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Vector Beams and Vectorial Vortex Beams

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Optical Vortex Beams

Part of the book series: Advances in Optics and Optoelectronics ((AOO))

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Abstract

Vector beams are a new class of beams whose polarization states are anisotropically distributed in transverse. Generally speaking, vector beams can take many forms. In this book, we only consider polarization vortices, which have a transverse inhomogenous polarization distribution and are the characteristic solutions of Maxwell's Eqs. in a cylindrical coordinate. To avoid ambiguity, beams with only polarization vortices, but no phase vortices, are usually called vector beams. Beams with both polarization vortices and phase vortices are called vectorial vortex beams. Vector beams carry no OAM, whereas vectorial vortex beams carry OAM due to their spiral phase structure.

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References

  1. Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv Opt Photon. 2009;1:1–57.

    Article  Google Scholar 

  2. Hall DG. Vector-beam solutions of Maxwell’s wave Eq. Opt Lett 1996;21(1):9–11.

    Google Scholar 

  3. Xin J, Study on the generation of vector beams and their applications. Doctoral dissertation of Beijing Institute of Technology, 2013 (in Chinese).

    Google Scholar 

  4. Tovar AA. Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams. J Opt Soc Am A 1998;15(10):2705–2711.

    Google Scholar 

  5. Xie J, Zhao D, Yan J. Physical optics. Beijing: Beijing Institute of Technology Press; 2012. (in Chinese).

    Google Scholar 

  6. Oron R, Blit S, Davidson N, et al. The formation of laser beams with pure azimuthal or radial polarization. Appl Phys Lett. 2000;77(21):3322–4.

    Article  ADS  Google Scholar 

  7. Naidoo D, Roux FS, Dudley A, et al. Controlled generation of higher-order Poincaré sphere beams from a laser. Nat Photonics. 2016;10:327–32.

    Article  ADS  Google Scholar 

  8. Yonezawa K, Kozawa Y, Sato S. Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal. Opt Lett. 2006;31(14):2151–3.

    Article  ADS  Google Scholar 

  9. Kozawa Y, Yonezawa K, Sato S. Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal. Appl Phys B. 2007;88(1):43–6.

    Article  ADS  Google Scholar 

  10. Machavariani G, Lumer Y, Moshe I, et al. Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes. Appl Opt. 2007;46(16):3304–10.

    Article  ADS  Google Scholar 

  11. Li JL, Ueda K, Zhong LX, et al. Efficient excitations of radially and azimuthally polarized Nd3+:YAG ceramic microchip laser by use of subwavelength multilayer concentric gratings composed of Nb2O5/SiO2. Opt Express. 2008;16(14):10841–8.

    Article  ADS  Google Scholar 

  12. Li JL, Ueda KI, Musha M, et al. Radially polarized and pulsed output from passively Q-switched Nd:YAG ceramic microchip laser. Opt Lett 2008;33(22):2686–2688.

    Google Scholar 

  13. Zhou Z, Tan Q, Li Q, et al. Achromatic generation of radially polarized beams in visible range using segmented subwavelength metal wire gratings. Opt Lett. 2009;34(21):3361–3.

    Article  ADS  Google Scholar 

  14. Xin J, Gao C, Li C. Combination of Hermit-Gaussian beams to arbitery order vector beams. Sci Sin Phys Mech Astron. 2012;10:1017–21 (in Chinese).

    Article  Google Scholar 

  15. Beijersbergen MW, Allen L, van der Veen HELO, et al. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt Commun 1993;96(1–3):123–132.

    Google Scholar 

  16. Wang T, Fu S, Zhang S, et al. A Sagnac-like interferometer for the generation of vector beams. Appl Phys B. 2016;122(9):231.

    Article  ADS  Google Scholar 

  17. Fu S, Gao C, Yang S, et al. Generating polarization vortices by using helical beams and a Twyman Green interferometer. Opt Lett. 2015;40(8):1775–8.

    Article  ADS  Google Scholar 

  18. Gao C, Fu S, Dai K. The method and setup for generating vector beams based on Twyman-Green interferometers. Chinese patent: ZL. 2017; 201510069408.9.

