## Compact on-chip plasmonic light concentration based on a hybrid photonic-plasmonic structure |

Optics Express, Vol. 21, Issue 2, pp. 1898-1910 (2013)

http://dx.doi.org/10.1364/OE.21.001898

Acrobat PDF (3191 KB)

### Abstract

We present a novel approach for achieving tightly concentrated optical field by a hybrid photonic-plasmonic device in an integrated platform, which is a triangle-shaped metal taper mounted on top of a dielectric waveguide. This device, which we call a plasmomic light concentrator (PLC), can achieve vertical coupling of light energy from the dielectric waveguide to the plasmonic region and light focusing into the apex of the metal taper(at the scale ∼ 10nm) at the same time. For a demonstration of the PLCs presented in this paper, we numerically investigate the performance of a gold taper on a Si_{3}N_{4} waveguide at working wavelengths around 800nm. We show that three major effects (mode beat, nanofocusing, and weak resonance) interplay to generate this light concentration phenomenon and govern the performance of the device. Combining these effects, the PLC can be designed to be super compact while maintaining high efficiency over a wide band. In particular, we demonstrate that under optimized size parameters and wavelength a field concentration factor (FCF), which is the ratio of the norm of the electric field at the apex over the average norm of the electric field in the inputting waveguide, of about 13 can be achieved with the length of the device less than 1*μ*m for a moderate tip radius 20nm. Moreover, we show that a FCF of 5 – 10 is achievable over a wavelength range of 700 – 1100nm with the length of the device further reduced (to about 400nm).

© 2013 OSA

## 1. Introduction

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

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

3. W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. **9**, 4320–4325 (2009). [CrossRef] [PubMed]

4. L Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Sub-wavelength focusing and guiding of surface plasmons,” Nano Lett. **5**, 1399–1402 (2005). [CrossRef] [PubMed]

5. A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express **17**, 13150–13157 (2009). [CrossRef]

6. L. Novotny, R. X. Bian, and X.S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. **79**, 645–648 (1997). [CrossRef]

24. M. Malerba, A. Alabastri, G. Cojoc, M. Francardi, M. P. Donnorso, R. P. Zaccaria, F. De Angelis, and E. Di Fabrizio, “Optimization of surface plasmon polariton generation in a nanocone through linearly polarized laser beams,” Microelectron. Eng. **97**, 204 (2012). [CrossRef]

25. R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficiently squeezing near infrared light into a 21nm-by-24nm nanospot,” Opt. Express **16**, 20142–20148 (2008). [CrossRef] [PubMed]

30. X. He, L Yang, and T. Yang, “Optical nanofocusing by tapering coupled photonic-plasmonic waveguides,” Opt. Express **19**, 12865–12872 (2011). [CrossRef] [PubMed]

*λ*” scale to a “<

*λ*/10” scale. Therefore, the lossy nature of metals has less impacts on the concentration efficiencies. Moreover, many of such structures can be integrated on the same chip in series or in parallel in a very small footprint. This opens up a new avenue for multiplex nanofocusing in applications such as on chip trapping and sensing.

*μ*m) are the smallest among the all the non-resonant on-chip plasmonic-light-concentrators that have been reported.

_{3}N

_{4}). The substrate is silicon dioxide (SiO

_{2}). In addition, a SiO

_{2}buffer layer is used to separate the metal triangle and the dielectric ridge waveguide. The ambient material is water. The dimensions of the ridge waveguide are chosen to support only the fundamental TM-like (vertical polarization) mode and the fundamental TE-like (horizontal polarization) mode. Only the fundamental TM-like mode can be used to generate light concentration. We set up the coordinate system with

*X*-axis in the horizontal direction,

*Y*-axis in the vertical direction and

*Z*-axis in the propagation direction of the input light.

*W*to denote the length of the base of the isosceles triangle, and

*L*to denote the the length of a perpendicular from the center of the curved tip to the middle point of the base side. For simplicity, we will call

*W*the (maximum) width of the triangle and

*L*the length of the triangle throughout this paper. Since the apex of the metal triangle is always rounded up in real fabrications, we introduce the radius of curvature

*a*at the tip as a parameter.

## 2. Mode analysis of the hybrid photonic-plasmonic waveguide

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

36. M. Chamanzar and A. Adibi, “Hybrid nanoplasmonic-photonic resonators for efficient coupling of light to single plasmonic nanoresonators,” Opt. Express **19**, invited for Focus Issue: Collective Phenomena, 22292–22304 (2011). [CrossRef] [PubMed]

_{3}N

_{4}ridge waveguide have been selected for single-mode operation (for each polarization) at wavelength

*λ*of 800nm with the ambient material being water. The Au strip has thickness of 40nm and width

*w*as a variable. For

*λ*= 800nm, the refractive indices of Si

_{3}N

_{4}, SiO

_{2}and water are assumed to be 2.00, 1.46, and 1.33, respectively, and the permittivity of Au is assumed to be −24.02 +

*j*1.18 (computation based on data from [37

37. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. **37**, 5271–5283 (1998). [CrossRef]

_{3}N

_{4}with SiO

_{2}). In the next step, we find the modes of the hybrid photonic-plasmonic waveguide by using the supermode analysis through adding and subtracting the modes of the two structures as shown in shown in Figs. 2(b) and 2(c).

