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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 19060–19066
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Deep subwavelength confinement and giant enhancement of light field by a plasmonic lens integrated with a metal-insulator-metal vertical nanocavity

Song Yue, Zhi Li, Jianjun Chen, and Qihuang Gong  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 19060-19066 (2012)
http://dx.doi.org/10.1364/OE.20.019060


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Abstract

A metal-insulator-metal vertical nanocavity is proposed to be integrated at the center of a plasmonic lens. Utilizing cavity resonance effect, the light intensity at the center of the integrated plasmonic lens gets enhancement up to 5500 times compared to that without the cavity, and the light field is tightly confined into a spot as small as 6.0 × 10−3λ02. The Purcell factor of the cavity reaches up to 1400, ensuring greatly enhanced light-matter interaction inside the cavity. Moreover, the proposed structure takes advantage of linearly polarized light excitation and easy fabrication.

© 2012 OSA

1. Introduction

2. Cavity resonance effect for field enhancement and confinement

The proposed structure is schematically shown in Fig. 1
Fig. 1 Schematic of the integrated structure, a rectangular shallow groove locates at the center of a PL. The incident light is linearly polarized along the X direction, and converging SPPs are supposed to excite the MIM waveguide mode in the central groove, which will be reflected back and forth to form a vertical cavity.
, which is an integration of a conventional PL and a rectangular shallow groove. In an optically thick Au film, a transparent circular slit etched from the upper Au-film surface down to the glass substrate serves as the PL. When X-direction linearly polarized light is normally incident upon the sample from the substrate side, SPPs at the upper Au surface will be effectively excited by the nanoslit and focused towards the center. At the center of the PL, a rectangular shallow groove etched from the upper surface not throughout but to a certain depth of the Au film, serves as the MIM vertical cavity. The converging SPPs at the edges of the groove are supposed to excite the MIM waveguide mode in the groove [14

14. Y. X. Cui and S. L. He, “Enhancing extraordinary transmission of light through a metallic nanoslit with a nanocavity antenna,” Opt. Lett. 34(1), 16–18 (2009). [CrossRef] [PubMed]

], which will be reflected back and forth between the bottom and top of the groove, resulting in a MIM vertical cavity. Under proper conditions, the cavity is on resonance, with the light field tightly confined and locally enhanced. Such a structure was analyzed numerically using finite element method (FEM, COMSOL Multiphysics) under an incident wavelength λ0 of 830 nm, where the refractive index of Au is 0.08 + 5i [15

15. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

]. In the paper, the ring diameter D and slit width w are fixed to 5 μm and 100 nm, which are common parameters for a conventional PL. Au film thickness T is chosen to be 750 nm, so that the thickness from the bottom of the groove to the substrate is much more than the penetration depth, preventing direct transmission of substrate-side-incident light. Groove gap width g is fixed to 20 nm, adapted from common literatures in order to form a pronounced MIM waveguide mode [16

16. G. Veronis and S. H. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005). [CrossRef] [PubMed]

] and ensure tight field confinement.

In order to illustrate the field enhancement effect of the central cavity, light intensity (|E|2) 10nm above the Au surface at the center of the PL without the central groove is used as the reference and set as the unit 1. Under the same PL geometry and illumination condition, a central groove with varying length L and depth h is added. The light intensity 10nm above the Au surface at the center is extracted and normalized with respect to the reference, and its variation with groove depth h is shown in Fig. 2(a)
Fig. 2 (a) Light intensity (|E|2) enhancement with respect to the geometric parameters of the central groove, green diamonds, black squares, red circles and blue triangles correspond to grooves with a length of 150 nm, 200 nm, 350 nm and 500 nm, respectively. Arrows marked by b and c correspond to the first and second peak in the L350 nm-curve. Field distribution (|E|) corresponds to cross sections along the yz-plane for a groove with a depth of (b) 90 nm and (c) 345 nm, showing the first and second order resonance mode. (d) Field distribution (|E|) corresponds to cross section along the xz-plane for a groove with the length of 350nm and depth of 90 nm, showing the accumulated charges at the sharp corners of the vertical cavity. White arrows indicate the electric field distribution.
, for certain groove lengths. On a first glance, at proper groove dimensions, the light intensity at the center of the PL with the central groove could be enhanced by at least 3 orders of magnitude compared to that of a PL without groove. Another distinct feature is that the enhancement presents pronounced geometric resonance behavior, shown as several resonance peaks in the curves. Typical resonant field distributions (|E|) corresponding to the first and second peaks of the L350 nm-curve marked by arrows b and c in Fig. 2(a) are displayed in Figs. 2(b) and 2(c). Obvious standing wave patterns corresponding to the first and second order resonances are recognized, implying that the groove behaves as a vertical cavity.

