] [PubMed]
  45. Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
    [Crossref] [PubMed]
  46. Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
    [Crossref]
  47. M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
    [Crossref]
  48. M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, “Synthesis of non-uniformly correlated partially coherent sources using a deformable mirror,” Appl. Phys. Lett. 111(10), 101106 (2017).
    [Crossref]
  49. F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24(21), 23735–23746 (2016).
    [Crossref] [PubMed]
  50. C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
    [Crossref]
  51. X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
    [Crossref]
  52. Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
    [Crossref]
  53. O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).
  54. S. Avramov-Zamurovic, C. Nelson, S. Guth, and O. Korotkova, “Flatness parameter influence on scintillation reduction for multi-Gaussian Schell-model beams propagating in turbulent air,” Appl. Opt. 55(13), 3442–3446 (2016).
    [Crossref] [PubMed]
  55. C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
    [Crossref]
  56. Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
    [Crossref]
  57. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  58. F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
    [Crossref] [PubMed]
  59. G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20(27), 28301–28318 (2012).
    [Crossref] [PubMed]
  60. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1–3), 35–43 (2005).
    [Crossref]
  61. J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
    [Crossref] [PubMed]
  62. http://www.arcoptix.com/radial_polarization_converter.htm

2017 (4)

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, “Synthesis of non-uniformly correlated partially coherent sources using a deformable mirror,” Appl. Phys. Lett. 111(10), 101106 (2017).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

2016 (5)

2015 (6)

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

P. Woźniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photonics Rev. 9(2), 231–240 (2015).
[Crossref]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

L. Ma and S. A. Ponomarenko, “Free-space propagation of optical coherence lattices and periodicity reciprocity,” Opt. Express 23(2), 1848–1856 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (8)

P. Suresh, C. Mariyal, K. B. Rajesh, T. V. Pillai, and Z. Jaroszewicz, “Generation of a strong uniform transversely polarized nondiffracting beam using a high-numerical-aperture lens axicon with a binary phase mask,” Appl. Opt. 52(4), 849–853 (2013).
[Crossref] [PubMed]

M. Cai, C. Tu, H. Zhang, S. Qian, K. Lou, Y. Li, and H. T. Wang, “Subwavelength multiple focal spots produced by tight focusing the patterned vector optical fields,” Opt. Express 21(25), 31469–31482 (2013).
[Crossref] [PubMed]

B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, “Experimental generation of ring-shaped beams with random sources,” Opt. Lett. 38(21), 4441–4444 (2013).
[Crossref] [PubMed]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

2012 (7)

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20(27), 28301–28318 (2012).
[Crossref] [PubMed]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

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

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

J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
[Crossref]

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (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]

2011 (4)

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. Dong, Y. Cai, and C. Zhao, “Degree of polarization of a tightly focused partially coherent dark hollow beam,” Appl. Phys. B 105(2), 405–414 (2011).
[Crossref]

G. H. Yuan, S. B. Wei, and X. C. Yuan, “Non-diffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[Crossref] [PubMed]

2010 (3)

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] [PubMed]

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
[Crossref]

2009 (3)

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

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

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34(9), 1399–1401 (2009).
[Crossref] [PubMed]

2008 (4)

2007 (1)

2005 (1)

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1–3), 35–43 (2005).
[Crossref]

2004 (2)

2003 (2)

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

J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

2000 (2)

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

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Avramov-Zamurovic, S.

C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, S. Guth, and O. Korotkova, “Flatness parameter influence on scintillation reduction for multi-Gaussian Schell-model beams propagating in turbulent air,” Appl. Opt. 55(13), 3442–3446 (2016).
[Crossref] [PubMed]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Banzer, P.

P. Woźniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photonics Rev. 9(2), 231–240 (2015).
[Crossref]

Basu, S.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Baykal, Y.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Borghi, R.

Bose-Pillai, S. R.

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, “Synthesis of non-uniformly correlated partially coherent sources using a deformable mirror,” Appl. Phys. Lett. 111(10), 101106 (2017).
[Crossref]

Brown, D. P.

Brown, T.

Brown, T. G.

