Fresnel and Fraunhofer diffraction of a Gaussian beam with several polarization singularities
Kovalev A.A., Kotlyar V.V.

 

Image Processing Systems Institute оf RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia

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Abstract:
Alongside phase singularities (optical vortices), there may be light fields with polarization singularities (PS), i.e. isolated intensity nulls with radial, azimuthal, or radial-azimuthal polarization around them. Here, we study Gaussian beams with several arbitrarily located PS. An analytic expression is obtained for their complex amplitude. A partial case is studied when the PS are at the vertices of a regular polygon. If the beam has one or two PS, then these are points with radial polarization. If there are four PS, then two of the points will have azimuthal polarization. It is shown that while propagating in free space, the PS can appear only in a discrete set of planes, in contrast to the phase singularities, which exist in any transverse plane. In the case of two PS, it is shown that their polarization transforms from radial in the initial plane to azimuthal in the far field.

Keywords:
Gaussian beam, polarization singularity, radial polarization, azimuthal polarization.

Citation:
Kovalev AA, Kotlyar VV. Fresnel and Fraunhofer diffraction of a Gaussian beam with several polarization singularities. Computer Optics 2018; 42(2): 179-189. DOI: 10.18287/2412-6179-2018-42-2-179-189.

References:

  1. Dennis MR, O'Holleran K, Padgett MJ. Singular optics: Optical vortices and polarization singularities. Progress in Optics 2009; 53: 293-363. DOI: 10.1016/S0079-6638(08)00205-9.
  2. Tidwell SC, Ford DH, Kimura WD. Generating radially polarized beams interferometrically. Appl Opt 1990; 29(15): 2234-2239. DOI: 10.1364/AO.29.002234.
  3. Oron R, Blit S, Davidson N, Friesem AA. Bomzon Z, Hasman E. The formation of laser beams with pure azimuthal or radial polarization. Appl Phys Lett 2000; 77(21): 3322. DOI: 10.1063/1.1327271.
  4. Flossmann F, Schwarz UT, Maier M, Dennis MR. Polarization singularities from unfolding an optical vortex through a birefringent crystal. Phys Rev Lett 2005; 95(25): 253901. DOI: 10.1103/PhysRevLett.95.253901.
  5. Kozawa Y, Sato S. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt Lett 2005; 30(22): 3063-3065. DOI: 10.1364/OL.30.003063.
  6. Lai WJ, Lim BC, Phua PB, Tiaw KS, Teo HH, Hong MH. Generation of radially polarized beam with a segmented spiral varying retarder. Opt Express 2008; 16(20): 15694-15699. DOI: 10.1364/OE.16.015694.
  7. Zhu S, Chen Y, Wang J, Wang H, Li Z, Cai Y. Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization. Opt Express 2015; 23(26): 33099-33115. DOI: 10.1364/OE.23.033099.
  8. Fu S, Gao C, Shi Y, Dai K, Zhong L, Zhang S. Generating polarization vortices by using helical beams and a Twyman Green interferometer. Opt Lett 2015; 40(8): 1775-1778. DOI: 10.1364/OL.40.001775.
  9. Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv Opt Photon 2009; 1(1): 1-57. DOI: 10.1364/AOP.1.000001.
  10. Fu S, Gao C, Wang T, Zhang S, Zhai Y. Simultaneous generation of multiple perfect polarization vortices with selective spatial states in various diffraction orders. Opt Lett 2016; 41(23): 5454-5457. DOI: 10.1364/OL.41.005454.
  11. Dorn R, Quabis S, Leuchs G. Sharper focus for a radially polarized light beam. Phys Rev Lett 2003; 91(23): 233901. DOI: 10.1103/PhysRevLett.91.233901.
  12. Urbach HP, Pereira SF. Field in focus with a maximum longitudinal electric component. Phys Rev Lett 2008; 100(12): 123904. DOI: 10.1103/PhysRevLett.100.123904.
  13. Segawa S, Kozawa Y, Sato S. Demonstration of subtraction imaging in confocal microscopy with vector beams. Opt Lett 2014; 39(15): 4529-4532. DOI: 10.1364/OL.39.004529.
  14. Yu A, Chen G, Zhang Z, Wen Z, Dai L, Zhang K, Jiang S, Wu Z, Li Y, Wang C, Luo X. Creation of sub-diffraction longitudinally polarized spot by focusing radially polarized light with binary phase lens. Sci Rep 2016; 6: 38859. DOI: 10.1038/srep38859.
  15. Sedukhin AG, Poleshchuk AG. Efficient tight focusing of laser beams optimally matched to their thin-film linear-to-radial polarization conversion: Method, implementation, and field near focus. Opt Commun 2018; 407: 217-226. DOI: 10.1016/j.optcom.2017.09.042.
  16. Tan Q, Xu Q, Xie N, Li C. A new optical voltage sensor based on radial polarization detection. IEEE Transactions on Instrumentation and Measurement 2017; 66(1): 158-164. DOI: 10.1109/TIM.2016.2621198.
  17. Bao Y, Zhu X, Fang Z. Plasmonic toroidal dipolar response under radially polarized excitation. Sci Rep 2015; 5: 11793. DOI: 10.1038/srep11793.