Such a vertical cavity is excited by converging SPPs residing at the edges of the central groove. When X-direction linearly polarized light impinges the PL, SPPs are excited and focused to the center by the circular nanoslit. Due to the symmetry of the PL and the linear polarization of the incident light, charges with opposite signs will accumulate at both sides of the central groove [8

8. 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]

]. The accumulated charges at the sharp corners act efficiently as a dipole source, exciting the symmetric MIM waveguide mode of the groove, as illustrated in Fig. 2(d). Here, the matching of the mirror symmetry of the structure by using linearly polarized light is essential in the excitation scheme, while circularly and radially polarized light can hardly excite the symmetric MIM waveguide mode. The excited SPPs inside the groove will then be reflected back and forth between the bottom and top of the groove, forming a Fabry-Pérot (F-P) cavity. The resonance condition should be
4πh/λSPP+θ1+θ2=2πN (1),
where h is the cavity depth, λSPP is the wavelength of the guided SPPs inside the groove, and θ1, 2 are reflection phases from the bottom and top of the cavity, N is an integer. It is easy to find that the period of resonances with respect to cavity depth h should be λSPP/2. To verify this point, we performed 2D simulations to obtain the eigenmode of the SPPs in the rectangular MIM waveguides with a given rectangular width g of 20 nm and varying length L, corresponding to the xy-plane cross section of the central groove. The resulting effective refractive index neff of the symmetric MIM waveguide mode are shown in Fig. 3
Fig. 3 Effective refractive index neff of the symmetric MIM waveguide mode for different groove length L, with a given groove width g of 20 nm. Stars mark the data correspond to the grooves with a length L of 200 nm, 350 nm and 500 nm, respectively. Inset shows the geometry of the simulated rectangular MIM waveguide.
. The effective refractive index is 1.64 and 1.80 for 350 nm- and 500 nm-long grooves, and corresponding half the effective SPP wavelength (λspp/2) is 253 nm and 231 nm, respectively. They consist well with the periods in Fig. 2(a) (distances between consecutive peaks are 255 nm and 230 nm for groove lengths of 350 nm and 500 nm, respectively). This quantitative accordance well verifies the MIM vertical cavity model. For the groove length L of 200 nm, λspp/2 is about 488 nm deduced from Fig. 3, so the second resonance peak should appear at a groove depth h of about 668 nm, which is beyond the range in Fig. 2(a).

