Abstract

We propose a generalized model for the creation of vector Bessel-Gauss (BG) beams having state of polarization (SoP) varying along the propagation direction. By engineering longitudinally varying Pancharatnam-Berry (PB) phases of two constituent components with orthogonal polarizations, we create zeroth- and higher-order vector BG beams having (i) uniform polarizations in the transverse plane that change along z following either the equator or meridian of the Poincaré sphere and (ii) inhomogeneous polarizations in the transverse plane that rotate during propagation along z. Moreover, we evaluate the self-healing capability of these vector BG beams after two disparate obstacles. The self-healing capability of spatial SoP information may enrich the application of BG beams in light-matter interaction, polarization metrology and microscopy.

© 2017 Optical Society of America

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References

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2016 (10)

I. Ouadghiri-Idrissi, R. Giust, L. Froehly, M. Jacquot, L. Furfaro, J. M. Dudley, and F. Courvoisier, “Arbitrary shaping of on-axis amplitude of femtosecond Bessel beams with a single phase-only spatial light modulator,” Opt. Express 24(11), 11495–11504 (2016).
[Crossref] [PubMed]

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref] [PubMed]

J. A. Davis, I. Moreno, K. Badham, M. M. Sánchez-López, and D. M. Cottrell, “Nondiffracting vector beams where the charge and the polarization state vary with propagation distance,” Opt. Lett. 41(10), 2270–2273 (2016).
[Crossref] [PubMed]

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6, 30765 (2016).
[Crossref] [PubMed]

A. Aleksanyan and E. Brasselet, “Spin–orbit photonic interaction engineering of Bessel beams,” Optica 3(2), 167–174 (2016).
[Crossref]

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[Crossref] [PubMed]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

S. Rekštytė, T. Jonavičius, D. Gailevičius, M. Malinauskas, V. Mizeikis, E. G. Gamaly, and S. Juodkazis, “Nanoscale precision of 3D polymerization via polarization control,” Adv. Opt. Mat. 4(8), 1209–1214 (2016).
[Crossref]

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[Crossref] [PubMed]

2015 (5)

2014 (6)

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113(26), 263901 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Quantum entanglement of complex photon polarization patterns in vector beams,” Phys. Rev. A 89(6), 060301 (2014).
[Crossref]

M. Zhong, L. Gong, D. Li, J. Zhou, Z. Wang, and Y. Li, “Optical trapping of core-shell magnetic microparticles by cylindrical vector beams,” Appl. Phys. Lett. 105(18), 181112 (2014).
[Crossref]

X. Chu and W. Wen, “Quantitative description of the self-healing ability of a beam,” Opt. Express 22(6), 6899–6904 (2014).
[Crossref] [PubMed]

A. Aiello and G. S. Agarwal, “Wave-optics description of self-healing mechanism in Bessel beams,” Opt. Lett. 39(24), 6819–6822 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (4)

2011 (2)

2010 (3)

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated Pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81(5), 053813 (2010).
[Crossref]

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

2009 (3)

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2007 (2)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[Crossref]

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[Crossref]

2006 (2)

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

A. F. Abouraddy and K. C. Toussaint., “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

2004 (3)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
[Crossref]

2000 (1)

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4–6), 207–211 (1998).
[Crossref]

1997 (1)

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 281(1), 1–64 (1997).
[Crossref]

1989 (1)

1988 (1)

R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60(13), 1211–1213 (1988).
[Crossref] [PubMed]

1987 (4)

M. Berry, “The adiabatic phase and Pancharatnam phase for polarized-light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

Abeysinghe, D. C.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint., “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

Abrams, K.

Agarwal, G. S.

Ahmed, N.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref] [PubMed]

Aiello, A.

Aleksanyan, A.

Alfano, R. R.

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40(21), 4887–4890 (2015).
[Crossref] [PubMed]

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
[Crossref]

Allegre, O. J.

Almaiman, A.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref] [PubMed]

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4–6), 239–245 (2001).
[Crossref]

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Ashrafi, S.