    Google Scholar 

  19. Li L, Huang YF, Wang YT. Applied optics. Beijing: Beijing Institute of Technology Press, 2005.

    Google Scholar 

  20. Xin J, Gao C, Li C, et al. Generation of polarization vortices with a Wollaston prism and an interferometric arrangement. Appl Opt. 2012;51(29):7094–7.

    Article  ADS  Google Scholar 

  21. Moreno I, Davis JA, Cottrell DM, et al. Encoding high-order cylindrically polarized light beams. Appl Opt. 2014;53(24):5493–501.

    Article  ADS  Google Scholar 

  22. Zheng X, Lizana A, Peinado A, et al. Compact LCOS–SLM based polarization pattern beam generator. J Lightwave Technol. 2015;33(10):2047–55.

    Article  ADS  Google Scholar 

  23. Fu S, Wang T, Gao C. Generating perfect polarization vortices through encoding liquid-crystal display devices. Appl Opt 2016;55(23):6501–6505.

    Google Scholar 

  24. Fu S, Zhang S, Gao C. Bessel beams with spatial oscillating polarization. Sci Rep. 2016;6:30765.

    Article  ADS  Google Scholar 

  25. Gao C, Fu S, Zhang S. A setup for the generation of three-dimensional vector beams. Chinese Patent: ZL201610007355.2, 2016-01-06 (in Chinese) .

    Google Scholar 

  26. H. Poincare, Theorie Mathematique de la Lumiere. Paris: Gauthiers-Villars; 1892, Vol. 2.

    Google Scholar 

  27. Milione G, Sztul HI, Nolan DA, et al. Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light. Phys Rev Lett. 2011;107(5): 053601.

    Article  ADS  Google Scholar 

  28. Yi X, Liu Y, Ling X, et al. Hybrid-order Poincare sphere. Phys Rev A. 2015;91: 023801.

    Article  MathSciNet  ADS  Google Scholar 

  29. Ren ZC, Kong LJ, Li SM, et al. Generalized Poincare sphere. Opt Express. 2015;23(20):26585–95.

    Article  ADS  Google Scholar 

  30. Galvez EJ. Light beams with spatially variable polarization[M]// Photonics: scientific foundations, technology and applications, vol. 1. John Wiley & Sons: Inc.; 2015. p. 61–76.

    Google Scholar 

  31. Pancharatnam S. Generalised theory of interference and its applications. Proc Ind Acad Sci Sect A. 1957;45(6):402–11.

    Article  MathSciNet  Google Scholar 

  32. Biener G, Niv A, Kleiner V, et al. Formation of helical beams by use of Pancharatnam-Berry phase optical elements. Opt Lett. 2002;27(21):1875–7.

    Article  ADS  Google Scholar 

  33. Liu Z, Liu Y, Ke Y, et al. Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere. Photon Res. 2017;5(1):15–21.

    Article  Google Scholar 

  34. Fu S, Zhai Y, Wang T, et al. Tailoring arbitrary hybrid Poincaré beams through single hologram. Appl Phys Lett. 2017;111: 211101.

    Article  ADS  Google Scholar 

  35. Fu S, Zhang S, Wang T, et al. Rectilinear lattices of polarization vortices with various spatial polarization distributions. Opt Express. 2016;24(16):18486–91.

    Article  ADS  Google Scholar 

  36. Fu S, Gao C, Wang T, et al. Simultaneous generation of multiple perfect polarization vortices with selective spatial states in various diffraction orders. Opt Lett. 2016;41(23):5454–7.

    Article  ADS  Google Scholar 

  37. Fu S, Wang T, Zhang Z, et al. Selective acquisition of multiple states on hybrid Poincare sphere. Appl Phys Lett. 2017;110: 191102.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Beijing Institute of Technology, Beijing, China

    Shiyao Fu & Chunqing Gao

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  1. Shiyao Fu
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  2. Chunqing Gao
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Correspondence to Shiyao Fu .

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Fu, S., Gao, C. (2023). Vector Beams and Vectorial Vortex Beams. In: Optical Vortex Beams. Advances in Optics and Optoelectronics. Springer, Singapore. https://doi.org/10.1007/978-981-99-1810-2_7

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