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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23603–23609
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Hybrid long-range surface plasmon-polariton modes with tight field confinement guided by asymmetrical waveguides

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


Optics Express, Vol. 17, Issue 26, pp. 23603-23609 (2009)
http://dx.doi.org/10.1364/OE.17.023603


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Abstract

A finite width dielectric-metal-dielectric (DMD) waveguide placed on a substrate is numerically investigated near the telecom wavelength λ = 1550 nm by the finite element method. With proper waveguide sizes, the asymmetrical DMD waveguide can support hybrid long-range surface plasmon-polariton modes which have tight field confinement (~700 nm) and long propagation lengths (L> 300 μm) simultaneously. Compact plasmonic waveguide-ring resonators (WRRs) based on such asymmetrical DMD waveguide show high quality factors compared with dielectric-loaded surface plasmon-polariton, channel plasmon polariton, plasmonic whispering-gallery microcavity, and pure dielectric waveguide cases.

© 2009 OSA

1. Introduction

Future photonic integrated circuits for optical information will have specific requirements on the density of integration. Surface plasmon plaritons [1

1. H. Raether, Surface plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).

] (SPPs), which can break the diffraction limit of light due to their tight field confinement to the metal surface, show great promise for applications in highly photonic integrated circuits [2

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

,3

3. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1(7), 402–406 (2007). [CrossRef]

]. Various waveguides and photonic devices based on SPPs have been reported in recent years [4

4. D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal-Films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981). [CrossRef]

12

12. Y. Binfeng, H. Guohua, and C. Yiping, “Bound modes analysis of symmetric dielectric loaded surface plasmon-polariton waveguides,” Opt. Express 17(5), 3610–3618 (2009). [CrossRef] [PubMed]

]. Among them, long-range surface plasmon-polariton (LRSPP) modes guided by thin metal stripes embedded in infinite homogeneous background dielectrics play an importance role for their long propagation lengths up to ~mm [4

4. D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal-Films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981). [CrossRef]

,5

5. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25(11), 844–846 (2000). [CrossRef] [PubMed]

]. However, the field confinement of LRSPP modes are very poor (effective mode sizes ~10 μm [5

5. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25(11), 844–846 (2000). [CrossRef] [PubMed]

8

8. A. Degiron, S. Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]

]), which brings large bend loss in tight radius structures (~μm), and the optimal bend radius is as large as about 10 mm [7

7. P. Berini, “Long-range surface plasmon-polariton waveguides in silica,” J. Appl. Phys. 102(5), 053105 (2007). [CrossRef]

,8

8. A. Degiron, S. Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]

]. In order to get higher densities of integration, dielectric-loaded surface plasmon-plariton (DLSPP) waveguides with strong field confinement (effective mode sizes ~1 μm) were proposed and demonstrated [9

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

11

11. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]

]. Due to the tight field confinement, the optimal bend radius of DLSPP waveguides is reduced to about 5 μm [10

10. A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]

,11

11. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]

]. While, the propagation lengths of DLSPP modes (~45 μm) [9

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

11

11. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]

] decreased significantly compared to LRSPP modes because the portion of electromagnetic field distributed in the lossy metal film increases greatly. SPP modes with both tight field confinement and long propagation lengths in a symmetrical waveguide structure have recently been presented theoretically [12

12. Y. Binfeng, H. Guohua, and C. Yiping, “Bound modes analysis of symmetric dielectric loaded surface plasmon-polariton waveguides,” Opt. Express 17(5), 3610–3618 (2009). [CrossRef] [PubMed]

]. But the difficulty to fabricate the symmetrical structure limits its real applications.

Here, by combining both merits of LRSPP and DLSPP modes, we numerically investigate a hybrid plasmonic waveguide, the finite width dielectric-metal-dielectric (DMD) waveguide placed on a substrate. Such asymmetrical DMD waveguide structure may be easily realized in experiments [13

13. K. Preston and M. Lipson, “Slot waveguides with polycrystalline silicon for electrical injection,” Opt. Express 17(3), 1527–1534 (2009). [CrossRef] [PubMed]

,14

14. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]

] and the hybrid property provides flexibility in the design of plasmonic circuits. Numerical simulations show that, with proper waveguide sizes, the hybrid LRSPP modes guided by the asymmetrical DMD waveguide exhibit tight field confinement (~700 nm) and long propagation lengths (>300 μm)) simultaneously. To show the advantage of such an asymmetrical DMD waveguide, compact and high performance waveguide-ring resonators (WRRs) base on the waveguide are simulated as a demonstration.

