Tightly Focusing Properties of Radially Polarized Double Ring Shaped Beam through a Uniaxial Birefringent Crystal
J. Environ. Nanotechnol., Volume 7, No 2 (2018) pp. 18-25
Abstract
The properties of radially polarized Double ring shaped beam tightly focused through a uniaxial birefringent crystal are studied numerically by the use vectorial diffraction theory for small birefringence. The intensity distribution of focal structure in the focal region can be shift along the longitudinal axis with increasing the birefringence value [Δn], and splitting of focal spot can be obtained by changing the pupil to beam ratio[β].and also splitting of single focal spot into double spot by changing the pupil to beam ratio[β].
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Avendaño-Alejo, M. and Rosete-Aguilar, M., Optical path difference in a plane-parallel uniaxial plate, J. Opt. Soc. Am. A., 23(4), 926-932(2006).
https://doi.org/10.1364/JOSAA.23.000926
Born, M., Wolf, E.: Principles of Optics 7th edn.(1999). (Cambridge: Cambridge University Press).
Cheng, Gonçalves, J. T., Golshani, P., Arisaka, K. and Portera-Cailliau, C., Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing, Nat. Methods., 8(2), 139–142(2011).
https://doi.org/10.1038/nmeth.1552
Ciattoni, A., Crosignani, B. and Di Porto, P., Vectorial theory of propagation in uniaxially anisotropic media, J. Opt. Soc. Am. A., 18(7), 1656-1661(2001a).
https://doi.org/10.1364/JOSAA.18.001656
Ciattoni, A., Cincotti, G. and Palma, C., Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals, Opt. Commun., 195(1-4), 55-61(2001b).
https://doi.org/10.1016/S0030-4018(01)01335-9
Cincotti, G., Ciattoni, A. and Palma, C., Hermite–Gauss Beams in Uniaxially Anisotropic Crystals, IEEE J. Quantum Electron., 37, 1517(2001c).
Ciattoni, A., Ciattoni, G. and Palma, C., Propagation of cylindrically symmetric fields in uniaxial crystals, J. Opt. Soc. Am. A., 19, 792-796(2002).
https://doi.org/10.1364/JOSAA.19.000792
Cincotti, G., Ciattoni, A. and Palma, C., Laguerre–Gauss and Bessel–Gauss beams in uniaxial crystals, J. Opt. Soc. Am. A., 19(8), 1680-1688(2002a).
https://doi.org/10.1364/JOSAA.19.001680
Ciattoni, A., Cincotti, G. and Palma, C., Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal, J. Opt. Soc. Am., A19(7), 1422-1431(2002b).
https://doi.org/10.1364/JOSAA.19.001422
Ciattoni, A., Cincotti, G., Palma, C. and Weber, H., Energy exchange between the Cartesian components of a paraxial beam in a uniaxial crystal, J. Opt. Soc. Am. A., 19(9), 1894-1900(2002c).
https://doi.org/10.1364/JOSAA.19.001894
Cincotti, G., Ciattoni, A. and Palma, C., Propagation-invariant beams in uniaxial crystals, J. Mod. Opt., 49(13),2267-2272(2002d).
https://doi.org/10.1080/09500340210133153
Ciattoni, A., Cincotti, D., Provenziani, C. and Palma, C., Paraxial propagation along the optical axis of a uniaxial medium, Phys. Rev., E66(3 pt 2B), 036614-1(2002).
https://doi.org/10.1103/PhysRevE.66.036614
Ciattoni, A., Cincotti, G. and Palma, C., Circularly polarized beams and vortex generation in uniaxial media, J. Opt. Soc. Am. A., 20(1), 163-171(2003).
https://doi.org/10.1364/JOSAA.20.000163
Ciattoni, G., Ciattoni, A. and Sapia, C., Radially and azimuthally polarized vortices in uniaxial crystals, Opt. Commun., 220, 33-40(2003). https://doi.org/10.1016/S0030-4018(03)01372-5
Deng, D., Chen, C., Zhao, X. and Li, H., Propagation of an Airy vortex beam in uniaxial crystals, Appl. Phys. B., 110(3), 433-436(2013).
https://doi.org/10.1007/s00340-012-5273-5
Deng, D., Shen, J., Tian, Y., Shao, J. and Fan, Z., Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals, Optik(Stuttgart)., 118(11), 547–551(2007).
https://doi.org/10.1016/j.ijleo.2006.05.006
Deng, D., Yu, H., Xu, S., Shao, J. and Fan, Z., Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals, Opt. Commun., 281(2), 202–209(2008).
https://doi.org/10.1016/j.optcom.2007.09.038
Dorn, R., Quabis, S. and Leuchs, G., Sharper Focus for a Radially Polarized Light Beam, Phys. Rev. Lett., 91, 233901 (2003).
