Abstract

In the field of nanophotonics, tuning the focus of near-field signals has been a great issue due to the demands on near-field imaging for, e.g., biomedical sensors and plasmonic tweezers. Using subwavelength structures for active control of plasmonic systems would be highly desirable. Here, we propose a plasmonic meta-slit, a simple but powerful structure that can switch the direction and length of its focus by changing optical polarization. It is composed of single or double arrays of nanoslit segments with a specific tilted angle distribution for a strong and flexible polarization dependency. Three representative examples of meta-slits for polarization-sensitive focusing, directional switching, and asymmetric focusing are theoretically and experimentally demonstrated. We expect that the proposed scheme can be applied not only to plasmonic switches and tunable lenses, but also as a design method for shaping near-field signals.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
  26. L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (4)

N. Yu, F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Z. Xu, T. Li, D.-H. Zhang, C. Yan, D. Li, L. Y. M. Tobing, F. Qin, Y. Wang, X. Shen, T. Yu, “Groove-structured metasurfaces for modulation of surface plasmon propagation,” Appl. Phys. Express 7, 052001 (2014).
[Crossref]

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, S. I. Bozhevolnyi, “Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons,” Light Sci. Appl. 3, e197 (2014).
[Crossref]

2013 (8)

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

A. Pors, O. Albrektsen, I. P. Radko, S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[Crossref]

N. Rotenberg, T. L. Krijger, B. le Feber, M. Spasenovic, F. J. Garcia de Abajo, L. Kuipers, “Magnetic and electric response of single subwavelength holes,” Phys. Rev. B 88, 241408(R) (2013).
[Crossref]

Y. Liu, X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103, 141101 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

A. V. Kildishev, A. Boltasseva, V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref]

X. Ni, S. Ishii, A. V. Kildishev, V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2, e72 (2013).
[Crossref]

2012 (3)

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref]

S.-W. Cho, H. Kim, J. Hahn, B. Lee, “Generation of multiple vortex-cones by direct-phase modulation of annular aperture array,” Appl. Opt. 51, 7295–7301 (2012).
[Crossref]

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

2011 (6)

X. Li, Q. Tan, B. Bai, G. Jin, “Experimental demonstration of tunable directional excitation of surface plasmon polaritons with a subwavelength metallic double slit,” Appl. Phys. Lett. 98, 251109 (2011).
[Crossref]

L. Li, T. Li, S. M. Wang, C. Zhang, S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[Crossref]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[Crossref]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, A. Lagendijk, “Active spatial control of plasmonic fields,” Nat. Photonics 5, 360–363 (2011).
[Crossref]

M. L. Juan, M. Righini, R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[Crossref]

Y. Zhao, A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

2010 (1)

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

2009 (2)

Z. Liu, Y. Wang, J. Yao, H. Lee, W. Srituravanich, X. Zhang, “Broad band two-dimensional manipulation of surface plasmons,” Nano Lett. 9, 462–466 (2009).
[Crossref]

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

2008 (2)

M. Righini, G. Volpe, C. Girard, D. Petrov, R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100, 186804 (2008).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

2007 (1)

G. Lévêque, O. J. F. Martin, J. Weiner, “Transient behavior of surface plasmon polaritons scattered at a subwavelength groove,” Phys. Rev. B 76, 155418 (2007).
[Crossref]

2006 (1)

2005 (1)

P. Lalanne, J. P. Hugonin, J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

2004 (1)

H. Ren, Y.-H. Fan, S. Gauza, S.-T. Wu, “Tunable-focus flat liquid crystal spherical lens,” Appl. Phys. Lett. 84, 4789–4791 (2004).
[Crossref]

2003 (2)

H. Ren, Y.-H. Fan, S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[Crossref]

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

2002 (1)

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Albrektsen, O.

A. Pors, O. Albrektsen, I. P. Radko, S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[Crossref]

Alu, A.

Y. Zhao, A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

Antoniou, N.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Aulbach, J.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, A. Lagendijk, “Active spatial control of plasmonic fields,” Nat. Photonics 5, 360–363 (2011).
[Crossref]

Azad, A. K.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref]

X. Li, Q. Tan, B. Bai, G. Jin, “Experimental demonstration of tunable directional excitation of surface plasmon polaritons with a subwavelength metallic double slit,” Appl. Phys. Lett. 98, 251109 (2011).
[Crossref]

Barnes, W. L.

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

Bernardin, T.

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, S. I. Bozhevolnyi, “Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons,” Light Sci. Appl. 3, e197 (2014).
[Crossref]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref]

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, S. I. Bozhevolnyi, “Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons,” Light Sci. Appl. 3, e197 (2014).
[Crossref]

A. Pors, O. Albrektsen, I. P. Radko, S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[Crossref]

Capasso, F.

N. Yu, F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Charrière, F.

Cheah, K.-W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

Chen, S.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

Chen, W. T.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Chen, X.

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref]

Chiang, I.-D.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Cho, S.-W.

S.-W. Cho, H. Kim, J. Hahn, B. Lee, “Generation of multiple vortex-cones by direct-phase modulation of annular aperture array,” Appl. Opt. 51, 7295–7301 (2012).
[Crossref]

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

Colomb, T.

Cuche, E.

Curtis, J. E.

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Depeursinge, C.

Dereux, A.

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

Dienstfrey, A.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

Ebbesen, T. W.

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

Emery, Y.

Fan, Y.-H.

