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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 8 — Sep. 4, 2013
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Polarization-sensitive characterization of the propagating plasmonic modes in silver nanowire waveguide on a glass substrate with a scanning near-field optical microscope

Priyamvada Venugopalan, Qiming Zhang, Xiangping Li, and Min Gu  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15247-15252 (2013)
http://dx.doi.org/10.1364/OE.21.015247


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Abstract

In this paper, we report on the experimental investigation of the polarization properties of the plasmonic modes along a silver nanowire waveguide on a glass substrate. Two orthogonal polarization light components at the distal end of the nanowire are observed in the far-field. The near-field mapping with a scanning near-field optical microscopic probe exhibiting an in-plane polarization sensitivity reveals the two polarization components of the propagating plasmonic modes along the nanowire.

© 2013 OSA

1. Introduction

Finite length silver (Ag) nanowires (NWs) are intriguing plasmonic structures due to their strong polarizibility compared with the spherical shaped structures and a low loss among the metallic NWs [1

1. E. R. Encina, E. M. Perassi, and E. A. Coronado, “Near-field enhancement of multipole plasmon resonances in Ag and Au nanowires,” J. Phys. Chem. A 113(16), 4489–4497 (2009). [CrossRef] [PubMed]

]. These kinds of anisotropic extended Ag nanostructures with sub-wavelength dimensions can support propagating surface plasmons (SPs) along the NW with a lateral confinement in the other two directions and with a micro-scale propagation length thereby acting as sub-wavelength plasmonic waveguides [2

2. A. Pucci, F. Neubrech, J. Aizpurua, T. Cornelius, and M. Chapelle, “Electromagnetic nanowire resonances for field-enhanced spectroscopy,” in One-Dimensional Nanostructures, Z. Wang, ed. (Springer-New York, 2008).

]. In addition, controlling the order and the polarization properties of the plasmonic modes in free-standing Ag NWs has enabled a wide range of applications such as beam splitters, polarization rotators, bio-sensors and so on [3

3. Y. Fang, Z. Li, Y. Huang, S. Zhang, P. Nordlander, N. J. Halas, and H. Xu, “Branched silver nanowires as controllable plasmon routers,” Nano Lett. 10(5), 1950–1954 (2010). [CrossRef] [PubMed]

6

6. S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res. 45(11), 1887–1895 (2012). [CrossRef] [PubMed]

]. On the other hand, Ag NWs on a dielectric substrate have been widely studied [7

7. X. Xiong, C.-L. Zou, X.-F. Ren, A.-P. Liu, Y.-X. Ye, F.-W. Sun, and G.-C. Guo, “Silver nanowires for photonics applications ,” Laser & Photo. Rev. doi: (2013). [CrossRef]

, 8

8. C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010). [CrossRef]

], owing to the relatively longer propagation length, stronger energy confinement and the enhanced evanescent field at the interface compared to the free-standing NW, which opens up the possibility for novel and high performance miniaturized optical devices [9

9. S. Xie, Z. Ouyang, B. Jia, and M. Gu, “Large-size, high-uniformity, random silver nanowire networks as transparent electrodes for crystalline silicon wafer solar cells,” Opt. Express 21(S3), A355–A362 (2013). [CrossRef]

, 10

10. Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20(17), 19006–19015 (2012). [CrossRef] [PubMed]

]. The presence of the substrate can break up the symmetry and fundamentally change the plasmonic modes supported in the hybrid structure. Thus the NW waveguide on the substrate can turn into a single-mode operation [10

10. Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20(17), 19006–19015 (2012). [CrossRef] [PubMed]

, 11

11. Q. Li and M. Qiu, “Plasmonic wave propagation in silver nanowires: guiding modes or not?” Opt. Express 21(7), 8587–8595 (2013). [CrossRef] [PubMed]

], which is crucial for practical optical waveguide applications. Because of its sensitivity to the evanescent wave and high spatial resolution, the scanning optical near-field microscope (SNOM) is widely used to study the localized plasmonic modes in Ag NWs [12

12. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

, 13

13. B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996). [CrossRef] [PubMed]

]. However, the near-field studies of Ag NWs are mainly focused on the intensity distribution [14

14. R. Fujimoto, A. Kaneta, K. Okamoto, M. Funato, and Y. Kawakami, “Interference of the surface plasmon polaritons with an Ag waveguide probed by dual-probe scanning near-field optical microscopy,” Appl. Surf. Sci. 258(19), 7372–7376 (2012). [CrossRef]

, 15

15. J. K. Lim, K. Imura, T. Nagahara, S. K. Kim, and H. Okamoto, “Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy,” Chem. Phys. Lett. 412(1-3), 41–45 (2005). [CrossRef]

]. The polarization properties of the plasmonic modes in Ag NWs on a dielectric substrate are yet to be determined, but are necessary prior to its practical applications.

In this paper, we report on the near-field analysis of the polarization properties of the propagating plasmonic modes along the NW on a glass substrate. The far-field result reveals the existence of two orthogonal polarization components of the plasmonic mode at the distal end. The near-field mapping of the propagating plasmonic modes of the NW on the substrate by a SNOM probe with an in-plane polarization-sensitivity provides a further insight into the two polarization components.

2. Experimental setup and far-field characterization

To analyze the polarization state at the distal end, a polarization analyzer was placed in front of the CCD. The dependence of the emission intensity at the distal end under three different incident polarization orientations on the direction of the analyzer is shown in Fig. 2(a)
Fig. 2 (a) Emission intensity from the distal end of the NW as a function of the analyzer angle for different excitation polarization orientations with respect to the axis of the NW. Plasmonic mode distribution on the Ag NW when the analyzer in front of the CCD detector is (b) parallel and (c) perpendicular to the axis of the NW (The scale bar is 2µm, the double headed arrows indicate the excitation polarization orientation and the dashed arrows indicate the direction of analyzer).
. In the current experimental geometry, only a single mode can be supported in the NW. Thus, the ratio of the scattered intensities in the two orthogonal directions is a characteristic of the single mode, which is independent of the input polarization. At the distal end, the intensity in the parallel direction is 2.5 times stronger than that in the perpendicular direction, which might be attributed to the additional contribution from the depolarized transverse fields collected by the high NA objective. The output polarization is sensitive to the shape of the distal end when high-order modes exist in the NW [16

16. Z. Li, K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, “Correlation between incident and emission polarization in nanowire surface plasmon waveguides,” Nano Lett. 10(5), 1831–1835 (2010). [CrossRef] [PubMed]

]. In contrast to the multimode case, the observed far-field polarization in the distal end is dominantly parallel to the direction of the NW, which is a characteristic of the single mode. As the analyzer in front of the CCD detector is rotated, different polarization components is observed. The parallel (when the direction of the analyzer is parallel to the axis of the NW) and perpendicular (when the analyzer is perpendicular to the axis of the NW) polarization observed in Figs. 2(b) and 2(c) are the scattered electric fields of the NW and collected by the objective. Figures 2(b) and 2(c) therefore correspond to the parallel electric fields located in the center of the NW and the perpendicular electric fields distributed along the edge of the NW, respectively. The different intensity distributions in Figs. 2(b) and 2(c) indicate that these field components originate from two different polarization components with different spatial distributions.