https://doi.org/10.1103/PhysRevLett.91.233901
Du, X. and Zhao, D., Propagation of uniformly polarized stochastic electromagnetic beams in uniaxial crystals, J. Electromagn. Waves Appl., 24(7), 971-981(2010).
https://doi.org/10.1163/156939310791285182
Fleck, J. A. Jr. and Feit, M. D., Beam propagation in uniaxial anisotropic media, J. Opt. Soc. Am., 73(7), 920-926(1983).
https://doi.org/10.1364/JOSA.73.000920
Gao, P., Tian, S., Weng, X., Guo, H.: Dynamically shifting the focal spot with tunable pupil filters, J. Mod. Opt., 63(16), 1558-1563(2016).
https://doi.org/10.1080/09500340.2016.1162334
Gao, X. M., Gao, M. Y., Hu, S., Guo, H. M., Wang, J. and Zhuang, S.L., Focal shift of radially polarized Bessel-modulated Gaussian beam by phase shifting, Nat. Science., 1(3), 229-233(2009).
https://doi.org/10.4236/ns.2009.13031
Gao, X., Hu, S., Gu, H. and Wang, J., Focal shift of three-portion concentric piecewise cylindrical vector beam, Optik. 120(11), 519-523(2009).
https://doi.org/10.1016/j.ijleo.2007.11.011
Gu, M., Advanced Optical Imaging Theory. (2000)(Berlin: Springer).
https://doi.org/10.1007/978-3-540-48471-4
Hayazawa, N., Saito, Y. S. and Kawata, S., Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy, Appl. Phys. Lett., 85, 6239–6241(2004).
https://doi.org/10.1063/1.1839646
Helseth, L. E., Focusing of atoms with strongly confined light potentials, Opt. Commun. 212, 343–352(2002).
https://doi.org/10.1016/S0030-4018(02)01998-3
Jain, M., Lotsberg, J. K., Stamnes, J. J., Frette, O., Velauthapillai, D., Jiang, D. and Zhao, X., Numerical and experimental results for focusing of three-dimensional electromagnetic waves into uniaxial crystals, J. Opt. Soc. Am. A Opt. Image Sci. Vis., 26(3), 691–698(2009). https://doi.org/10.1364/JOSAA.26.000691
Jiang, D. and Stamnes, J. J., Numerical and experimental results for focusing of two-dimensional waves in uniaxial crystals, Opt. Commun., 174(5-6), 321–334(2000).
https://doi.org/10.1016/S0030-4018(99)00671-9
Kozawa, Y. and Sato, S., Focusing property of a double-ring shaped radially polarized beam, Opt. Lett., 31(6), 820–822(2006).
https://doi.org/10.1364/OL.31.000820
Kozawa, Y. and Sato, S., Sharper focal spot formed by higher-order radially polarized laser beams, J. Opt. Soc. Am. A., 24(6), 1793-98(2007).
https://doi.org/10.1364/JOSAA.24.001793
Lalithambigai, K., Saraswathi, R. C., Anbarasan, P. M., Rajesh, K. B. and Jaroszewicz, Z., Generation of Multiple Focal Hole Segments Using Double-Ring Shaped Azimuthally Polarized Beam, J. At. Mol. Phy., 451715(2013).
https://doi.org/10.1155/2013/451715
Lerman, G. M. and Levy, U., Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization, Opt. Lett., 32, 2194–2196(2007).
https://doi.org/10.1364/AO.48.001288
Li, J. and Chen, Y., Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis, Opt. Laser Technol., 44(5), 1603-1610(2012).
https://doi.org/10.1016/j.optlastec.2011.11.041
Li, J., Chen, Y., Xin, Y. and Xu, S., Propagation of higher-order cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis, Eur. Phys. J., D57(3), 419–425 (2010).
https://doi.org/10.1140/epjd/e2010-00068-9R
Li, J., Gao, X., Zhuang, S., Huang, C.: Focal shift and focusing properties generation by radial cosine phase masks, Optik, 121(9), 821-825(2010).
https://doi.org/10.1016/j.ijleo.2008.09.030
Liu, D. and Zhou, Z., Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis, Opt. Laser Technol., 41(7), 877–884 (2009a).
https://doi.org/10.1016/j.optlastec.2009.02.008
Liu, D. and Zhou, Z., Propagation of partially coherent flat-topped beams in uniaxial crystals orthogonal to the optical axis, J. Opt. Soc. Am. A., 26(4), 924-930(2009b).
https://doi.org/10.1364/JOSAA.26.000924
Liu, D. and Zhou, Z., Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis, Eur. Phys. J., D54, 95-101(2009c).
https://doi.org/10.1140/epjd/e2009-00166-9
Liu, D. and Zhou, Z., Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis, J. Opt. A, Pure Appl. Opt., 10(9), 095005(2008).
