Abstract

We report the tetrad phase vortex structure in the scattered surface plasmon polariton (SPP) field produced by a silver nano-ring-slit with linearly polarized illumination. In the experiment, Mach-Zehnder type interferometer is constructed in which a microscopic objective (MO) is used to collect and image the scattered SPP field, and the phase map is extracted by Fourier transform of the interference intensity. To explain the formation of the tetrad phase vortices in the central area of the ring, we propose an empirical model for the ring-slit-excited SPP source field by trial calculations with the Huygens-Fresnel principle for SPP propagations. It is shown that the azimuthal variation of the amplitude of the source SPP is roughly a half of a constant base, and the variation of the phase is a little greater than π/2. The intensity and the phase distributions of the SSP field calculated with the formulations of this model phenomenologically conform the experimental results.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102(15), 153903 (2009).
    [CrossRef] [PubMed]

2012 (2)

2011 (1)

2010 (1)

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

2009 (4)

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79(19), 195414 (2009).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102(15), 153903 (2009).
[CrossRef] [PubMed]

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized Light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[CrossRef] [PubMed]

2008 (1)

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[CrossRef] [PubMed]

2007 (2)

L. Aigouy, P. Lalanne, H. T. Liu, G. Julié, V. Mathet, and M. Mortier, “Near-field scattered by a single nanoslit in a metal film,” Appl. Opt. 46(36), 8573–8577 (2007).
[CrossRef] [PubMed]

K. J. Chau, M. Johnson, and A. Y. Elezzabi, “Electron-spin-dependent terahertz light transport in spintronic-plasmonic Media,” Phys. Rev. Lett. 98(13), 133901 (2007).
[CrossRef] [PubMed]

2006 (3)

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

J. M. Steele, Z. W. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14(12), 5664–5670 (2006).
[CrossRef] [PubMed]

2005 (3)

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86(7), 071103 (2005).
[CrossRef]

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

2002 (1)

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

1999 (2)

K. T. Gahagan and G. A. Swartzlander., “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16(4), 533 (1999).
[CrossRef]

J. Scheuer and M. Orenstein, “Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities,” Science 285(5425), 230–233 (1999).
[CrossRef] [PubMed]

1998 (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2–3), 81–197 (1998).
[CrossRef]

Aigouy, L.

Archambault, A.

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[CrossRef] [PubMed]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79(19), 195414 (2009).
[CrossRef]

Aussenegg, F. R.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

Barclay, P. E.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86(7), 071103 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Chau, K. J.

K. J. Chau, M. Johnson, and A. Y. Elezzabi, “Electron-spin-dependent terahertz light transport in spintronic-plasmonic Media,” Phys. Rev. Lett. 98(13), 133901 (2007).
[CrossRef] [PubMed]

Cho, S. W.

S. W. Cho, J. Park, S. Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[CrossRef] [PubMed]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Christ, A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Davis, C. C.

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ditlbacher, H.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

Drezet, A.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Elezzabi, A. Y.

K. J. Chau, M. Johnson, and A. Y. Elezzabi, “Electron-spin-dependent terahertz light transport in spintronic-plasmonic Media,” Phys. Rev. Lett. 98(13), 133901 (2007).
[CrossRef] [PubMed]

Elliott, J.

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

Friedman, M. D.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86(7), 071103 (2005).
[CrossRef]

Gahagan, K. T.

Giessen, H.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Gippius, N. A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Gorodetski, Y.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[CrossRef] [PubMed]

Greffet, J. J.

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79(19), 195414 (2009).
[CrossRef]

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[CrossRef] [PubMed]

Guo, G.

Guo, G. C.

Hasman, E.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[CrossRef] [PubMed]

Hohenau, A.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

Johnson, M.

K. J. Chau, M. Johnson, and A. Y. Elezzabi, “Electron-spin-dependent terahertz light transport in spintronic-plasmonic Media,” Phys. Rev. Lett. 98(13), 133901 (2007).
[CrossRef] [PubMed]

Julié, G.

Kang, M.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Kim, H.

S. W. Cho, J. Park, S. Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[CrossRef] [PubMed]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Kivshar, Y. S.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2–3), 81–197 (1998).
[CrossRef]

Kleiner, V.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[CrossRef] [PubMed]

Krenn, J. R.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

Kuhl, J.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Lalanne, P.