3. Near-field characterization

For a comparison, we employed the finite element method to simulate the field distribution under the same excitation condition. The excitation geometry was depicted in Fig. 1(a) with a Gaussian excitation beam. Optical constants of Ag at wavelength 632.8 nm are taken as refractive index, R.I = 0.1437 + i3.8082 [23

23. C. J. Powell, “Analysis of optical- and inelastic-electron-scattering data. II. application to Al,” J. Opt. Soc. Am. 60(1), 78–93 (1970). [CrossRef]

]. In our case, only the first order modes was excited due to the symmetry breaking when the NW was on the glass substrate [10

10. Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20(17), 19006–19015 (2012). [CrossRef] [PubMed]

]. The electric field components of the plasmonic modes in x and y-directions are shown in Figs. 4(c) and 4(d), respectively. The separation of the intensity peaks is measured as 350 nm, which is slightly larger than the simulation result of 250 nm. This discrepancy might be attributed to the Tien effect [24

24. S. Bourzeix, J. M. Moison, F. Mignard, F. Barthe, A. C. Boccara, C. Licoppe, B. Mersali, M. Allovon, and A. Bruno, “Near-field optical imaging of light propagation in semiconductor waveguide structures,” Appl. Phys. Lett. 73(8), 1035–1037 (1998). [CrossRef]

] considering the refractive-index gradient in the radial direction caused by the quick oxidation of the surface of the Ag NW in air. While, the qualitative agreement between the simulation and experimental results confirms that individual polarization components have been revealed distinctively by the in-plane sensitive probe.

4. Conclusion

In conclusion, we have experimentally investigated the polarization components of the propagating plasmonic mode of the Ag NW waveguide on a glass substrate by the scanning near-field optical microscope. Experimental results in the near-field mapping by an in-plane polarization sensitive probe reveal two orthogonal polarization components of the plasmon modes along the axis of the NW. Our results constitute a comprehensive polarization study of the propagating plasmonic mode of an Ag NW on a dielectric substrate. The polarization feature of the hybrid NW structure discovered here may open up a new avenue for developing polarization-sensitive applications [25

25. X. Li, T.-H. Lan, C.-H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3, 998 (2012). [CrossRef] [PubMed]

] such as optical nano-polarizers.

Acknowledgment

This work was supported by the Australian Research Council (ARC) Laureate Fellowship scheme (FL100100099).

References and links

1.

E. R. Encina, E. M. Perassi, and E. A. Coronado, “Near-field enhancement of multipole plasmon resonances in Ag and Au nanowires,” J. Phys. Chem. A 113(16), 4489–4497 (2009). [CrossRef] [PubMed]

2.

A. Pucci, F. Neubrech, J. Aizpurua, T. Cornelius, and M. Chapelle, “Electromagnetic nanowire resonances for field-enhanced spectroscopy,” in One-Dimensional Nanostructures, Z. Wang, ed. (Springer-New York, 2008).

3.

Y. Fang, Z. Li, Y. Huang, S. Zhang, P. Nordlander, N. J. Halas, and H. Xu, “Branched silver nanowires as controllable plasmon routers,” Nano Lett. 10(5), 1950–1954 (2010). [CrossRef] [PubMed]

4.

S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011). [CrossRef] [PubMed]

5.

Q. Li, S. Wang, Y. Chen, M. Yan, L. Tong, and M. Qiu, “Experimental demonstration of plasmon propagation, coupling, and splitting in silver nanowire at 1550-nm wavelength,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1107–1111 (2011). [CrossRef]

6.

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res. 45(11), 1887–1895 (2012). [CrossRef] [PubMed]

7.

X. Xiong, C.-L. Zou, X.-F. Ren, A.-P. Liu, Y.-X. Ye, F.-W. Sun, and G.-C. Guo, “Silver nanowires for photonics applications ,” Laser & Photo. Rev. doi: (2013). [CrossRef]

8.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010). [CrossRef]

9.

S. Xie, Z. Ouyang, B. Jia, and M. Gu, “Large-size, high-uniformity, random silver nanowire networks as transparent electrodes for crystalline silicon wafer solar cells,” Opt. Express 21(S3), A355–A362 (2013). [CrossRef]

10.

Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20(17), 19006–19015 (2012). [CrossRef] [PubMed]

11.

Q. Li and M. Qiu, “Plasmonic wave propagation in silver nanowires: guiding modes or not?” Opt. Express 21(7), 8587–8595 (2013). [CrossRef] [PubMed]

12.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

13.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996). [CrossRef] [PubMed]

14.

