Abstract
The intensity maxima position shift and the focal pattern evolution principle of spirally polarized hollow Gaussian beams (HGBs), with radial cosine phase wavefront modulation, are researched by the vector diffraction theory with Debye approximation. Significant intensity maxima position shift and focal pattern transformation of spirally polarized HGBs were found by changing the value of the spiral parameter, phase parameter or beam order. The spiral parameter contributes considerably to focal splitting, the phase parameter contributes to the intensity maxima position shift, and the beam order induces a sharper radial focal pattern. When the phase parameter equals 1, the intensity maxima position shift curves dependent on spiral parameter are initially smooth, then they begin to oscillate, and their vertical coordinates gradually increase. When the phase parameter equals 2, the intensity maxima position shift curves are initially smooth, then they begin to oscillate across the focal plane along the propagation direction with increasing amplitude. The spiral parameter, phase parameter and beam order greatly affect the intensity distribution, with the appearance of many novel focal patterns in evolution process, including intensity bowl, spheroidal shell and intensity ring. Spirally polarized HGBs with radial cosine phase modulation may be applied widely in optical manipulation, particle limitation systems, laser surface modification and laser direct writing techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45(11), 8185–8189 (1992). https://doi.org/10.1103/PhysRevA.45.8185
Apurv Chaitanya, N., Amrit, C., Banerji, J., Samanta, G.K.: High power, higher order ultrafast hollow Gaussian beams. Appl. Phys. Lett. 110(21), 211103 (2017). https://doi.org/10.1063/1.4983788
Cai, Y., Lu, X., Lin, Q.: Hollow Gaussian beams and their propagation properties. Opt. Lett. 28(13), 1084–1086 (2003). https://doi.org/10.1364/OL.28.001084
Cai, Y., Zhang, L.: Propagation of a hollow Gaussian beam through a paraxial misaligned optical system. Opt. Commun. 265(2), 607–615 (2006). https://doi.org/10.1016/j.optcom.2006.03.070
Chaitanya, N.A., Jabir, M.V., Banerji, J., Samanta, G.K.: Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum. Sci. Rep. 6, 32464 (2016). https://doi.org/10.1038/srep32464
Dai, Z., Ling, X., Tang, S.: Analytic expression and propagation properties of hollow Gaussian beams for the off-waist incident case in strongly nonlocal media. Results Phys. 9, 215–217 (2018). https://doi.org/10.1016/j.rinp.2018.02.029
Deng, D.: Generalized M2-factor of hollow Gaussian beams through a hard-edge circular aperture. Phys. Lett. A 341(1), 352–356 (2005). https://doi.org/10.1016/j.physleta.2005.04.081
Duocastella, M., Arnold, C.B.: Bessel and annular beams for materials processing. Laser Photonics Rev. 6(5), 607–621 (2012)
El Halba, E.M., Ez-zariy, L., Belafhal, A.: Creation of generalized spiraling bessel beams by fresnel diffraction of Bessel–Gaussian laser beams. Opt. Quant. Electron. 49(7), 236 (2017). https://doi.org/10.1007/s11082-017-1071-y
Gao, X., Zhou, F., Xu, W., Gan, F.: Gradient force pattern, focal shift, and focal switch in an apodized optical system. Opt. Int. J. Light Electron Opt. 116(3), 99–106 (2005)
Gao, X., Gao, M., Zhan, Q., Li, J., Guo, H., Wang, J., Zhuang, S.: Focal shift in radially polarized hollow Gaussian beam. Optik 122(8), 671–676 (2011a). https://doi.org/10.1016/j.ijleo.2010.05.003
