(46-4) 04 * << * >> * Russian * English * Content * All Issues

Peculiarities of focusing circularly and radially polarized super-Gaussian beams using ring gratings with varying relief height
D.A. Savelyev 1,2

1 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34;
2 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151

 PDF, 3096 kB

DOI: 10.18287/2412-6179-CO-1131

Pages: 537-546.

Full text of article: Russian language.

Abstract:
The focusing features of a super-Gaussian beam, as well as Laguerre-super-Gaussian (1,0) modes with radial and circular polarizations on ring gratings (direct and inverse) with a variable height of individual relief rings were investigated in this paper. The change in the height of the relief from the maximum height in the center to the minimum at the edges of the element (direct ring grating) is considered and the reverse case, when the maximum height of the relief was at the edges and the minimum in the center (reverse ring grating). The comparison was carried out with the action of a diffractive axicon with a comparable grating period. Numerical simulation was carried out by the finite differences in the time domain method. It was shown that the direction of change in the height of the relief rings of elements significantly affects the diffraction pattern in the near zone. In particular, for a super-Gaussian beam, the use of a direct ring grating made it possible to reduce the size of the focal spot by 18.7% for radial polarization ('sigma'=5 μm), the use of a reverse ring grating led to a decrease in the focal spot by 36.9% ('sigma'=12.25 µm) in comparison with the action of a diffractive axicon. It was also shown in the paper that when the reverse ring grating is illuminated by the Laguerre-superGauss (1,0) mode with circular polarization, the formation of a narrow and extended region of reduced intensity on the optical axis (optical trap) is observed.

Keywords:
ring gratings, super-Gaussian beam, Laguerre-super-Gaussian (1,0) modes, sharp focusing, FDTD, diffractive axicon, optical trap.

Citation:
Savelyev DA. Peculiarities of focusing circularly and radially polarized super-Gaussian beams using ring gratings with varying relief height. Computer Optics 2022; 46(4): 537-546. DOI: 10.18287/2412-6179-CO-1131.

Acknowledgements:
The work was supported by the RF Ministry of Science and Higher Education within government project no. 0777-2020-0017 (Section "Introduction") and the Russian Science Foundation under project no. 20-72-00051 (the other sections).