R. Fujimoto, A. Kaneta, K. Okamoto, M. Funato, and Y. Kawakami, “Interference of the surface plasmon polaritons with an Ag waveguide probed by dual-probe scanning near-field optical microscopy,” Appl. Surf. Sci. 258(19), 7372–7376 (2012). [CrossRef]

15.

J. K. Lim, K. Imura, T. Nagahara, S. K. Kim, and H. Okamoto, “Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy,” Chem. Phys. Lett. 412(1-3), 41–45 (2005). [CrossRef]

16.

Z. Li, K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, “Correlation between incident and emission polarization in nanowire surface plasmon waveguides,” Nano Lett. 10(5), 1831–1835 (2010). [CrossRef] [PubMed]

17.

J. Kottmann, O. Martin, D. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64(23), 235402 (2001). [CrossRef]

18.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-out in silver nanowires,” Nano Lett. 6(8), 1822–1826 (2006). [CrossRef] [PubMed]

19.

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, “Directional light emission from propagating surface plasmons of silver nanowires,” Nano Lett. 9(12), 4383–4386 (2009). [CrossRef] [PubMed]

20.

P. Biagioni, D. Polli, M. Labardi, A. Pucci, G. Ruggeri, G. Cerullo, M. Finazzi, and L. Duo, “Unexpected polarization behavior at the aperture of hollow-pyramid near-field probes,” Appl. Phys. Lett. 87(22), 223112 (2005). [CrossRef]

21.

Z. 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]

22.

M. Zhang, J. Du, H. Shi, S. Yin, L. Xia, B. Jia, M. Gu, and C. Du, “Three-dimensional nanoscale far-field focusing of radially polarized light by scattering the SPPs with an annular groove,” Opt. Express 18(14), 14664–14670 (2010). [CrossRef] [PubMed]

23.

C. J. Powell, “Analysis of optical- and inelastic-electron-scattering data. II. application to Al,” J. Opt. Soc. Am. 60(1), 78–93 (1970). [CrossRef]

24.

S. Bourzeix, J. M. Moison, F. Mignard, F. Barthe, A. C. Boccara, C. Licoppe, B. Mersali, M. Allovon, and A. Bruno, “Near-field optical imaging of light propagation in semiconductor waveguide structures,” Appl. Phys. Lett. 73(8), 1035–1037 (1998). [CrossRef]

25.

X. Li, T.-H. Lan, C.-H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3, 998 (2012). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(180.4243) Microscopy : Near-field microscopy
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 6, 2013
Revised Manuscript: June 9, 2013
Manuscript Accepted: June 11, 2013
Published: June 18, 2013

Virtual Issues
Vol. 8, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Priyamvada Venugopalan, Qiming Zhang, Xiangping Li, and Min Gu, "Polarization-sensitive characterization of the propagating plasmonic modes in silver nanowire waveguide on a glass substrate with a scanning near-field optical microscope," Opt. Express 21, 15247-15252 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-13-15247