D. P. Brown and T. G. Brown, “Partially correlated azimuthal vortex illumination: coherence and correlation measurements and effects in imaging,” Opt. Express 16(25), 20418–20426 (2008).
[Crossref] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Cai, M.

Cai, Y.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
[Crossref]

F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24(21), 23735–23746 (2016).
[Crossref] [PubMed]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

C. Liang, C. Zhao, C. Zhao, K. Wang, and Y. Cai, “Degree of polarization of a tightly focused, partially coherent anomalous hollow beam,” J. Opt. Soc. Am. A 31(12), 2753–2758 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (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]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20(27), 28301–28318 (2012).
[Crossref] [PubMed]

Y. Dong, Y. Cai, and C. Zhao, “Degree of polarization of a tightly focused partially coherent dark hollow beam,” Appl. Phys. B 105(2), 405–414 (2011).
[Crossref]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
[Crossref] [PubMed]

Chen, Y.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
[Crossref]

F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24(21), 23735–23746 (2016).
[Crossref] [PubMed]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Chong, C.

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]

Cui, Y.

Dong, Y.

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]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

Y. Dong, Y. Cai, and C. Zhao, “Degree of polarization of a tightly focused partially coherent dark hollow beam,” Appl. Phys. B 105(2), 405–414 (2011).
[Crossref]

Dorn, R.

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

Du, L.

Eyyuboglu, H. T.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
[Crossref] [PubMed]

Fan, H.

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]

Fourmaux, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Friberg, A.

Galow, B. J.

J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
[Crossref]

Gbur, G.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

Gori, F.

Gu, B.

Gu, J.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Gu, M.

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

Gu, Y.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

Guo, L.

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]

Guth, S.

C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, S. Guth, and O. Korotkova, “Flatness parameter influence on scintillation reduction for multi-Gaussian Schell-model beams propagating in turbulent air,” Appl. Opt. 55(13), 3442–3446 (2016).
[Crossref] [PubMed]

Han, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

He, H.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Hecht, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Huang, K.

Huang, W.

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]

Hyde, M. W.

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, “Synthesis of non-uniformly correlated partially coherent sources using a deformable mirror,” Appl. Phys. Lett. 111(10), 101106 (2017).
[Crossref]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Jaroszewicz, Z.

Jia, B.

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

Kang, H.

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

Kang, X. L.

Keitel, C.

J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
[Crossref]

Kieffer, J. C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Korotkova, O.

C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, S. Guth, and O. Korotkova, “Flatness parameter influence on scintillation reduction for multi-Gaussian Schell-model beams propagating in turbulent air,” Appl. Opt. 55(13), 3442–3446 (2016).
[Crossref] [PubMed]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

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

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

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1–3), 35–43 (2005).
[Crossref]

Kumar, A.

Lajunen, H.

Légaré, F.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Leger, J.

Leuchs, G.

P. Woźniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photonics Rev. 9(2), 231–240 (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] [PubMed]

Li, J.

J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
[Crossref]

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

Li, Y.

Li, Y. P.

Liang, C.

C. Liang, C. Zhao, C. Zhao, K. Wang, and Y. Cai, “Degree of polarization of a tightly focused, partially coherent anomalous hollow beam,” J. Opt. Soc. Am. A 31(12), 2753–2758 (2014).
[Crossref] [PubMed]

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]

Lieb, M. A.

Lin, Q.

Liu, L.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Liu, X.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24(21), 23735–23746 (2016).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Lou, K.

Lukyanchuk, B.

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]

Ma, L.

MacLean, J. P.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Malek-Madani, R.

C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
[Crossref]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Man, Z.

Mariyal, C.

Martínez-Herrero, R.

Mei, T.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Mei, Z.

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

Mejías, P. M.

Min, C.

Morrish, D.

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

Nelson, C.

C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
[Crossref]

S. Avramov-Zamurovic, C. Nelson, S. Guth, and O. Korotkova, “Flatness parameter influence on scintillation reduction for multi-Gaussian Schell-model beams propagating in turbulent air,” Appl. Opt. 55(13), 3442–3446 (2016).
[Crossref] [PubMed]

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Novotny, L.

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210–1215 (2004).
[Crossref]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Pan, Y.

Payeur, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Peng, X.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Piché, M.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Pillai, T. V.