References:
  1. Kotlyar VV, Kovalev AA. Topological charge of optical vortices devoid of radial symmetry. Computer Optics 2020; 44(4): 510-518. DOI: 10.18287/2412-6179-CO-719.
  2. Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv Opt Photonics 2009; 1: 1-57. DOI: 10.1364/AOP.1.000001.
  3. Volotovskiy SG, Karpeev SV, Khonina SN. Algorithm for reconstructing complex coefficients of Laguerre–Gaussian modes from the intensity distribution of their coherent superposition. Computer Optics 2020; 44(3): 352-362. DOI: 10.18287/2412-6179-CO-727.
  4. Savelyev DA, Khonina SN, Golub I. Tight focusing of higher orders Laguerre-Gaussian modes. AIP Conf Proc 2016; 1724: 020021. DOI: 10.1063/1.4945141.
  5. Hamazaki J, Morita R, Chujo K, Kobayashi Y, Tanda S, Omatsu T. Optical-vortex laser ablation. Opt Express 2010; 18(3): 2144-2151. DOI: 10.1364/OE.18.002144.
  6. Mourka A, Baumgartl J, Shanor C, Dholakia K, Wright EM. Visualization of the birth of an optical vortex using diffraction from a triangular aperture. Opt Express 2011; 19(7): 5760-5771. DOI: 10.1364/OE.19.005760.
  7. Tkachenko G, Chen M, Dholakia K, Mazilu M. Is it possible to create a perfect fractional vortex beam? Optica 2017; 4(3): 330-333. DOI: 10.1364/OPTICA.4.000330.
  8. Khonina SN, Porfirev AP. Harnessing of inhomogeneously polarized Hermite–Gaussian vector beams to manage the 3D spin angular momentum density distribution. Nanophotonics 2021; 11(4): 0418. DOI: 10.1515/nanoph-2021-0418.
  9. LiS, Pan X, Ren Y, Liu H, Yu S, Jing J. Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement. Phys Rev Lett 2020; 124(8): 083605. DOI: 10.1103/PhysRevLett.124.083605.
  10. Ma X, Pu M, Li X, Huang C, Wang Y, Pan W,Zhao B, Cui J, Wang Ch, Zhao Z, Luo X. A planar chiral meta-surface for optical vortex generation and focusing. Sci Rep 2015; 5(1): 10365. DOI: 10.1038/srep10365.
  11. Pryamikov A, Alagashev G, Falkovich G, Turitsyn S. Light transport and vortex-suppoted wave-guiding in micro-structured optical fibers. Sci Rep 2020; 10(1): 2507. DOI: 10.1038/s41598-020-59508-z.
  12. Khonina SN, Alferov SV, Karpeev SV. Strengthening the longitudinal component of the sharply focused electric field by means of higher-order laser beams. Opt Lett 2013; 38(17): 3223-3226. DOI: 10.1364/OL.38.003223.
  13. Savelyev DA, Khonina SN. Characteristics of sharp focusing of vortex Laguerre-Gaussian beams. Computer Optics 2015; 39(5): 654-662. DOI: 10.18287/0134-2452-2015-39-5-654-662.
  14. Zhu L, Wang J. A review of multiple optical vortices generation: methods and applications. Front Optoelectron 2019; 12(1): 52-68. DOI: 10.1007/s12200-019-0910-9.
  15. Khonina SN. Vortex beams with high-order cylindrical polarization: features of focal distributions. Appl Phys B 2019; 125: 100. DOI: 10.1007/s00340-019-7212-1.
  16. Khonina SN, Porfirev AP, Kazanskiy NL. Variable transformation of singular cylindrical vector beams using anisotropic crystals. Sci Rep 2020; 10: 5590. DOI: 10.1038/s41598-020-62546-2.
  17. Khonina SN, Golub I. Engineering the smallest 3D symmetrical bright and dark focal spots. J Opt Soc Am A 2013; 30(10): 2029-2033. DOI: 10.1364/JOSAA.30.002029.
  18. Savelyev DA. The investigation of focusing of cylindrically polarized beams with the variable height of optical elements using high-performance computer systems. Proc SPIE 2021; 11793: 117930X. DOI: 10.1117/12.2591993.
  19. 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.
  20. Fu S, Gao C, Wang T, Zhai Y, Yin C. Anisotropic polarization modulation for the production of arbitrary Poincaré beams. J Opt Soc Am B 2018; 35(1): 1-7. DOI: 10.1364/JOSAB.35.000001.
  21. Fadeyeva T, Shvedov V, Shostka N, Alexeyev C, Volyar A. Natural shaping of the cylindrically polarized beams. Opt Lett 2010; 35(22): 3787-3789. DOI: 10.1364/OL.35.003787.
  22. Khonina SN, Karpeev SV, Paranin VD, Morozov AA. Polarization conversion under focusing of vortex laser beams along the axis of anisotropic crystals. Phys Lett A 2017: 381(30): 2444-2455. DOI: 10.1016/j.physleta.2017.05.025.
  23. Savelyev D. The investigation of the cylindrically polarized beams focusing by a diffractive axicon using high-performance computer systems. 2020 Int Conf on Information Technology and Nanotechnology (ITNT) 2020: 1-5. DOI: 10.1109/ITNT49337.2020.9253243.
  24. Wang H, Shi L, Lukyanchuk B, Sheppard C, Chong CT. Creation of a needle of longitudinally polarized light in vacuum using binary optics. Nat Photonics 2008; 2(8): 501-505. DOI: 10.1038/nphoton.2008.127.