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References

  1. E. R. Encina, E. M. Perassi, and E. A. Coronado, “Near-field enhancement of multipole plasmon resonances in Ag and Au nanowires,” J. Phys. Chem. A113(16), 4489–4497 (2009). [CrossRef] [PubMed]
  2. A. Pucci, F. Neubrech, J. Aizpurua, T. Cornelius, and M. Chapelle, “Electromagnetic nanowire resonances for field-enhanced spectroscopy,” in One-Dimensional Nanostructures, Z. Wang, ed. (Springer-New York, 2008).
  3. Y. Fang, Z. Li, Y. Huang, S. Zhang, P. Nordlander, N. J. Halas, and H. Xu, “Branched silver nanowires as controllable plasmon routers,” Nano Lett.10(5), 1950–1954 (2010). [CrossRef] [PubMed]
  4. S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett.107(9), 096801 (2011). [CrossRef] [PubMed]
  5. Q. Li, S. Wang, Y. Chen, M. Yan, L. Tong, and M. Qiu, “Experimental demonstration of plasmon propagation, coupling, and splitting in silver nanowire at 1550-nm wavelength,” IEEE J. Sel. Top. Quantum Electron.17(4), 1107–1111 (2011). [CrossRef]
  6. S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res.45(11), 1887–1895 (2012). [CrossRef] [PubMed]
  7. X. Xiong, C.-L. Zou, X.-F. Ren, A.-P. Liu, Y.-X. Ye, F.-W. Sun, and G.-C. Guo, “Silver nanowires for photonics applications,” Laser & Photo. Rev. doi: (2013). [CrossRef]
  8. C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett.97(18), 183102 (2010). [CrossRef]
  9. S. Xie, Z. Ouyang, B. Jia, and M. Gu, “Large-size, high-uniformity, random silver nanowire networks as transparent electrodes for crystalline silicon wafer solar cells,” Opt. Express21(S3), A355–A362 (2013). [CrossRef]
  10. Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express20(17), 19006–19015 (2012). [CrossRef] [PubMed]
  11. Q. Li and M. Qiu, “Plasmonic wave propagation in silver nanowires: guiding modes or not?” Opt. Express21(7), 8587–8595 (2013). [CrossRef] [PubMed]
  12. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95(25), 257403 (2005). [CrossRef] [PubMed]
  13. B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett.77(9), 1889–1892 (1996). [CrossRef] [PubMed]
  14. R. Fujimoto, A. Kaneta, K. Okamoto, M. Funato, and Y. Kawakami, “Interference of the surface plasmon polaritons with an Ag waveguide probed by dual-probe scanning near-field optical microscopy,” Appl. Surf. Sci.258(19), 7372–7376 (2012). [CrossRef]
  15. J. K. Lim, K. Imura, T. Nagahara, S. K. Kim, and H. Okamoto, “Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy,” Chem. Phys. Lett.412(1-3), 41–45 (2005). [CrossRef]
  16. Z. Li, K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, “Correlation between incident and emission polarization in nanowire surface plasmon waveguides,” Nano Lett.10(5), 1831–1835 (2010). [CrossRef] [PubMed]
  17. J. Kottmann, O. Martin, D. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B64(23), 235402 (2001). [CrossRef]
  18. A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-out in silver nanowires,” Nano Lett.6(8), 1822–1826 (2006). [CrossRef] [PubMed]
  19. Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, “Directional light emission from propagating surface plasmons of silver nanowires,” Nano Lett.9(12), 4383–4386 (2009). [CrossRef] [PubMed]
  20. P. Biagioni, D. Polli, M. Labardi, A. Pucci, G. Ruggeri, G. Cerullo, M. Finazzi, and L. Duo, “Unexpected polarization behavior at the aperture of hollow-pyramid near-field probes,” Appl. Phys. Lett.87(22), 223112 (2005). [CrossRef]
  21. Z. 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]
  22. M. Zhang, J. Du, H. Shi, S. Yin, L. Xia, B. Jia, M. Gu, and C. Du, “Three-dimensional nanoscale far-field focusing of radially polarized light by scattering the SPPs with an annular groove,” Opt. Express18(14), 14664–14670 (2010). [CrossRef] [PubMed]
  23. C. J. Powell, “Analysis of optical- and inelastic-electron-scattering data. II. application to Al,” J. Opt. Soc. Am.60(1), 78–93 (1970). [CrossRef]
  24. S. Bourzeix, J. M. Moison, F. Mignard, F. Barthe, A. C. Boccara, C. Licoppe, B. Mersali, M. Allovon, and A. Bruno, “Near-field optical imaging of light propagation in semiconductor waveguide structures,” Appl. Phys. Lett.73(8), 1035–1037 (1998). [CrossRef]
  25. X. Li, T.-H. Lan, C.-H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun.3, 998 (2012). [CrossRef] [PubMed]

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