3. Optimization of cavity geometry and its performance

On cavity resonance, the electromagnetic field gains great enhancement at the center of the PL. The cavity dimension could be optimized to get the best performance with respect to field confinement and enhancement. From the result in Fig. 2(a), it is noticed that the enhancement factor drops down with increasing cavity depth for a given groove length (this is also true for the groove length L of 200 nm, which gives a decreased enhancement factor of 1626 at the second order resonance, although the data is not shown in Fig. 2(a)). This is because the resonant field at the upper surface of the groove mainly comes from the constructive interference of the guided SPPs in the cavity of different round trips. A deeper groove means longer travel distance for a round trip and correspondingly more propagation loss of the guided SPPs. So that the SPP intensities of different round trips decay faster with increasing groove depth, resulting in less total field intensity. Besides, shallower groove means easier fabrication. So it is better to choose the first order resonance depth. Concerning to the groove length, shorter groove length implies better field confinement in the Y-direction. Due to the increase in confinement, energy density increases, resulting in higher field enhancement, which could be noticed in Fig. 2(a) for the first order resonances. Thus, it is better to choose a shorter groove length. However, from the 2D simulation result in Fig. 3, it is suggested that the groove length could not be too small because the MIM waveguide mode will be cut-off below a groove length of about 180 nm. Below the cut-off dimension, the cavity cannot obtain resonant enhancement effect. A cavity with a length of 150 nm is calculated as an example, and the enhancement factor is depicted as green diamonds in Fig. 2(a). It is obvious that such a cavity does not show pronounced resonant effect, and the enhancement factor is always low. From the above analysis, first order resonance depth with a properly short groove length should be chosen as the optimized geometry. Here, we choose a cavity with a groove length of 200 nm, ensuring no cut-off, with its first order resonance depth of 180 nm. Under this cavity resonance condition, the light intensity enhancement factor reaches up to 5455, and the field distribution 10 nm above the Au film is shown as solid curves in Fig. 4
Fig. 4 Light intensity distribution (|E|2) 10 nm above the Au film along the (a) X- and (b) Y-directions. Solid curves stand for the PL with dimension-optimized cavity, and dashed curves stand for the conventional PL under radial polarization excitation. Insets show the schematic.
. The full-width at half-maximum (FWHM) widths for X- and Y-directions are 33.6 nm and 122 nm, respectively, which means the integrated PL could focus the SPPs into a lateral spot as small as 6.0 × 10−3 λ02, truly deep subwavelength in size. For comparison, the focal field distribution of a conventional PL under radial polarization excitation is displayed by the dashed curves in Fig. 4. The FWHM widths for both X- and Y-directions of the focus are 288 nm, which means a lateral spot size of 0.12λ02, about 20 times as large as that of the with cavity case.

The enhancement and confinement effect of the central cavity can also be evaluated by using Purcell factor, an important quantity to evaluate the performance of a cavity. The Purcell factor Fp is calculated by the following equation:
Fp=34π2(λcn)3(QVm) (2),
where λc is the resonant wavelength of the cavity, n is the refractive index of the dielectric medium inside the cavity, Q is the quality factor of the cavity and Vm is the effective mode volume. For the geometry-optimized cavity, the normalized spectrum response was calculated around the resonance peak of 830 nm with result shown in Fig. 5
Fig. 5 Normalized spectrum response of the geometry-optimized cavity.
. The central wavelength λ0 is 830 nm and the FWHM width of the resonance peak Δλ is 34.6 nm, so that the quality factor Q is calculated to be about 24 according to the relation Q = λ0λ. The mode volume could be estimated by the cavity geometric volume, because the mode is well confined by the metallic cavity here. Thus the estimated Purcell factor of the geometry-optimized cavity reaches up to 1400. Such a large Purcell factor ensures strong light-matter interactions inside the cavity, and nonlinear optical effects like high harmonic generation and enhanced fluorescence from single quantum emitter could be expected. The intense local field achieved here could find other applications such as SERS and vertical emission on-chip metal cavity lasers, etc. Additional benefit of the structure includes improved signal to noise ratio in enhanced spectroscopy, because the direct transmission of the excitation light at the cavity position is absent due to the thick bottom of the metal cavity.

The light intensity at the center of the integrated PL could be further enhanced. The integrated PL structure could be viewed as a tandem antenna made up of a receiving antenna (PL) and an energy storing antenna (MIM cavity), and the excitation of the cavity mode could be viewed as a two-step process. First, the PL converts part of the far-field incident energy into near-field region by exciting SPP; second, the converging SPP excite the cavity resonance mode. Thus, by engaging multiple rings instead of a single ring as a resonant effect in the receiving process, more far-field energy could be converted to the near-field, and further enhancement of the focal field could be achieved. For instance, if the PL is made up of ten concentric rings [17

17. 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]

] with a period of 814 nm, which equals to the SPP wavelength at the Au/air interface, the same cavity gives an enhancement factor up to 7.08 × 104, which is 13 times larger than that of the single ring with cavity case. Here, we still use the light intensity 10 nm above the gold film at the center of the single ring plasmonic lens as the reference to illustrate the advantage of multiple rings in the light receiving process.