Ponomarenko, S. A.

Prabhakar, S.

Premaratne, M.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Qian, S.

Qu, J.

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. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Quabis, S.

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

Rajesh, K. B.

Ramírez-Sánchez, V.

Reddy, S. G.

Saastamoinen, T.

Sahin, S.

Salamin, Y.

J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
[Crossref]

Salamin, Y. I.

Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
[Crossref]

Sanchez, V. R.

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

Santarsiero, M.

Schmidt, B. E.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Setälä, T.

Shang, W.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Shchepakina, E.

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

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

Sheppard, C.

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]

Shi, L.

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]

Shi, P.

Shirai, T.

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

Sick, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Singh, R. P.

Suresh, P.

Tan, Z.

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]

Tang, Z.

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]

Tchervenkov, C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Tervo, J.

Tu, C.

Voelz, D. G.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Wang, F.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24(21), 23735–23746 (2016).
[Crossref] [PubMed]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (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]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20(27), 28301–28318 (2012).
[Crossref] [PubMed]

Wang, H.

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]

Wang, H. T.

Wang, K.

Wei, S. B.

Wolf, E.

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1–3), 35–43 (2005).
[Crossref]

Wood, R. A.

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, “Synthesis of non-uniformly correlated partially coherent sources using a deformable mirror,” Appl. Phys. Lett. 111(10), 101106 (2017).
[Crossref]

Wozniak, P.

P. Woźniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photonics Rev. 9(2), 231–240 (2015).
[Crossref]

Wu, G.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20(27), 28301–28318 (2012).
[Crossref] [PubMed]

Wu, J. L.

Xiao, F.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Xiao, X.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Xu, H.

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]

Youngworth, K.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Yu, J.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Yu, Y.

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

Yuan, G. H.

Yuan, X.

Yuan, X. C.

Yuan, Y.

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Zavislan, J. M.

Zhan, Q.

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

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

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

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

Zhang, H.

Zhang, X.

Zhang, Y.

Zhang, Z.

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]

Zhao, C.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

C. Liang, C. Zhao, C. Zhao, K. Wang, and Y. Cai, “Degree of polarization of a tightly focused, partially coherent anomalous hollow beam,” J. Opt. Soc. Am. A 31(12), 2753–2758 (2014).
[Crossref] [PubMed]

C. Liang, C. Zhao, C. Zhao, K. Wang, and Y. Cai, “Degree of polarization of a tightly focused, partially coherent anomalous hollow beam,” J. Opt. Soc. Am. A 31(12), 2753–2758 (2014).
[Crossref] [PubMed]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (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]

Y. Dong, Y. Cai, and C. Zhao, “Degree of polarization of a tightly focused partially coherent dark hollow beam,” Appl. Phys. B 105(2), 405–414 (2011).
[Crossref]

Zhao, J.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Zhu, S.

Zhu, W.

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

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

Appl. Opt. (2)

Appl. Phys. B (1)

Y. Dong, Y. Cai, and C. Zhao, “Degree of polarization of a tightly focused partially coherent dark hollow beam,” Appl. Phys. B 105(2), 405–414 (2011).
[Crossref]

Appl. Phys. Lett. (6)

S. Payeur, S. Fourmaux, B. E. Schmidt, J. P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. C. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, “Enhanced photothermal therapy assisted with gold nanorods using a radially polarized beam,” Appl. Phys. Lett. 96(6), 063702 (2010).
[Crossref]

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, “Synthesis of non-uniformly correlated partially coherent sources using a deformable mirror,” Appl. Phys. Lett. 111(10), 101106 (2017).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
[Crossref]

J. Appl. Phys. (1)

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

J. Opt. (4)

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[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. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. 11(8), 085706 (2009).