Gao, X., Zhan, Q., Li, J., Wang, J., Zhuang, S.: Spirally polarized axisymmetric Bessel-modulated Gaussian beam. Opt. Int. J. Light Electron Opt. 122(6), 524–528 (2011b)
Gao, X., Zhan, Q., Li, J., Wang, J., Zhuang, S.: Spirally polarized axisymmetric Bessel-modulated Gaussian beam. Optik 122(6), 524–528 (2011c). https://doi.org/10.1016/j.ijleo.2010.04.005
Gao, X., Zhan, Q., Yun, M., Guo, H., Dong, X., Zhuang, S.: Focusing properties of spirally polarized hollow Gaussian beam. Opt. Quant. Electron. 42(14/15), 827–840 (2011d). https://doi.org/10.1007/s11082-011-9491-6
Gao, X., Zhan, Q., Yun, M., Guo, H., Dong, X., Zhuang, S.: Focusing properties of spirally polarized hollow Gaussian beam. Opt. Quant. Electron. 42(14–15), 827–840 (2011e)
Gerdova, I., Zhang, X., Haché, A.: Optically tunable hollow Gaussian beams with thin metal films. J. Opt. Soc. Am. B 23(9), 1934–1937 (2006). https://doi.org/10.1364/JOSAB.23.001934
Hao, B.: Spatially inhomogeneous polarization and its application in beam shaping. Doctor, University of Minnesota (2007)
He, S., Wang, Z., Liu, Q., Wang, W.: Study of focal shift effect in planar GaN high contrast grating lenses. Opt. Express 23(23), 29360–29368 (2015). https://doi.org/10.1364/OE.23.029360
Hricha, Z., Belafhal, A.: Focal shift in the axisymmetric Bessel-modulated Gaussian beam. Optics communications 255(4–6), 235–240 (2005)
Li, Q.: Optimization of point spread function of a high numerical aperture objective lens: application to high resolution optical imaging and fabrication. Doctor, École normale supérieure de Cachan - ENS Cachan (2014)
Li, Y., Wolf, E.: Focal shifts in diffracted converging spherical waves. Opt. Commun. 39(4), 211–215 (1981)
Liu, Z., Dai, J., Sun, X., Liu, S.: Generation of hollow Gaussian beam by phase-only filtering. Opt. Express 16(24), 19926–19933 (2008). https://doi.org/10.1364/OE.16.019926
MacDonald, M.P., Paterson, L., Sibbett, W., Dholakia, K., Bryant, P.E.: Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap. Opt. Lett. 26(12), 863–865 (2001)
Makov, Y.N., Sánchez-Morcillo, V., Camarena, F., Espinosa, V.: Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect. Ultrasonics 48(8), 678–686 (2008)
Martínez-Herrero, R., Maluenda, D., Juvells, I., Carnicer, A.: Effect of linear polarizers on highly focused spirally polarized fields. Opt. Lasers Eng. 98, 176–180 (2017). https://doi.org/10.1016/j.optlaseng.2017.06.027
Miao, Y., Wang, G., Shan, X., Zeng, X., Zhang, Q., Gao, X.: Focal pattern evolution of azimuthally polarized lorentz-gaussian vortex beam. Optik 187, 17–24 (2019)
Pleasants, S.: Hollow Gaussian beams. Nat. Photonics 8, 55–60 (2014). https://doi.org/10.1038/nphoton.2014.128
Prabakaran, K., Rajesh, K., Pillai, T., Chandrasekaran, R.: Focal shift of radially polarized axisymmetric Bessel modulated Gaussian beam with radial variance phase plate. Optik 124(22), 5454–5457 (2013a)
Prabakaran, K., Rajesh, K.B., Pillai, T.V.S., Chandrasekaran, R., Jaroszewicz, Z.: Focal shift in radially polarized beam with high NA lens axicon by using radial cosine phase wavefront. Opt. Quant. Electron. 45(6), 563–570 (2013b). https://doi.org/10.1007/s11082-013-9670-8
Prabakaran, K., Rajesh, K., Pillai, T.: Focal shifting of transversely polarized beam using cosine phase plate. Opt. Int. J. Light Electron Opt. 125(21), 6550–6553 (2014)
Pu, J., Zhang, Z.: Tight focusing of spirally polarized vortex beams. Opt. Laser Technol. 42(1), 186–191 (2010). https://doi.org/10.1016/j.optlastec.2009.06.008