N. Ahmed, Z. Zhao, L. Li, H. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref] [PubMed]

Badham, K.

Banzer, P.

Berry, M.

M. Berry, “The adiabatic phase and Pancharatnam phase for polarized-light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

Bhandari, R.

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 281(1), 1–64 (1997).
[Crossref]

R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60(13), 1211–1213 (1988).
[Crossref] [PubMed]

Biener, G.

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Figures (7)

Fig. 1
Fig. 1 Schematic representation of the experimental setup. L1-L4: lenses; HWP: half-wave plate; PBS: polarized beam splitter; M1-M4: mirrors; PSLM: phase spatial light modulator; QWP: quarter-wave plate; P: polarizer; CCD: charge coupled device. Insets: (a) schematic diagram of transverse-to-longitudinal structuring strategy for creating three-dimensionally changed PB phases; (b) schematic diagram of vector BG beam propagating through an obstacle in the non-diffractive region. Insets in (b) are the recorded intensity distributions at different propagation distances.
Fig. 2
Fig. 2 (a) Schematic of z-dependent SoP and (b)-(g) experimentally recorded intensity distributions. (b) Intensity distribution in y-z plane; (c)-(g) intensity distributions in cross section after a polarizer at different propagation distances shown in (b). The arrows in (c)-(g) denote the polarization orientations of the polarizer.
Fig. 3
Fig. 3 (a)-(e) Intensity (top row) and Stokes parameters distributions at planes z1 to z5. (f) SoP transformation trajectory on the Poincaré sphere. The red line corresponds to the transformation trajectory. The points A-E correspond to the SoPs shown in (a)-(e).
Fig. 4
Fig. 4 (a) Schematic representation of SoP distribution and transformation. (b)-(f) Experimentally measured intensity distributions of output beam propagating through a vertical polarizer at planes z1 to z5.
Fig. 5
Fig. 5 Measured transverse intensity and local SoP distributions of second-order vector BG beam with hybrid SoPs at planes z1 to z5, respectively. The red and green ellipses denote the RH and LH elliptical polarizations, respectively. The long axis of ellipse indicates the azimuthal angle of local SoP.
Fig. 6
Fig. 6 Measured reconstruction of zeroth-order vector BG beams after circle (a-c) and linear (d-f) obstacles. (a), (d) Intensity distributions of the obstructed beams; (b), (e) intensity distributions in the y-z plane; (c1-c5), (f1-f5) transverse intensity and local SoP distributions of the reconstructed beams at planes z1 to z5, respectively. The red and green ellipses in (c1-c5) and (f1-f5) denote the RH and LH elliptical polarizations, respectively. The long axis of ellipse indicates the azimuthal angle of local SoP. The diameters of two obstacles are D = 335μm and 70μm, respectively.
Fig. 7
Fig. 7 Measured transverse intensity and local SoP distributions of the reconstructed second-order BG beam with hybrid SoPs at planes z1 to z5. The red and green ellipses denote the RH and LH elliptical polarizations, respectively. The linear obstacle having a diameter about D = 70μm is placed at plane z = 16.6cm.

Equations (4)

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E( r,ϕ,z )=[ E 1 ( r,ϕ,z )| Ψ 1 + E 2 ( r,ϕ,z )| Ψ 2 ] e iωt ,
E( r,ϕ,z )= E 0 ( r,ϕ,z )| Ψ( r,ϕ,z ) = E 0 ( r,ϕ,z )[ u 1 ( r,ϕ,z ) e i Φ 1 ( r,ϕ,z ) | Ψ 1 + u 2 ( r,ϕ,z ) e i Φ 2 ( r,ϕ,z ) | Ψ 2 ].
| Ψ( r,ϕ,z=0 ) = 1 2 e imϕ ( cosψ|H+sinψ|V )+ 1 2 e imϕ ( sinψ|H+cosψ|V ),
S 0 =I= | E H | 2 + | E V | 2 S 1 = I 0° I 90° = | E H | 2 | E V | 2 S 2 = I 45° I 135° =2Re[ E H E V ] S 3 = I R I L =2Im[ E H E V ] ,

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