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102(15), 153903 (2009).
[CrossRef] [PubMed]

L. Aigouy, P. Lalanne, H. T. Liu, G. Julié, V. Mathet, and M. Mortier, “Near-field scattered by a single nanoslit in a metal film,” Appl. Opt. 46(36), 8573–8577 (2007).
[CrossRef] [PubMed]

Lee, B.

S. W. Cho, J. Park, S. Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[CrossRef] [PubMed]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Lee, S. Y.

S. W. Cho, J. Park, S. Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[CrossRef] [PubMed]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Leitner, A.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

Lerman, G. M.

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized Light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

Levy, U.

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized Light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

Liu, A. P.

Liu, H. T.

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102(15), 153903 (2009).
[CrossRef] [PubMed]

L. Aigouy, P. Lalanne, H. T. Liu, G. Julié, V. Mathet, and M. Mortier, “Near-field scattered by a single nanoslit in a metal film,” Appl. Opt. 46(36), 8573–8577 (2007).
[CrossRef] [PubMed]

Liu, Z. W.

J. M. Steele, Z. W. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14(12), 5664–5670 (2006).
[CrossRef] [PubMed]

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2–3), 81–197 (1998).
[CrossRef]

Maier, S. A.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86(7), 071103 (2005).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Marquier, F.

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79(19), 195414 (2009).
[CrossRef]

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[CrossRef] [PubMed]

Mathet, V.

Mortier, M.

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[CrossRef] [PubMed]

Orenstein, M.

J. Scheuer and M. Orenstein, “Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities,” Science 285(5425), 230–233 (1999).
[CrossRef] [PubMed]

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Painter, O.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86(7), 071103 (2005).
[CrossRef]

Park, J.

S. W. Cho, J. Park, S. Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[CrossRef] [PubMed]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Pikus, Y.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Ren, X. F.

Rui, G. H.

Schaefer, D.

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

Scheuer, J.

J. Scheuer and M. Orenstein, “Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities,” Science 285(5425), 230–233 (1999).
[CrossRef] [PubMed]

Schider, G.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

Smolyaninova, V. N.

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

Srituravanich, W.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Steele, J. M.

J. M. Steele, Z. W. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14(12), 5664–5670 (2006).
[CrossRef] [PubMed]

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Steinberger, B.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

Stepanov, A. L.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

Sun, C.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Swartzlander, G. A.

Tan, P. S.

Teperik, T. V.

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[CrossRef] [PubMed]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79(19), 195414 (2009).
[CrossRef]

Tikhodeev, S. G.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Wang, Q.

Wang, Y.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Yanai, A.

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized Light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

Yang, X. Y.

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102(15), 153903 (2009).
[CrossRef] [PubMed]

Yuan, G. H.

Yuan, X. C.

Zayats, A. V.

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Zhan, Q. W.

Zhang, D. H.

Zhang, N.

Zhang, X.

J. M. Steele, Z. W. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14(12), 5664–5670 (2006).
[CrossRef] [PubMed]

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86(7), 071103 (2005).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81(10), 1762–1764 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nano Lett. (3)

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized Light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[CrossRef] [PubMed]

Nature (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rep. (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2–3), 81–197 (1998).
[CrossRef]

Phys. Rev. B (2)

I. I. Smolyaninov, C. C. Davis, V. N. Smolyaninova, D. Schaefer, J. Elliott, and A. V. Zayats, “Plasmon-induced magnetization of metallic nanostructures,” Phys. Rev. B 71(3), 035425 (2005).
[CrossRef]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79(19), 195414 (2009).
[CrossRef]

Phys. Rev. Lett. (4)

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102(15), 153903 (2009).
[CrossRef] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the Spin-Based Plasmonic Effect in Nanoscale Structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[CrossRef] [PubMed]

K. J. Chau, M. Johnson, and A. Y. Elezzabi, “Electron-spin-dependent terahertz light transport in spintronic-plasmonic Media,” Phys. Rev. Lett. 98(13), 133901 (2007).
[CrossRef] [PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Plasmonics (1)

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon polariton Mach–Zehnder Interferometer and oscillation fringes,” Plasmonics 1(2–4), 141–145 (2006).
[CrossRef]