  18. Roy S, Ushakova K, van den Berg Q, Pereira SF, Urbach HP. Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate. Phys Rev Lett 2015; 114(10): 103903. DOI: 10.1103/PhysRevLett.114.103903.
  19. Milione G, Lavery MPJ, Huang H, Ren Y, Xie G, Nguyen TA, Karimi E, Marrucci L, Nolan DA, Alfano RR, Willner AE. 4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer. Opt Lett 2015; 40(9): 1980-1983. DOI: 10.1364/OL.40.001980.
  20. Peng X, Liu L, Yu J, Liu X, Cai Y, Baykal Y, Li W. Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere. J Opt 2016; 18(12): 125601. DOI: 10.1088/2040-8978/18/12/125601.
  21. Tang M, Zhao D. Propagation of radially polarized beams in the oceanic turbulence. Appl Phys B 2013; 111(4): 665-670. DOI: 10.1007/s00340-013-5394-5.
  22. Hao X, Kuang C, Wang T, Liu X. Phase encoding for sharper focus of the azimuthally polarized beam. Opt Lett 2010; 35(23): 3928-3930. DOI: 10.1364/OL.35.003928.
  23. Lew MD, Moerner WE. Azimuthal polarization filtering for accurate, precise, and robust single-molecule localization microscopy. Nano Lett 2014; 14(11): 6407-6413. DOI: 10.1021/nl502914k.
  24. Backlund MP, Arbabi A, Petrov PN, Arbabi E, Saurabh S, Faraon A, Moerner WE. Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask. Nat Photon 2016; 10: 459-462. DOI: 10.1038/nphoton.2016.93.
  25. Carretero L, Acebal P, García C, Blaya S. Periodic trajectories obtained with an active tractor beam using azimuthal polarization: design of particle exchanger. IEEE Photonics Journal 2015; 7(1): 3400112. DOI: 10.1109/JPHOT.2015.2402123.
  26. Yan S, Yao B. Exact description of a cylindrically symmetrical complex-argument Laguerre-Gauss beam. Opt Lett 2008; 33(10): 1074-1076. DOI: 10.1364/OL.33.001074.
  27. Schimpf DN, Putnam WP, Grogan MDW, Ramachandran S, Kärtner FX. Radially polarized Bessel-Gauss beams: decentered Gaussian beam analysis and experimental verification. Opt Express 2013; 21(15): 18469-18483. DOI: 10.1364/OE.21.018469.
  28. Madhi D, Ornigotti M, Aiello A. Cylindrically polarized Bessel–Gauss beams. J Opt 2015; 17(2): 025603. DOI: 10.1088/2040-8978/17/2/025603.
  29. Wu G, Wang F, Cai Y. Generation and self-healing of a radially polarized Bessel-Gauss beam. Phys Rev A 2014; 89(4): 043807. DOI: 10.1103/PhysRevA.89.043807.
  30. Lewis W, Vyas R. Maxwell-Gaussian beams with cylindrical polarization. J Opt Soc Am A 2014; 31(7): 1595-1603. DOI: 10.1364/JOSAA.31.001595.
  31. Ornigotti M, Conti C, Szameit A. Cylindrically polarized nondiffracting optical pulses. J Opt 2016; 18(7): 075605. DOI: 10.1088/2040-8978/18/7/075605.
  32. Bar-David J, Voloch-Bloch N, Mazurski N, Levy U. Unveiling the propagation dynamics of self-accelerating vector beams. Sci Rep 2016; 6: 34272. DOI: 10.1038/srep34272.
  33. Guo J, Wang X, He J, Zhao H, Feng S, Han P, Ye J, Sun W, Situ G, Zhang Y. Generation of radial polarized Lorentz beam with single layer metasurface. Adv Opt Mater 2017; 2017: 1700925.
  34. Vyas S, Kozawa Y, Sato S. Polarization singularities in superposition of vector beams. Opt Express 2013; 21(7): 8972-8986. DOI: 10.1364/OE.21.008972.
  35. He H-S, Chen Z, Dong J. Direct generation of vector vortex beams with switchable radial and azimuthal polarizations in a monolithic Nd:YAG microchip laser. Appl Phys Express 2017; 10(5): 052701. DOI: 10.7567/APEX.10.052701.
  36. Khonina SN, Karpeev SV, Alferov SV, Soifer VA. Generation of cylindrical vector beams of high orders using uniaxial crystals. J Opt 2015; 17(6): 065001. DOI: 10.1088/2040-8978/17/6/065001.
  37. Ferrando A, García-March MA. Analytical solution for multi-singular vortex Gaussian beams: the mathematical theory of scattering modes. J Opt 2016; 18(6): 064006. DOI: 10.1088/2040-8978/18/6/064006.
  38. Abramochkin EG, Volostnikov VG. Modern optics of Gaussian beams [In Russian]. Moscow: “Fizmatlit” Publisher; 2010. ISBN: 978-5-9221-1216-1.
  39. Moreno I, Davis JA, Ruiz I, Cottrell DM. Decomposition of radially and azimuthally polarized beams using a circular-polarization and vortex-sensing diffraction grating. Opt Express 2010; 18(7): 7173-7183. DOI: 10.1364/OE.18.007173.
  40. Bochove EJ, Moore GT, Scully MO. Acceleration of particles by an asymmetric Hermite-Gaussian laser beam. Phys Rev A 1992; 46(10): 6640-6653.
  41. Indebetouw G. Optical vortices and their propagation. J Mod Opt 1993; 40(1): 73-87. DOI: 10.1080/09500349314550101.
  42. Siegman AE. Lasers. Sausalito, California: University Science Books; 1986. ISBN: 978-0-935702-11-8.
  43. Kotlyar VV, Kovalev AA, Soifer VA. Diffraction-free asymmetric elegant Bessel beams with fractional orbital angular momentum. Computer Optics 2014; 38(1): 4-10.
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