2. Hybrid LRSPP mode guided by the finite width symmetrical DMD waveguide without a substrate

To illustrate the propagation characteristics of the waveguide, the finite width symmetrical DMD waveguide without a substrate is simulated first. The waveguide structure is schematically shown in Fig. 1(a)
Fig. 1 (a) Schematic of the finite width symmetrical DMD waveguide without a substrate. (b) Electric field (E y) distribution of the hybrid LRSPP mode in the symmetrical DMD waveguide with w = 600 nm and h = 800 nm.
, which consists of a thin metal strip (Au) with thickness t and finite width w symmetrically embedded inside a dielectric ridge with thickness h and width w surrounded by air. A similar symmetrical DMD structure surrounded by a low index cladding has been discussed before [15

15. R. Adato and J. Guo, “Modification of dispersion, localization, and attenuation of thin metal stripe symmetric surface plasmon-polariton modes by thin dielectric layers,” J. Appl. Phys. 105(3), 034306 (2009). [CrossRef]

], and it has been found that the higher refractive index dielectric layers in combination with the low index cladding can achieve tight mode confinement which cannot be obtained by using either a high or low index homogeneous dielectric cladding. The main difference for the structure in Fig. 1(a) is that the low index cladding is replaced by the air, which ensures even tighter mode confinement and better bending characteristic. For such a symmetrical structure, there exists a hybrid LRSPP mode [8

8. A. Degiron, S. Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]

] which is a combination of the pure LRSPP mode and waveguide mode of the dielectric ridge. Here, we choose a high refractive index dielectric (Si3N4) as the ridge, so the hybrid LRSPP mode can be confined in the core of the DMD waveguide well due to the large refractive index difference between Si3N4 and the air.

In the letter, we mainly focus on the hybrid LRSPP modes for their long propagation lengths. In highly photonic integrated circuits, both the field confinement and the propagation length are important factors. To satisfy both these two aspects, simulations show that waveguide with moderate dimensions (width from about 600 to 800 nm and thickness from about 700 to 900 nm) is appropriate. As an example, with width w = 600 nm and thickness h = 800 nm, the hybrid LRSPP mode performs simultaneously a tight field confinement (effective mode sizes along the x-axis and the y-axis are W x = 726 nm and W y = 670 nm respectively) and a long propagation length (L = 300 μm, while the propagation length of SPP along a single Au/Si3N4 interface is only 41 μm.). Here the effective mode size is defined as the distance over which the field decreases down to 1/e of its maximum value. The corresponding distribution of the electric field (E y) of the hybrid LRSPP mode is displayed in Fig. 1(b), and it is noted that the electromagnetic field is localized in the core of the DMD waveguide very well.

3. Hybrid LRSPP mode guided by the asymmetrical DMD waveguide with a substrate

The solid lines in Fig. 2(b) display the calculated dependences of the effective refractive index and the propagation length of the hybrid LRSPP mode on the adjustable Si3N4 thickness below the Au strip h down. The propagation length reaches to its maximum (L = 321 μm) at h down = 310 nm. The electromagnetic field at this point [see Fig. 2(c)] is almost symmetrically distributed with respect to the thin Au strip. This symmetrical field distribution means that by adjusting h down to the proper value the dielectric environments in the asymmetrical DMD waveguides can also satisfy the index-matching condition, thus the propagation length of the hybrid LRSPP mode is the longest. At this maximum point, important properties of the hybrid LRSPP mode like the field confinement (W x = 726 nm and W y = 647 nm), the effective refractive index (n eff = 1.63), and the propagation length (L = 321 μm) are all very close to their values in the symmetrical DMD waveguide case. Thus, by choosing the thickness of the Si3N4 ridge below the Au strip, the experimentally realizable asymmetrical DMD waveguide with the substrate can perform as the ideal symmetrical DMD waveguide in the air. From Fig. 2(b), it is also noticed that a small thickness deviation from the maximum point (e.g. Δh down = ± 30 nm) will not bring large propagation loss, which means the requirement on the thickness h down to achieve long propagation lengths is not critical. To ensure single-mode operation, the propagation characteristics of the first waveguide mode (TE polarized, and it mainly distributed in the bottom part of the Si3N4 ridge) are also calculated. The cutoff thickness for the first waveguide mode is h down = 594 nm [see the dashed lines in Fig. 2(b)] when w and h up are fixed at 600 nm and 400 nm respectively. The cutoff width for the high order SPP mode (first order hybrid LRSPP) is w = 1011 nm when the thicknesses of the Si3N4 ridge are fixed at h up = 400 nm and h down = 310 nm. Both the two dimensions of the Si3N4 ridge for supporting the first waveguide mode and high order SPP mode are far beyond the maximum point of the hybrid LRSPP mode.

4. WRRs of high performance based on the asymmetrical DMD waveguide

Adding 20 nm Si3N4 film to the pure dielectric waveguide to achieve exactly the same cross section of ridges doesn’t affect the conclusion above. For example, at r = 3 μm, the hybrid LRSPP resonator has Q spp = 470, when changing the metal film to Si3N4 film, the pure dielectric waveguide resonator has Q die = 287, and Q spp/Q die = 1.64, which is very close to 1.8 as calculated in Fig. 3(b).