Last, one practical advantage of the proposed structure is that it is easy to fabricate, for example, directly using focused ion-beam (FIB) milling method. The quality of the fabricated cavity may be influenced by the inhomogeneity of the Au film. However, one can also choose other methods such as template stripping (TS) to fabricate the proposed structure. Ultrafine and smooth metal nanocavities with high aspect ratio could be fabricated with such a method [18

18. X. L. Zhu, Y. Zhang, J. S. Zhang, J. Xu, Y. Ma, Z. Y. Li, and D. P. Yu, “Ultrafine and smooth full metal nanostructures for plasmonics,” Adv. Mater. (Deerfield Beach Fla.) 22(39), 4345–4349 (2010). [CrossRef] [PubMed]

, 19

19. X. L. Zhu, J. S. Zhang, J. Xu, and D. P. Yu, “Vertical plasmonic resonant nanocavities,” Nano Lett. 11(3), 1117–1121 (2011). [CrossRef] [PubMed]

], where the upper surface of the Au film is quite smooth and the rectangular shape of the sharp corners of the cavity is warrantable. Thus, it is now possible to fabricate the proposed structure with high quality.

4. Conclusion

In summary, an integrated PL composed of a MIM vertical cavity at the center of a conventional PL is proposed. Utilizing cavity resonance effect, the light intensity at the center get enhancement up to 5500 times compared to that without the cavity, while the light field could be tightly confined into deep subwavelength scale with a spot size as small as 6.0 × 10−3 λ02 simultaneously. The Purcell factor of the cavity reaches 1400, which enables strongly enhanced optical nonlinearity inside the cavity. With the benefit of confined and enhanced local field, such an integrated PL could find potential important applications from trace detection of chemical and bio-molecules to vertical emission on-chip metal cavity lasers. Linearly polarized light excitation is crucial in this scheme and brings convenience to its application, avoiding the use of radially polarized light and precise alignment of the center of the PL and the center of the excitation beam. Moreover, the fabrication of the proposed structure is quite straightforward.

Acknowledgments

This work was supported by the National Basic Research Program of China (Grant Nos. 2009CB930504 and 2007CB307001) and the National Natural Science Foundation of China (Grant Nos. 10804004, 11121091, 11134001 and 90921008).

References and links

1.

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

2.

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

3.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]

4.

B. A. Liu, D. X. Wang, C. Shi, K. B. Crozier, and T. Yang, “Vertical optical antennas integrated with spiral ring gratings for large local electric field enhancement and directional radiation,” Opt. Express 19(11), 10049–10056 (2011). [CrossRef] [PubMed]

5.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

6.

S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and superlensing,” Nat. Photonics 3(7), 388–394 (2009). [CrossRef]

7.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009). [CrossRef] [PubMed]

8.

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]

9.

Z. Y. Fang, Q. Peng, W. T. Song, F. H. Hao, J. Wang, P. Nordlander, and X. Zhu, “Plasmonic focusing in symmetry broken nanocorrals,” Nano Lett. 11(2), 893–897 (2011). [CrossRef] [PubMed]

10.

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]

11.

A. Normatov, P. Ginzburg, N. Berkovitch, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Efficient coupling and field enhancement for the nano-scale: plasmonic needle,” Opt. Express 18(13), 14079–14086 (2010). [CrossRef] [PubMed]

12.

G. H. Rui, W. B. Chen, Y. H. Lu, P. Wang, H. Ming, and Q. W. Zhan, “Plasmonic near-field probe using the combination of concentric rings and conical tip under radial polarization illumination,” J. Opt. 12(3), 035004 (2010). [CrossRef]

13.

P. Ginzburg, A. Nevet, N. Berkovitch, A. Normatov, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Plasmonic resonance effects for tandem receiving-transmitting nanoantennas,” Nano Lett. 11(1), 220–224 (2011). [CrossRef] [PubMed]

14.