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

J. Opt. Soc. Am. A (4)

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

Laser Photonics Rev. (1)

P. Woźniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photonics Rev. 9(2), 231–240 (2015).
[Crossref]

Nat. Photonics (1)

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]

Opt. Commun. (3)

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1–3), 35–43 (2005).
[Crossref]

C. Nelson, S. Avramov-Zamurovic, O. Korotkova, S. Guth, and R. Malek-Madani, “Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime,” Opt. Commun. 364, 145–149 (2016).
[Crossref]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[Crossref]

Opt. Express (12)

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

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

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

J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
[Crossref] [PubMed]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
[Crossref] [PubMed]

D. P. Brown and T. G. Brown, “Partially correlated azimuthal vortex illumination: coherence and correlation measurements and effects in imaging,” Opt. Express 16(25), 20418–20426 (2008).
[Crossref] [PubMed]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20(27), 28301–28318 (2012).
[Crossref] [PubMed]

B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
[Crossref] [PubMed]

M. Cai, C. Tu, H. Zhang, S. Qian, K. Lou, Y. Li, and H. T. Wang, “Subwavelength multiple focal spots produced by tight focusing the patterned vector optical fields,” Opt. Express 21(25), 31469–31482 (2013).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Free-space propagation of optical coherence lattices and periodicity reciprocity,” Opt. Express 23(2), 1848–1856 (2015).
[Crossref] [PubMed]

Z. Man, C. Min, L. Du, Y. Zhang, S. Zhu, and X. Yuan, “Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes,” Opt. Express 24(2), 874–882 (2016).
[Crossref] [PubMed]

F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24(21), 23735–23746 (2016).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

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]

Opt. Lett. (10)

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
[Crossref] [PubMed]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38(9), 1395–1397 (2013).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

S. G. Reddy, A. Kumar, S. Prabhakar, and R. P. Singh, “Experimental generation of ring-shaped beams with random sources,” Opt. Lett. 38(21), 4441–4444 (2013).
[Crossref] [PubMed]

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34(9), 1399–1401 (2009).
[Crossref] [PubMed]

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] [PubMed]

G. H. Yuan, S. B. Wei, and X. C. Yuan, “Non-diffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[Crossref] [PubMed]

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

Phys. Rev. A (4)

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[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]

J. Li, Y. Salamin, B. J. Galow, and C. Keitel, “Acceleration of proton bunches by petawatt chirped radially polarized laser pulses,” Phys. Rev. A 85(6), 063832 (2012).
[Crossref]

Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
[Crossref]

Phys. Rev. Lett. (3)

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

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

Proc. SPIE (1)

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, R. Malek-Madani, Y. Gu, and G. Gbur, “Scintillation reduction in multi-Gaussian Schell-model beams propagating in atmospheric turbulence,” Proc. SPIE 9224, 92240M (2014).

Prog. Opt. (1)

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Sci. Rep. (1)

W. Shang, F. Xiao, W. Zhu, H. He, M. Premaratne, T. Mei, and J. Zhao, “Fano resonance with high local field enhancement under azimuthally polarized excitation,” Sci. Rep. 7(1), 1049 (2017).
[Crossref] [PubMed]

Other (4)

J. W. Goodman, Statistical optics (Wiley, 1995).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

http://www.arcoptix.com/radial_polarization_converter.htm

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (8)

Fig. 1
Fig. 1 Scheme of tight focusing of a light beam focused by a high NA objective lens.
Fig. 2
Fig. 2 Contour graphs of the total intensity Itotal, transverse intensity Itra and longitudinal intensity Iz of a tightly focused radially polarized MGSM beam in the focal plane for different values of beam index M. The white solid line denotes the cross line of the intensity distribution at ρy = 0.
Fig. 3
Fig. 3 Contour graphs of the total intensity Itotal, transverse intensity Itra and longitudinal intensity Iz of a tightly focused radially polarized MGSM beam in the focal plane for different values of coherence width δ0. The white solid line denotes the cross line of the intensity distribution at ρy = 0.
Fig. 4
Fig. 4 Contour graph of the longitudinal intensity Iz of the focused radial polarized MGSM beam in x-z plane for different values of M and δ0 [see (a)-(c) and (g)-(i)]. The cross lines of the longitudinal intensity at y = 0 at z = 0 (black solid curve), z = 0.5λ (red dashed curve) and z = λ (blue dash-doted curve) are shown in (d)-(f) and (j)-(l).
Fig. 5
Fig. 5 Experimental setup for generating a radially polarized MGSM beam and measuring its intensity distribution and squared modulus of the degree of coherence. BE: beam expander; SLM: spatial light modulator; BS: intensity beam splitter; L1 and L2, thin lenses; CA: circular aperture; HWP: half-wave plate; RPC: radial polarization converter; CCD: charge-coupled device.
Fig. 6
Fig. 6 Experimental results of (a) the intensity distribution of the generated radially polarized MGSM beam with M = 10 just after the RPC, and (b)-(d) the corresponding intensity distribution of the generated beam after passing through a linear polarizer. The white arrows denote the transmission axis of the polarizer.
Fig. 7
Fig. 7 Experimental result of the squared modulus of the degree of coherence | μ( r 1 - r 2 ) | 2 of the generated radially polarized MGSM beam with (a) M = 1 and (b) M = 10 just after the RPC.
Fig. 8
Fig. 8 Experimental result of the intensity distribution of the generated radially polarized MGSM beam focused by a thin lens with focal length f = 15cm in the focal plane with (a) M = 1 and (b) M = 10.