Next, let us further clarify the role of the metal stripe in improving the bending characteristic of the waveguide. When the size of the dielectric ridge is large, the electromagnetic field can be well confined in the dielectric ridge, so adding a metal stripe to this ridge cannot improve its lateral confinement and bending characteristics. However, in order to improve density of integration and avoid the multimode, waveguide with small ridge size (<1000 nm) is much more important in applications. In this case, the effective refractive index of the pure dielectric waveguide is still much greater than the refractive index of the air, but it is close to the refractive index of the substrate. So the electromagnetic field distributed in the substrate increases with decreasing the dimension of the dielectric ridge, which can result in large radiation loss in tight radius structures. While, as we known, SPP has larger effective refractive index and stronger field confinement, so adding a metal stripe to support hybrid LRSPP can decease the proportion of the electromagnetic field distributed in the substrate and decrease the radiation loss significantly. That’s why the hybrid LRSPP based WRR possesses higher Q factor than the pure dielectric waveguide case [as shown in Fig. 3(b)] despite of the SPP ohmic loss. The above result implies that metal structure and SPP can improve the device performance in the small structure size region. And since strong lateral confinement and tight radius structures both can improve the density of integration, the asymmetrical DMD waveguide may have wide and important applications in the field of highly integrated optics.

5. Conclusion

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 10821062 and 10804004), the National Basic Research Program of China (Grant Nos. 2007CB307001), and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200800011023).

References and links

1.

H. Raether, Surface plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).

2.

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

3.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1(7), 402–406 (2007). [CrossRef]

4.

D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal-Films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981). [CrossRef]

5.

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25(11), 844–846 (2000). [CrossRef] [PubMed]

6.

I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation,” Appl. Phys. Lett. 88(5), 051119 (2006). [CrossRef]

7.

P. Berini, “Long-range surface plasmon-polariton waveguides in silica,” J. Appl. Phys. 102(5), 053105 (2007). [CrossRef]

8.

A. Degiron, S. Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]

9.

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

10.

A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]

11.

T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]

12.

Y. Binfeng, H. Guohua, and C. Yiping, “Bound modes analysis of symmetric dielectric loaded surface plasmon-polariton waveguides,” Opt. Express 17(5), 3610–3618 (2009). [CrossRef] [PubMed]

13.

K. Preston and M. Lipson, “Slot waveguides with polycrystalline silicon for electrical injection,” Opt. Express 17(3), 1527–1534 (2009). [CrossRef] [PubMed]

14.

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]

15.

R. Adato and J. Guo, “Modification of dispersion, localization, and attenuation of thin metal stripe symmetric surface plasmon-polariton modes by thin dielectric layers,” J. Appl. Phys. 105(3), 034306 (2009). [CrossRef]

16.

E. D. Palik, Handbook of Optical Constants of Solids, 1st ed. (Academic, New York, 1985).

17.

R. Slavík and J. Homola, “Optical multilayers for LED-based surface plasmon resonance sensors,” Appl. Opt. 45(16), 3752–3759 (2006). [CrossRef] [PubMed]

18.

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007). [CrossRef]

19.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]

20.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

21.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63(12), 125417 (2001). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.7390) Optical devices : Waveguides, planar
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 29, 2009
Revised Manuscript: December 3, 2009
Manuscript Accepted: December 6, 2009
Published: December 9, 2009

Citation
Jianjun Chen, Zhi Li, Song Yue, and Qihuang Gong, "Hybrid long-range surface plasmon-polariton modes with tight field confinement guided by asymmetrical waveguides," Opt. Express 17, 23603-23609 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23603


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References

  1. H. Raether, Surface plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  3. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1(7), 402–406 (2007). [CrossRef]
  4. D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal-Films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981). [CrossRef]
  5. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25(11), 844–846 (2000). [CrossRef] [PubMed]
  6. I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation,” Appl. Phys. Lett. 88(5), 051119 (2006). [CrossRef]
  7. P. Berini, “Long-range surface plasmon-polariton waveguides in silica,” J. Appl. Phys. 102(5), 053105 (2007). [CrossRef]
  8. A. Degiron, S. Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]
  9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]
  10. A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008). [CrossRef]
  11. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]
  12. Y. Binfeng, H. Guohua, and C. Yiping, “Bound modes analysis of symmetric dielectric loaded surface plasmon-polariton waveguides,” Opt. Express 17(5), 3610–3618 (2009). [CrossRef] [PubMed]
  13. K. Preston and M. Lipson, “Slot waveguides with polycrystalline silicon for electrical injection,” Opt. Express 17(3), 1527–1534 (2009). [CrossRef] [PubMed]
  14. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]
  15. R. Adato and J. Guo, “Modification of dispersion, localization, and attenuation of thin metal stripe symmetric surface plasmon-polariton modes by thin dielectric layers,” J. Appl. Phys. 105(3), 034306 (2009). [CrossRef]
  16. E. D. Palik, Handbook of Optical Constants of Solids, 1st ed. (Academic, New York, 1985).
  17. R. Slavík and J. Homola, “Optical multilayers for LED-based surface plasmon resonance sensors,” Appl. Opt. 45(16), 3752–3759 (2006). [CrossRef] [PubMed]
  18. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007). [CrossRef]
  19. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]
  20. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]
  21. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63(12), 125417 (2001). [CrossRef]

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