https://doi.org/10.1088/1464-4258/10/9/095005
Lü, B. and Luo, S., Propagation properties of three-dimensional flatted Gaussian beams in uniaxially anisotropic crystals, Opt. Laser Technol., 36(1), 51-56(2004).
https://doi.org/10.1016/S0030-3992(03)00132-4
Meier, M., Romano, V. and Feurer, T., Material processing with pulsed radially and azimuthally polarized laser radiation, Appl. Phys. A., 86(3), 329–334(2007).
https://doi.org/10.1007/s00339-006-3784-9
Moser, T., Glur, H., Romano, V., Pigeon, F., Parriaux, O., Ahmed, M. A. and Graf, T., Polarization-selective grating mirrors used in the generation of radial polarization, Appl. Phys. B., 80(6), 707-713(2005).
https://doi.org/10.1007/s00340-005-1794-5
Nie, Z., Li, Z., Shi, G., Zhang, X., Wang, Y. and Song, Y., Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam, Opt. Lasers Eng., 59, 93-97(2014).
https://doi.org/10.1016/j.optlaseng.2014.03.006
Niziev, V. G. and Nesterov, A. V., Influence of beam polarization on laser cutting efficiency, J. Phys. D., 32(13), 1455–1461(1999).
https://doi.org/10.1088/0022-3727/32/13/304
Novotny, L., Beversluis, M. R., Youngworth, K. S. and Brown, T. G., Continuum generation from single gold nanostructures through near-field mediated intraband transitions, Phys. Rev. B., 68(11), 115433(2003).
https://doi.org/10.1103/PhysRevB.68.115433
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(2013).
https://doi.org/10.1007/s11082-013-9670-8
Provenziani, D., Ciattoni, A., Cincotti, G. and Palma, C., Diffraction by elliptic and circular apertures in uniaxially anisotropic crystals: theory and experiment, J. Opt. A. Pure Appl. Opt., 4(4), 424(2002).
https://doi.org/10.1088/1464-4258/4/4/310
Qiufang Zhan, Jinsong Li , Xiumin Gao, Alterable focal shift of concentric piecewise cylindrical vector beam, Proc. of SPIE, 7497, 74970X-1(2009).
https://doi.org/10.1117/12.832338
Quabis, S., Dorn, R., Eberler, M., Glöcke, O. and Leuchs, G., Focusing light to a tighter spot, Opt. Commun., 179, 01–07(2000).
https://doi.org/10.1007/s00339-006-3784-9
Rajesh, K. B., Veerabagu Suresh, N., Anbarasan, P. M., Gokulakrishnan, K. and Mahadevan, G., Tight focusing of double ring shaped radially polarized beam with high NA lens axicon, Opt. Laser Tech., 43(7), 1037-1040(2011).
https://doi.org/10.1016/j.optlastec.2010.11.009
Rao, L. Z., Wang, Z. C., and Zheng, X. X., Tightly Focusing of Circularly Polarized Vortex Beams through a Uniaxial Birefringent Crystal, Chin. Phys. Lett., 25(9), 3223-3226(2008).
Romea, R. D. and Kimura, W. D., Modeling of inverse Cerenkov laser acceleration with axicon laser-beam focusing, Phys. Rev. D., 42(5), 1807–1818(1990).
https://doi.org/10.1103/PhysRevD.42.1807 •
Shen, Y., Liu, L., Zhao, C., Yuan, Y. and Cai, Y., Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal, J. Opt. Soc. Am. A., 31(2), 238-245(2014).
https://doi.org/10.1364/JOSAA.31.000238
Stallinga, S., Axial birefringence in high-numerical-aperture optical systems and the light distribution close to focus, J. Opt. Soc. Am. A., 18(11), 2846-2859(2001).
https://doi.org/10.1364/JOSAA.18.002846
Stamnes, J. J. and Jiang, D., Focusing of electromagnetic waves into a uniaxial crystal, Opt. Commun., 150(1-6), 251–262(1998).
https://doi.org/10.1016/S0030-4018(98)00055-8
Tang, B., Hermite-cosine-Gaussian beams propagating in uniaxial crystals orthogonal to the optical axis, J. Opt. Soc. Am. A., 26(12), 2480–2487(2009).
https://doi.org/10.1364/JOSAA.26.002480
Tian, B. and Pu, J., Tight focusing of a double-ring-shaped, azimuthally polarized beam, Opt. Lett., 36(11), 2014-2016(2011).
https://doi.org/10.1364/OL.36.002014
Tidwell, S. C., Kim, G. H. and Kimura, W. D., Efficient radially polarized laser beam generation with a double interferometer, Appl. Opt., 32(27), 5222–5229(1993).