Equations (36)

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W αβ ( r 1 , r 2 ,ω,0 )= E α * ( r 1 ,ω,0 ) E β ( r 2 ,ω,0 ) ,( α,β= x,y ),
W αβ ( r 1 , r 2 ,0 )= S αα ( r 1 ,0 ) S ββ ( r 2 ,0 ) μ αβ ( r 1 r 2 ),( α,β=x,y ),
W αβ ( r 1 , r 2 ,0 )= α 1 β 2 exp( r 1 2 + r 2 2 4 w 0 2 ) μ αβ ( r 1 r 2 ),( α,β=x,y ),
μ αβ ( r 1 r 2 ) =B αβ 1 C 0 m=1 M ( M m ) ( 1 ) m1 m exp[ ( r 1 r 2 ) 2 2m δ αβ 2 ],
B xx = B yy =1, B xy = B yx * , δ xy = δ yx .
W αβ ( r 1 , r 2 ,0 )= p αβ ( v ) H α ( r 1 ,v ) H β ( r 2 ,v ) d 2 v,(α,β=x,y),
p ( v )=( p xx ( v ) p xy ( v ) p yx ( v ) p yy ( v ) ).
p xx ( v )0, p yy ( v )0, p xx ( v ) p yy ( v ) | p xy ( v ) | 2 0.
H α ( r,v )=αexp( r 2 4 w 0 2 )exp( ivr ), (α=x,y),
p αβ (v)= B αβ δ αβ 2 C 0 × m=1 M ( M m ) ( 1 ) m1 exp( m δ αβ 2 v 2 2 ).
p αβ (v)= B αβ δ αβ 2 C 0 ×{ 1 [ 1exp( δ αβ 2 v 2 /2 ) ] M }.
δ xx 2 δ yy 2 ×{ 1 [ 1exp( δ xx 2 v 2 /2 ) ] M }×{ 1 [ 1exp( δ yy 2 v 2 /2 ) ] M }. | B xy | 2 δ xy 4 × { 1 [ 1exp( δ xy 2 v 2 /2 ) ] M } 2
δ xy δ xx δ yy | B xy | ,
Min{ 1 [ 1exp( δ xx 2 v 2 /2 ) ] M ,1 [ 1exp( δ yy 2 v 2 /2 ) ] M }, 1 [ 1exp( δ xy 2 v 2 /2 ) ] M
δ xy Max{ δ xx , δ yy }.
Max{ δ xx , δ yy } δ xy δ xx δ yy | B xy | .
δ xx 2 + δ yy 2 2 δ xy δ xx δ yy | B xy | .
θ( r,0 )= 1 2 arctan[ 2Re[ W xy ( r,r,0 ) ] W xx ( r,r,0 ) W yy ( r,r,0 ) ],
ε( r,0 )= A ( r,0 )/ A + ( r,0 ) ,( 0ε1 ),
A ± ( r )= 1 2 [ [ W xx ( r,r,0 ) W yy ( r,r,0 ) ] 2 +4 | W xy ( r,r,0 ) | 2 ± [ W xx ( r,r,0 ) W yy ( r,r,0 ) ] 2 +4 ( Re[ W xy ( r,r,0 ) ] ) 2 ].
tan2θ( r,0 )=Re[ B xy ] 2y/x 1 y 2 / x 2 ,
A ( r,0 )= 1 2 [ ( x 2 y 2 ) 2 +4 | B xy | 2 x 2 y 2 ( x 2 y 2 ) 2 +4Re [ B xy ] 2 x 2 y 2 ],
