Abstract
The focusing characteristics of the Bessel–Gaussian (BG) beam, characterized by a tailored space-variant quadratic (SQ) phase, are explored based on the principles of vector diffraction theory. The effects of different parameters on the optical field distribution and the optical gradient force distribution are discussed in detail. The results show that the two intensity peaks will move toward the central region and merge into a single intensity peak when the beam parameter less than 3.2 and will separate along the X-axis when the beam parameter exceeds 3.2. Moreover, an optical trap appears in the focal area, and multiplied small-intensity peaks will be observed due to adjusting the fractional topological charge number. Besides, gradient force evolution differs for the variation of beam parameter and topological charge number. Novel patterns of gradient force emerge as a result, such as force rings, banded gradient force, square array gradient force. Our research results will benefit the development of optical manipulation fields, such as optical tweezers systems, particle capture and particle classification applications.
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References
Ahmed Alkelly, A., Al-Ahsab, H.T., Mingjian, C., Lqman, I.G.H.: Tight focusing of azimuthally polarized Laguerre-Gaussian vortex beams by diffractive axicons. Phys. Scr. 99, 025508 (2024)
Arabinda, M., Satyajit, M., Maruthi, M.: Common-path generation of stable cylindrical perfect vector vortex beams of arbitrary order. Opt. Commun. 469, 125807 (2020)
Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E.: Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11, 288–290 (1986)
Bozinovic, N., Yue, Y., Ren, Y.: Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545–1548 (2013)
Chen, Z., Pu, J.: Propagation dynamics and experimental observation of quadratic vortex beam. Chin. Phys. B 21(2), 024201 (2012)
Chen, W., Zhan, Q.: Realization of an evanescent Bessel beam via surface plasmon interference excited by a radially polarized beam. Opt. Lett. 34(6), 722–724 (2009)
Cheng, A., Goncalves, J.: Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing. Nat. Methods 8(2), 139–142 (2011)
Guo, L., Min, C., Yuan, G.: Optically stitched arbitrary fan-sectors with selective polarization states for dynamic manipulation of surface plasmon polaritons. Opt. Express 20(22), 24748–24753 (2012)
Hao, X., Kuang, C., Li, Y.: Evanescent-wave-induced frequency shift for optical superresolution imaging. Opt. Lett. 38(14), 2455–2458 (2013)
Hosseini-Saber, S., Akhlaghi, E.A., Saber, A.: Diffractometry based vortex beams fractional topological charge measurement. Opt. Lett. 45(13), 3478–3481 (2020)
Kim, J., Siahmakoun, A.: Evanescent coupling to silicon waveguides using-surface plasmon polaritons. Appl. Opt. 59(13), D64–D68 (2020)
Kotlyar, V.V., Kovalev, A.A., Nalimov, A.G.: Evolution of an optical vortex with initial fractional topological charge. Phys. Rev. Lett. 102(2), 023516 (2020)
Li, X., Zhu, X., Liu, L.: Generation of optical 3D unpolarized lattices in a tightly focused random beam. Opt. Lett. 48(14), 3829–3832 (2023)
Lynch, C., Devaney, N., Dainty, C.: Locally adaptive super-resolution through spatially variant interpolation. Appl. Opt. 58(11), 2920–2928 (2019)
Ma, X., Ye, J., Zhang, Y.: Vortex random fiber laser with controllable orbital angular momentum mode. Photonics Res. 9(2), 266–271 (2021)
Mei, Z.: Modified Bessel-correlated vortex beams and their propagation properties. Opt. Laser Technol. 126, 106088 (2020)
Nie, Z., Ning, Z., Liu, X.: Creating multiple ultra-long longitudinal magnetization textures by strongly focusing azimuthally polarized circular Airy vortex beams. Opt. Lett. 31(12), 19089–19101 (2023)
O’Neil, A.T., MacVicar, I., Allen, L.: Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Phys. Rev. Lett. 88(5), 053601 (2002)
Paterson, L., MacDonald, M.P., Arlt, J.: Controlled rotation of optically trapped microscopic particles. Science 292, 912–914 (2001)
Petrov, D.V., Kostenko, M.A., Shcherbakov, A.A.: Silver holographic gratings as substrates for SERS gas analysis. Appl. Opt. 59(9), 2929–2934 (2020)
Qu, Q., Lu, X., Peng, J.: Radially polarized Lorentz-Gauss vortex beam with sine-azimuthal variation wavefront. Optik 129, 50–56 (2017)
Romanato, F., Lee, K.H., Ruffato, G.: The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting. Appl. Phys. Lett. 96, 111103 (2010)
Schäfer, F.P.: On some properties of axicons. Appl. Phys. B 39, 1–8 (1986)
Wang, J.: Advances in communications using optical vortices. Photonics Res. 4(5), B14–B28 (2016)
Wang, H., Shi, L., Lukyanchuk, B.: Creation of a needle of longitudinally polarized light in vacuum using binary optics. Nat. Photon. 2(8), 501–505 (2008)
Wang, J., Yan, J., Fazal, I.M.: Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 6(7), 488–496 (2012)
Willner, A.E., Huang, H., Yan, Y.: Optical communications using orbital angular momentum beams. Adv. Opt. Photonics. 7, 66–106 (2015)
Xia, T., Tao, S., Cheng, S.: A spiral-like curve with an adjustable opening generated by a modified helico-conical beam. Opt. Commun. 458, 124824 (2020)
Xuejuan, L., Meidi, W., Lei, G., Shubo, C., Shaohua, T.: Measuring the photonic topological charge of power-exponent-phase vortex beam via cross phase. Appl. Phys. Lett. 123, 034104 (2023)
Yao, Z., Li, X., Wang, Z.: High-efficiency fabrication of computer-generated holograms in silica glass using a femtosecond Bessel beam. Opt. Laser Technol. 135, 106729 (2021)
Youngworth, K.S., Brown, T.G.: Focusing of high numerical aperture cylindrical vector beams. Opt. Express 7(2), 77–87 (2000)
Yuqi, P., Minglin, Z., Mingming, Z., Jiantai, D., Jiang, Z., Bo, L., Youyou, H.: Propagation properties of rotationally-symmetric power-exponent-phase vortex beam through oceanic turbulence. Opt. Laser Technol. 159, 109024 (2023)
Zhan, Q.: Trapping metallic Rayleigh particles with radial polarization. Opt. Express 12(15), 3377–3382 (2004)
Zhan, Q.: Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam. Opt. Lett. 31(11), 1726–1728 (2006)
Zhan, Q., Zhang, R., Ding, S.: Focusing pattern of axisymmetric Bessel–Gaussian beam with helical polarization under triangular modulation. Appl. Opt. 59(3), 648–652 (2020)
Zhang, X., Xia, T., Cheng, S.: Free-space information transfer using the elliptic vortex beam with fractional topological charge. Opt. Commun. 431, 238–244 (2018)
Zhang, H., Li, J., Chen, Y.: Bjorkholm, Focusing properties of power order space-variant phase modulate Bessel-Gaussian vortex beam. Optik 249, 168235 (2022)
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YC: Conceptualization, Writing–original draft, Writing–review & editing. HX: Methodology, Validation, Visualization. HS, YY, XL, and SF: Supervision.
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Chen, Y., Xu, H., Sun, H. et al. Focusing characteristics of space-variant quadratic phase modulated linearly polarized Bessel–Gaussian vortex beam. Opt Quant Electron 56, 912 (2024). https://doi.org/10.1007/s11082-024-06867-w
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DOI: https://doi.org/10.1007/s11082-024-06867-w