Y. X. Cui and S. L. He, “Enhancing extraordinary transmission of light through a metallic nanoslit with a nanocavity antenna,” Opt. Lett. 34(1), 16–18 (2009). [CrossRef] [PubMed]

15.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

16.

G. Veronis and S. H. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005). [CrossRef] [PubMed]

17.

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]

18.

X. L. Zhu, Y. Zhang, J. S. Zhang, J. Xu, Y. Ma, Z. Y. Li, and D. P. Yu, “Ultrafine and smooth full metal nanostructures for plasmonics,” Adv. Mater. (Deerfield Beach Fla.) 22(39), 4345–4349 (2010). [CrossRef] [PubMed]

19.

X. L. Zhu, J. S. Zhang, J. Xu, and D. P. Yu, “Vertical plasmonic resonant nanocavities,” Nano Lett. 11(3), 1117–1121 (2011). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(140.3945) Lasers and laser optics : Microcavities
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 22, 2012
Revised Manuscript: July 19, 2012
Manuscript Accepted: July 20, 2012
Published: August 3, 2012

Citation
Song Yue, Zhi Li, Jianjun Chen, and Qihuang Gong, "Deep subwavelength confinement and giant enhancement of light field by a plasmonic lens integrated with a metal-insulator-metal vertical nanocavity," Opt. Express 20, 19060-19066 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-19060


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References

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
  3. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1(11), 641–648 (2007). [CrossRef]
  4. B. A. Liu, D. X. Wang, C. Shi, K. B. Crozier, and T. Yang, “Vertical optical antennas integrated with spiral ring gratings for large local electric field enhancement and directional radiation,” Opt. Express19(11), 10049–10056 (2011). [CrossRef] [PubMed]
  5. J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010). [CrossRef] [PubMed]
  6. S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and superlensing,” Nat. Photonics3(7), 388–394 (2009). [CrossRef]
  7. P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature459(7245), 410–413 (2009). [CrossRef] [PubMed]
  8. 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]
  9. Z. Y. Fang, Q. Peng, W. T. Song, F. H. Hao, J. Wang, P. Nordlander, and X. Zhu, “Plasmonic focusing in symmetry broken nanocorrals,” Nano Lett.11(2), 893–897 (2011). [CrossRef] [PubMed]
  10. 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]
  11. A. Normatov, P. Ginzburg, N. Berkovitch, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Efficient coupling and field enhancement for the nano-scale: plasmonic needle,” Opt. Express18(13), 14079–14086 (2010). [CrossRef] [PubMed]
  12. G. H. Rui, W. B. Chen, Y. H. Lu, P. Wang, H. Ming, and Q. W. Zhan, “Plasmonic near-field probe using the combination of concentric rings and conical tip under radial polarization illumination,” J. Opt.12(3), 035004 (2010). [CrossRef]
  13. P. Ginzburg, A. Nevet, N. Berkovitch, A. Normatov, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Plasmonic resonance effects for tandem receiving-transmitting nanoantennas,” Nano Lett.11(1), 220–224 (2011). [CrossRef] [PubMed]
  14. Y. X. Cui and S. L. He, “Enhancing extraordinary transmission of light through a metallic nanoslit with a nanocavity antenna,” Opt. Lett.34(1), 16–18 (2009). [CrossRef] [PubMed]
  15. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).
  16. G. Veronis and S. H. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett.30(24), 3359–3361 (2005). [CrossRef] [PubMed]
  17. 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. Express14(12), 5664–5670 (2006). [CrossRef] [PubMed]
  18. X. L. Zhu, Y. Zhang, J. S. Zhang, J. Xu, Y. Ma, Z. Y. Li, and D. P. Yu, “Ultrafine and smooth full metal nanostructures for plasmonics,” Adv. Mater. (Deerfield Beach Fla.)22(39), 4345–4349 (2010). [CrossRef] [PubMed]
  19. X. L. Zhu, J. S. Zhang, J. Xu, and D. P. Yu, “Vertical plasmonic resonant nanocavities,” Nano Lett.11(3), 1117–1121 (2011). [CrossRef] [PubMed]

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