Re[ B xy ]=1, | B xy |=1.
B xy(yx) = B xx = B yy =1, δ xy(yx) = δ xx = δ yy = δ 0 .
μ 2 ( r 1 r 2 )= α,β | W αβ ( r 1 , r 2 ,0 ) | 2 α,β W αα ( r 1 , r 1 ,0 ) W ββ ( r 2 , r 2 ,0 ) .
μ 2 ( r 1 r 2 )= μ αβ 2 ( r 1 r 2 ), ( α,β=x,y ).
E f ( r,φ,z )=( E fx E fy E fz )= i k 1 f 2π 0 2π dϕ 0 α sinθ cos 1 2 θexp( i k 1 ζ ){ l x (θ,ϕ)[cosθ+sinϕ(1cosθ)]+ l y (θ,ϕ)cosϕsinϕ(cosθ1) l x (θ,ϕ)cosϕsinϕ(cosθ1)+ l y (θ,ϕ)[cosθ+ cos 2 ϕ(1cosθ)] l x (θ,ϕ)cosϕsinθ l y (θ,ϕ)sinϕsinθ }dθ,
W fαβ ( r 1 , φ 1 , r 2 , φ 2 ,z )= E fα * ( r 1 , φ 1 ,z) E fβ ( r 2 , φ 2 ,z) ,(α,β=x,y,z).
W fxx ( r 1 , φ 1 , r 2 , φ 2 ,z)= f 2 n 1 λ 2 0 θ max 0 θ max 0 2π 0 2π d θ 1 d θ 2 d ϕ 1 d ϕ 2 W 0 ( θ 1 , ϕ 1 , θ 2 , ϕ 2 ) , ×exp[ i k 1 ( ζ 2 ζ 1 ) ] cos 3/2 θ 1 cos 3/2 θ 2 sin 2 θ 1 sin 2 θ 2 cos ϕ 1 cos ϕ 2
W fyy ( r 1 , φ 1 , r 2 , φ 2 ,z)= f 2 n 1 λ 2 0 θ max 0 θ max 0 2π 0 2π d θ 1 d θ 2 d ϕ 1 d ϕ 2 W 0 ( θ 1 , ϕ 1 , θ 2 , ϕ 2 ) , ×exp[ i k 1 ( ζ 2 ζ 1 ) ] cos 3/2 θ 1 cos 3/2 θ 2 sin 2 θ 1 sin 2 θ 2 sin ϕ 1 sin ϕ 2
W fzz ( r 1 , φ 1 , r 2 , φ 2 ,z)= f 2 n 1 λ 2 0 θ max d θ 1 0 θ max d θ 2 0 2π d ϕ 1 0 2π d ϕ 2 W 0 ( θ 1 , ϕ 1 , θ 2 , ϕ 2 ) , ×exp[ i k 1 ( ζ 2 ζ 1 ) ] cos 1/2 θ 1 cos 1/2 θ 2 sin 3 θ 1 sin 3 θ 2
ζ i =zcos θ i + r i sin θ i cos( ϕ i φ i ),(i=1,2),
W 0 ( θ 1 , ϕ 1 , θ 2 , ϕ 2 )= f 2 C 0 exp[ f 2 sin 2 θ 1 + sin 2 θ 2 4 ω 0 2 ] m=1 M ( M m ) (1) m1 m . ×exp[ f 2 sin 2 θ 1 + sin 2 θ 2 2m δ 0 2 ]exp( f 2 sin θ 1 sin θ 2 cos( ϕ 1 ϕ 2 ) m δ 0 2 )
I tra (r,φ,z)= W fxx (r,φ,r,φ,z)+ W fyy (r,φ,r,φ,z),
I z (r,φ,z)= W fzz (r,φ,r,φ,z),
I total ( r,φ,z )= I tra ( r,φ,z )+ I z ( r,φ,z )

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