Science (2)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

J. Scheuer and M. Orenstein, “Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities,” Science 285(5425), 230–233 (1999).
[CrossRef] [PubMed]

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

S. A. Maier, Plamonics: Fundamentals and Applications (Springer, 2006).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. The linearly polarized beam from a He-Ne laser is splitted into two by beam-splitter (BS1). The laser beam in the lower arm is used as reference wave; in upper arm, the beam illuminates the sample S at normal incidence to excite the SPPs on the sample surface. The CCD records both the scattered SPP pattern and interference pattern, respectively, with reference beam blocked or not. The left pattern in Inset (a) is the SEM image of the sample, and the right one is the enlarged view of part within the labeled square, in which the rough fluctuations of the silver film may be seen. Inset (b) shows the mechanism of the SPP scattering at the silver film surface.

Fig. 2
Fig. 2

The experimental patterns of the scattered SPP field distribution of the circular ring structure obtained by Fourier transform. (a) intensity pattern, with the small inset on the upper right corner the minified view of the pattern, and the red arrow showing the direction of incident polarization. (b) The enlarged view of central part of Fig. 2(a) with enhanced brightness. (c) The reconstructed phase distribution. (d) The enlarged view of central part of Fig. 2(c). The tetrad phase vortex structure is seen in (c) and (d).

Fig. 3
Fig. 3

(a) The diagram of the ring-slit and the coordinates for the calculations. The diameter and the width of the ring are the same as the sample. (b) The intensity pattern calculated according to Eq. (8) in assumption of E 0z ( r 0 =R, φ 0 ) having both constant amplitude and phase. (c) The intensity pattern calculated according to Eq. (8) in assumption of E 0z ( r 0 =R, φ 0 )=A| sin φ 0 | with constant A . (d) Experimental intensity pattern the same as Fig. 2(a). The red dash circle indicates where the data of the amplitude and the phase are read. (e) The experimental (black) and empirical (red) amplitude and the phase curves on the red circle in (d). The upper part is amplitude curves and the lower part is the phase curves. (f) and (g) The intensity and the phase patterns calculated according to Eq. (8) with B a =0.5 , C a =0.5 , B Φ =0.9 and C Φ =0.23 , respectively. (h) and (i) The intensity and the phase patterns calculated according to Eq. (8) with B a =0.3 , C a =0.6 , B Φ =0.9 and C Φ =0.785 , respectively.

Equations (12)

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U(x,y)=A(x,y)exp[jϕ(x,y)]= U r (x,y)+j U i (x,y),
r(x,y)=exp[j2π( f 0x x+ f 0y y)],
I 1 (x,y)=| U(x,y)+r(x,y) | , 2 =U(x,y) U (x,y)+r(x,y) r * (x,y)+U(x,y) r * (x,y)+ U * (x,y)r(x,y),
I f ( f x , f y )= B f ( f x , f y )+ U f ( f x , f y )δ( f x + f 0x , f y + f 0y ) + U f * ( f x , f y )δ( f x f 0x , f y f 0y ) = B f ( f x , f y )+ U f ( f x + f 0x , f y + f 0y )+ U f * ( f x f 0x , f y f 0y ),
E(x, y)= d k y 2π E( k y )exp[i( k SP 2 k y 2 x+ k y y)],
k SP 2 = k x 2 + k y 2 = ω 2 c 2 ε 1 ε 2 ε 1 + ε 2 ,
E z (x, y)= i λ SP d y 0 cosα E 0z ( x 0 =0, y 0 ) exp(i k SP ρ) ρ exp(iπ/4),
E z (r, φ)= i λ SP Rd φ 0 cosα E 0z ( r 0 =R, φ 0 ) exp(i k SP ρ) ρ exp(iπ/4),
E 0z ( r 0 =R, φ 0 )= A 0 ( r 0 =R, φ 0 )exp[i Φ 0 ( r 0 =R, φ 0 )],
A 0 ( r 0 =R, φ 0 )= B a sin 2 φ 0 + C a ,
Φ 0 ( r 0 =R, φ 0 )= B Φ cos2 φ 0 + C Φ ,
E 0z ( r 0 =R, φ 0 )=C ( sin 2 φ 0 +2)exp[i(0.9cos2 φ 0 + C Φ )].

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