https://doi.org/10.1364/AO.32.005222
Torok, P., Varga, P., Laczik, Z. and Booker, G. R., Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation, J. Opt. Soc. Am. A., 12(2), 325-332(1995).
https://doi.org/10.1364/JOSAA.12.000325
Urbach, H. P. and Pereira, S. F., Field in Focus with a Maximum Longitudinal Electric Component, Phys. Rev. Lett., 100(12), 123904(2008).
https://doi.org/10.1103/PhysRevLett.100.123904
Varin, C. and Piche, M., Acceleration of ultra-relativistic electrons using high-intensity TMo1 laser beams, Appl. Phys. B., 74(S1), S83–S88(2002).
https://doi.org/10.1007/s00340-002-0906-8
Walker, E. P. and Milster, T. D., Beam shaping for optical data storage, Proc. SPIE 4443, 73–92(2001).
Xiangping Li, James W. M. Chon, Shuhui Wu, Richard A. Evans and Min Gu, Rewritable polarization-encoded multilayer data storage in a 2,5-dimethyl-4-(p-nitrophenylazo)anisole doped polymer, Opt. Lett., 32(3), 277-279(2007).
https://doi.org/10.1364/OL.32.000277
Yan, S., Yao, B. and Rupp, R., Shifting the spherical focus of a 4Pi focusing system, Opt. Express., 19(2), 673-678(2011).
https://doi.org/10.1364/OE.19.000673
Yan, S., Yao, B., Rupp, R.: Shifting the spherical focus of a 4Pi focusing system, Opt. Express., 19(2), 673-678(2011).
https://doi.org/10.1364/OE.19.000673
Yew, E. and Sheppard, C., Second-harmonic generation microscopy with tightly focused linearly and radially polarized beams, Opt. Commun., 275(2), 453–457(2007).
https://doi.org/10.1016/j.optcom.2007.03.065
Yonezawa, K., Kozawa, Y. and Sato, S., Focusing of radially and azimuthally polarized beams through a uniaxial crystal, J. Opt. Soc. Am. A., 25(2), 469-472(2008).
https://doi.org/10.1364/JOSAA.25.000469
Youngworth, K. S. and Brown, T. G., Focusing of high numerical aperture cylindrical vector beams, Opt. Express., 7, 77–87(2000).
https://doi.org/10.1364/OE.7.000077
Yun, M., Liang, W., Kong, W., Gao, X., Zhu, H., Liang, J.: Transverse super-resolution and focal shift with rotational tunable phase mask, Opt. Commun., 283(10), 2079-2083(2010).
https://doi.org/10.1016/j.optcom.2010.01.039
Zhan, Q., Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam, Opt. Lett., 31(11), 1726–1728(2006).
https://doi.org/10.1364/OL.31.001726
Zhan, Q., Trapping metallic Rayleigh particles with radial polarization, Opt. Express., 12(15), 3377–3382(2004).
https://doi.org/10.1364/OPEX.12.003377
Zhang, L. and Cai, Y., Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal, J. Mod. Opt., 58(14), 1224-1232(2011).
https://doi.org/10.1080/09500340.2011.599503
Zhang, L. and Cai, Y., Statistical properties of a Nonparaxial Gaussian Schell-model beam in a uniaxial crystal, Opt. Express., 19(14), 13312-13325(2011).
https://doi.org/10.1364/OE.19.013312
Zhang, Y., Suyama, T. and Ding, B., Longer axial trap distance and larger radial trap stiffness using a double-ring radially polarized beam, Opt. Lett., 35(8), 1281-1283(2010).
https://doi.org/10.1364/OL.35.001281
Zhang, Y., Xu, X. and Okuno, Y., Theoretical study of optical recording with a solid immersion lens illuminated by focused double-ring-shaped radially-polarized beam, Opt. Commun., 282(23), 4481–4485(2009).
https://doi.org/10.1016/j.optcom.2009.08.031
Zhang, Z., Pu, J. and Wang, X., Focusing of partially coherent Bessel–Gaussian beams through a high numerical-aperture objective, Opt. Lett., 33(1), 49–51(2008).
https://doi.org/10.1364/OL.33.000049
Zhang, Z., Pu, J. and Wang, X., Tight focusing of radially and azimuthally polarized vortex beams through a uniaxial birefringent crystal, Appl. Opt., 47(12), 1963-1967(2008).
https://doi.org/10.1364/AO.47.001963
Zhou, G., Chen, R. and Chu, X., Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis, Opt. Express., 20(3), 2196-2205(2012).
https://doi.org/10.1364/OE.20.002196
Zhou, Y., Wang, X., Dai, C., Chu, X. and Zhou, G., Nonparaxial analysis in the propagation of a cylindrical vector Laguerre-Gaussian beam in a uniaxial crystal orthogonal to the optical axis, Opt. Commun., 305, 113-125(2013).