  25. Kozawa Y, Sato S. Sharper focal spot formed by higher-order radially polarized laser beams. J Opt Soc Am A 2007; 24(6): 1793-1798. DOI: 10.1364/JOSAA.24.001793.
  26. Sheppard CJ, Choudhury A. Annular pupils, radial polarization, and superresolution. Appl Opt 2004; 43(22): 4322-4327. DOI: 10.1364/AO.43.004322.
  27. Kotlyar VV, Stafeev SS. Modeling the sharp focus of a radially polarized laser mode using a conical and a binary microaxicon. J Opt Soc Am B 2010; 27(10): 1991-1997. DOI: 10.1364/JOSAB.27.001991.
  28. Khonina SN, Degtyarev SA. A longitudinally polarized beam generated by a binary axicon. J Russ Laser Res 2015; 36(2): 151-161. DOI: 10.1007/s10946-015-9488-x.
  29. Lerman GM, Levy U. Effect of radial polarization and apodization on spot size under tight focusing conditions. Opt Express 2008; 16(7): 4567-4581. DOI: 10.1364/OE.16.004567.
  30. 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.
  31. Khonina SN, Volotovsky SG. Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures. J Opt Soc Am A 2010; 27(10): 2188-2197. DOI: 10.1364/JOSAA.27.002188.
  32. Pereira SF, Van de Nes AS. Superresolution by means of polarisation, phase and amplitude pupil masks. Opt Commun 2004; 234(1-6): 119-124. DOI: 10.1016/j.optcom.2004.02.020.
  33. Chen Z, Hua L, Pu J. Tight focusing of light beams: effect of polarization, phase, and coherence. In Book: Wolf E, ed. Progress in Optics. Ch 4. Oxford: Elsevier; 2012: 219-260. DOI: 10.1016/B978-0-44-459422-8.00004-7.
  34. McLeod JH. The axicon: a new type of optical element. J Opt Soc Am 1954; 44(8): 592-597. DOI: 10.1364/JOSA.44.000592.
  35. Golub I, Chebbi B, Shaw D, Nowacki D. Characterization of a refractive logarithmic axicon. Opt Lett 2010; 35(16): 2828-2830. DOI: 10.1364/OL.35.002828.
  36. Savelyev DA. The sub-wavelength complex micro-axicons for focal spot size reducing using high-performance computer systems. Proc SPIE 2021; 11769: 1176918. DOI: 10.1117/12.2589220.
  37. Chi W, George N. Electronic imaging using a logarithmic asphere. Opt Lett 2001; 26(12): 875-877. DOI: 10.1364/OL.26.000875.
  38. Khonina SN, Kazanskiy NL, Khorin PA, Butt MA. Modern types of axicons: New functions and applications. Sensors 2021; 21(19): 6690. DOI: 10.3390/s21196690.
  39. Savelyev D, Kazanskiy N. Near-field vortex beams diffraction on surface micro-defects and diffractive axicons for polarization state recognition. Sensors 2021; 21(6): 1973. DOI: 10.3390/s21061973.
  40. Savelyev DA. The investigation of the features of focusing vortex super-Gaussian beams with a variable-height diffractive axicon. Computer Optics 2021; 45(2): 214-221. DOI: 10.18287/2412-6179-CO-862.
  41. Savelyev DA. The comparison of laser radiation focusing by diffractive axicons and annular gratings with variable height using high-performance computer systems. 2021 Photonics & Electromagnetics Research Symposium (PIERS) 2021: 2709-2716. DOI: 10.1109/PIERS53385.2021.9694860.
  42. Savelyev D. Diffraction of vortex beams by annular gratings with variable height in the near zone. 2021 International Conference on Information Technology and Nanotechnology (ITNT) 2021: 1-6. DOI: 10.1109/ITNT52450.2021.9649245.
  43. Prather DW, Shi S. Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements. J Opt Soc Am A 1999; 16(5): 1131-1142. DOI: 10.1364/JOSAA.16.001131.
  44. Oskooi AF, Roundy D, Ibanescu M, Bermel P, Joannopoulos JD, Johnson SG. MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method. Comput Phys Commun 2010; 181(3): 687-702. DOI: 10.1016/j.cpc.2009.11.008.
  45. Ding X, Ren Y, Lu R. Shaping super-Gaussian beam through digital micro-mirror device. Sci China Phys Mech 2015; 58(3): 1-6. DOI: 10.1007/s11433-014-5499-9.
  46. Malik HK, Devi L. Relativistic self focusing and frequency shift of super-Gaussian laser beam in plasma. Results Phys 2020; 17: 103070. DOI: 10.1016/j.rinp.2020.103070.
  47. Ashkin A, Dziedzic JM, Bjorkholm JE, Chu S. Observation of a single-beam gradient force optical trap for dielectric particles. Opt Lett 1986; 11(5): 288-290. DOI: 10.1364/OL.11.000288.
  48. Gouesbet G. Generalized Lorenz--Mie theories and mechanical effects of laser light, on the occasion of Arthur Ashkin's receipt of the 2018 Nobel prize in physics for his pioneering work in optical levitation and manipulation: A review. J Quant Spectrosc Radiat Transf 2019; 225: 258-277. DOI: 10.1016/j.jqsrt.2018.12.015.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20