H. Ren, Y.-H. Fan, S. Gauza, S.-T. Wu, “Tunable-focus flat liquid crystal spherical lens,” Appl. Phys. Lett. 84, 4789–4791 (2004).
[Crossref]

H. Ren, Y.-H. Fan, S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[Crossref]

Garcia de Abajo, F. J.

N. Rotenberg, T. L. Krijger, B. le Feber, M. Spasenovic, F. J. Garcia de Abajo, L. Kuipers, “Magnetic and electric response of single subwavelength holes,” Phys. Rev. B 88, 241408(R) (2013).
[Crossref]

Gauza, S.

H. Ren, Y.-H. Fan, S. Gauza, S.-T. Wu, “Tunable-focus flat liquid crystal spherical lens,” Appl. Phys. Lett. 84, 4789–4791 (2004).
[Crossref]

Girard, C.

M. Righini, G. Volpe, C. Girard, D. Petrov, R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100, 186804 (2008).
[Crossref]

Gjonaj, B.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, A. Lagendijk, “Active spatial control of plasmonic fields,” Nat. Photonics 5, 360–363 (2011).
[Crossref]

Gorodetski, Y.

Y. Gorodetski, A. Niv, V. Kleiner, E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

Grier, D. G.

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Hahn, J.

Hasman, E.

Y. Gorodetski, A. Niv, V. Kleiner, E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

Hecht, B.

L. Novotny, B. Hecht, Principle of Nano-Optics (Cambridge Unversity, 2006).

Holloway, C. L.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

Hsu, W.-L.

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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
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Zhang, S.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic and (b) SEM image of the single-lined meta-slit for polarization-sensitive focusing of the surface plasmon. (c), (d) Same for the double-lined Fresnel zone (DFZ) meta-slit for directional switching of the plasmonic focus. (e), (f) Same for the case of hybrid DFZ meta-slit for asymmetric focusing of plasmonic focus. Insets of lower figures show magnified images of the meta-slits.

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Fig. 2.
Fig. 2. (a) Angular distribution of propagating SPPs excited from a 300     nm × 75     nm single nanoslit for the incident polarizations of perpendicular (blue) and parallel (red) to the longer axis. (b) Normalized overlap integral between the E z field excited from an array of tilted nanoslits and that of a bare slit when a left-handed circular polarized light is incident. The field integration was calculated along the y direction at a distance of 20 μm from the slit along the x direction. Insets show the distribution of the E z field at P y = 450     nm (upper), 1.75 μm (lower-left), and 3.2 μm (lower-right), respectively. (c), (d) Changes in amplitude and phase of SPPs generated by the nanoslit array for circularly polarized light incidences varying the tilted angles of nanoslits. Amplitude profiles are independent of optical handedness. The incident wavelength is set to λ 0 = 980     nm , and the relative permittivity of Ag is ε Ag = − 43.9 + 2.8 i [31].

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Fig. 3.
Fig. 3. (a) Structure of single-lined meta-slit and numerically calculated E z field distributions for LCP (upper) and RCP (lower) light incidences. (b) Normalized near-field images measured by NSOM. (c) Calculated (red) and measured (blue) intensity distributions along the (yellow) dotted line shown in (b). Dotted and solid lines correspond to the LCP (focus-off) and RCP (focus-on) cases, respectively. The size of each nanoslit segment was set to be 300     nm × 75     nm , and we assume P y = 400     nm , l = 10.4     μm , and f 0 = 15     μm . (d) Wavelength dependency characteristics of the proposed meta-slit. Solid lines indicate the focal length f , whereas dotted lines show the value of λ SPP f / λ 0 .

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Fig. 4.
Fig. 4. (a) Overall structure of DFZ meta-slit. The inset shows a magnified image of two lines of the nanoslit array having tilted angles of θ 0 and − θ 0 . (b) Phase diagram explaining the directional launching characteristics of the meta-slit shown in (a). (c) Numerical calculation results based on dipole modeling. (d) Experimental results obtained by the NSOM for LCP (upper) and RCP (lower) incidence, respectively. Insets show the far-field measurements with grating couplers. We set d = 1210     nm ( 1.25 λ SPP ), P y = 400     nm , l = 23.2     μm , and f 0 = 20     μm .

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Fig. 5.
Fig. 5. (a) Three types of nanosilt segment pairs used in the hybrid DFZ meta-slit. (b) Design method of hybrid DFZ meta-slit for generating asymmetric foci. (c) Numerically calculated intensity ( E z field) distributions and (d) experimentally observed NSOM images of surface fields generated from the hybrid DFZ meta-slit for LCP (left-side images) and RCP (right-side images) cases. The total length of the meta-slit and intended focal lengths were set to l = 32     μm , f 1 = 20     μm , and f 2 = 30     μm , respectively. Other parameters were the same as those of Fig. 4.

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Equations (5)

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E s ( r ) = j ω μ 0 ∑ m = 1 N ( G 0 ( r , r m ) + G σ ( r , r m ) ) p ( r − r m ) e j ϕ m ,
E z ( x , y , z ) = A ( θ ( y ) ) e j Φ ( θ ( y ) ) e − κ a z e j ( k SPP | x | − ω t ) | y | < l / 2 ,
E z ( x , y , z ) = cos ( k SPP y 2 / 4 f 0 ) e ± j k SPP y 2 / 4 f 0 e − κ a z e j ( k SPP | x | − ω t ) .
d = ( n + π − 2 θ 0 2 π ) λ SPP ( n = 0 , 1 , 2 … ) .
R m = m f λ SPP + λ SPP 2 m 2 4 ,

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