Purohit, G., Rawat, P., Gauniyal, R.: Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma. Phys. Plasmas 23(1), 013103 (2016). https://doi.org/10.1063/1.4939544
Ramírez-Sánchez, V., Piquero, G., Santarsiero, M.: Generation and characterization of spirally polarized fields. J. Opt. A: Pure Appl. Opt. 11(8), 085708 (2009)
Rahimi, R., Ochoa, M., Ziaie, B.: Direct laser writing of porous-carbon/silver nanocomposite for flexible electronics. ACS Appl. Mater. Interfaces. 8(26), 16907–16913 (2016)
Suresh, P., Mariyal, C., Rajesh, K., Pillai, T., Jaroszewicz, Z.: Tightly focusing of spirally polarized Quadratic Bessel Gaussian beam through a dielectric interface. Opt. Int. J. Light Electron Opt. 125(3), 1264–1266 (2014a)
Suresh, P., Mariyal, C., Saraswathi Rajesh, K.B., Pillai, T.V.S., Jaroszewicz, Z.: Tightly focusing of spirally polarized Quadratic Bessel Gaussian beam through a dielectric interface. Optik 125(3), 1264–1266 (2014b). https://doi.org/10.1016/j.ijleo.2013.08.039
Tian, H., Xu, Y., Yang, T., Ma, Z., Wang, S., Dan, Y.: Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path. J. Mod. Opt. 64(4), 422–429 (2017). https://doi.org/10.1080/09500340.2016.1241441
Wang, P., Li, X., Shang, Y., Xu, X.: Theoretical research of beam combination between hollow beam and Gaussian beam. In: XXI International Symposium on High Power Laser Systems and Applications 2016. International Society for Optics and Photonics, p. 1025404 (2017)
Wu, G., Lou, Q., Zhou, J.: Analytical vectorial structure of hollow Gaussian beams in the far field. Opt. Express 16(9), 6417–6424 (2008). https://doi.org/10.1364/OE.16.006417
Wu, B., Zeng, X., Miao, Y., Fan, Y., Gao, X., Zhuang, S.: Focal shift of radial varying polarized Bessel–Gauss beam with radial phase modulation. Optik 157, 675–683 (2018). https://doi.org/10.1016/j.ijleo.2017.11.005
Xiumin Gao, X.G., Xiangmei Dong, X.D., Jiancheng Yu, J.Y., Qing Xin, Q.X., Songlin Zhuang, S.Z.: Axial multiple foci of radially polarized hollow Gaussian beam. Chin. Opt. Lett. 10(s1), S11406–311408 (2012). https://doi.org/10.3788/col201210.s11406
Xu, Y., Tian, H., Dan, Y., Feng, H., Wang, S.: Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence. J. Mod. Opt. 64(8), 844–854 (2017). https://doi.org/10.1080/09500340.2016.1262073
Youngworth, K.S., Brown, T.G.: Focusing of high numerical aperture cylindrical-vector beams. Opt. Express 7(2), 77–87 (2000). https://doi.org/10.1364/OE.7.000077
Zhan, Q.: Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1(1), 1–57 (2009). https://doi.org/10.1364/AOP.1.000001
Zhan, Q., Leger, J.R.: Focus shaping using cylindrical vector beams. Opt. Express 10(7), 324–331 (2002). https://doi.org/10.1364/OE.10.000324
Zhang, M., Chen, Y., Liu, L., Cai, Y.: Focal shift of a focused partially coherent Laguerre–Gaussian beam of all orders. J. Mod. Opt. 63(21), 2226–2234 (2016). https://doi.org/10.1080/09500340.2016.1191687
Acknowledgements
This work was supported by National key research and development plan “earth observation and navigation” key special project (2017YFB0503102).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, S., Miao, Y., Sui, G. et al. Intensity maxima position shift of spirally polarized hollow Gaussian beam with radial cosine phase modulation. Opt Quant Electron 52, 22 (2020). https://doi.org/10.1007/s11082-019-2112-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-019-2112-5