_{0}) and the fundamental TE-like mode (denoted by TE

_{0}). The TM

_{0}mode can only couple with symmetric modes of the purely plasmonic waveguide, and the TE

_{0}mode can only couple with the asymmetric modes of the purely plasmonic waveguide. We only consider the fundamental symmetric (S

_{0}) and asymmetric (A

_{0}) modes of the purely plasmonic waveguide, since higher order modes are cut off with the dimensions of our structure at the wavelength

*λ*of 800nm. Figure 2(b) shows two supermodes, H

_{TM,0}and H

_{TM,1}, are derived from the superposition of the TM

_{0}mode and the S

_{0}mode. Analogously, Fig. 2(c) shows two supermodes, H

_{TE,0}and H

_{TE,1}, are derived from the superposition of the TE

_{0}mode and the A

_{0}mode.

*λ*of 800nm. Note that the effective indices

*n*

_{eff}of the propagating modes must have real parts greater than 1.46, which is the refractive index of the SiO

_{2}substrate.

_{0}, S

_{0}, H

_{TM,0}and H

_{TM,1}modes, with the width

*w*of the Au strip set to 620nm. The electric field lines are plotted. The effective indices of the modes are also listed in Fig. 3(a). Figure 3(b) illustrates similar data for the modes TE

_{0}, A

_{0}, H

_{TE,0}and H

_{TE,1}. The electric field lines in Fig. 3 clearly show the validity of the supermode analysis approach as shown in Fig. 2.

_{TM,0}, H

_{TM,1}, H

_{TE,0}and H

_{TE,1}) of the hybrid photonic-plasmonic waveguide are plotted in Fig. 4 in the form of the real and imaginary parts of the effective index versus the width

*w*of the Au strip. The coordinate “Real(

*n*

_{eff})” has a minimum at 1.46 as only propagating modes are considered. The imaginary part of the effective index accounts for the propagation loss.

*n*

_{eff}) of H

_{TM,0}is greater than the Real(

*n*

_{eff}) of H

_{TM,1}, and as

*w*decreases, the difference between the two becomes larger. The imaginary parts follow the same trend. This is because as

*w*decreases, the light energy becomes more concentrated around the lossy metal region for H

_{TM,0}, while it becomes more concentrated in the dielectric region for H

_{TM,1}. The mode profiles of both supermodes at

*w*= 60nm are illustrated in Fig. 5. As

*w*approaches 0, both the real and imaginary parts of the effective index of H

_{TM,0}go to infinity. This means that the phase velocity goes to 0, and the H

_{TM,0}mode becomes more and more like a localized mode. When

*w*= 0, there is no metal strip, and the H

_{TM,1}mode is actually the purely photonic mode TM

_{0}. Note that as the width of the metal layer continuously and gradually shrinks down, the amplitude of the H

_{TM,0}mode increases since its propagating velocity slows down. Such a process is common to most geometry-induced plasmonic nanofocusing techniques, and is one of the main mechanisms to generate light concentration in our triangle-shaped plasmonic device. Analogously, we observe that the H

_{TE,0}mode evolves into the purely photonic mode TE

_{0}as

*w*approaches 0. Moreover, when

*w*< 180nm, the H

_{TE,1}mode is cut off. Therefore we can not take use of the supermodes H

_{TE,0}and H

_{TE,1}for our application of light concentration.

_{0}in the bare waveguide can excite two supermodes (H

_{TM,0}and H

_{TM,1}) of the hybrid waveguide. The super-position of these two supermodes at the input end has field in the dielectric region to match the incident TM

_{0}mode. Since they have different effective indices, as can be seen from the dispersion diagram in Fig. 4, the two supermodes undergo a beat effect with light energy bouncing back and forth between the dielectric region and the metal region. For a specific width

*w*of the Au strip, we have where BL(

*w*) is the beat length. In particular, at a distance about half the beat length from the input end, the light energy is vertically coupled efficiently into the metal region.

## 3. The performance of a PLC with specific size parameters

_{TM,0}and H

_{TM,1}); the nanofocusing effect comes from the triangle taper; and the weak resonance effect comes from the reflections at the input end and the apex of the taper.

_{3}N

_{4}ridge has a width of 620nm and a thickness of 200nm; the SiO

_{2}buffer has a width of 620nm and a thickness of 100nm. The thickness of the Au triangle is 40nm. The ambient material is also water. These parameters are the same as the hybrid photonic-plasmonic waveguide we analyzed in the previous section. The coordinate system is chosen to be the same as that in Fig. 1. In particular, the coordinate origin is chosen such that the plane

*X*= 0 cuts through the middle of the Si

_{3}N

_{4}ridge vertically, the plane

*Y*= 0 coincides with the boundary between the Si

_{3}N

_{4}layer and the SiO

_{2}substrate, and the plane

*Z*= 0 goes through the center of the curved tip.

## 4. The three underlying effects of the device

_{0}in the bare photonic waveguide can excite two supermodes, H

_{TM,0}and H

_{TM,1}, in the corresponding hybrid waveguide with a metal (Au) strip integrated on top. The triangle-shaped PLC can be considered as a taper with the width of the Au strip gradually going down to 0. Therefore, we can still use the two supermodes for the Au taper in our analysis. The mode beat between the two supermodes can make a vertical coupling (or side-coupling), which transfers light energy quickly from the dielectric region to the metal region, and the triangular taper performs plasmonic nanofocusing at the same time. This simultaneous light coupling and focusing in a single triangle-shaped metal taper is a major advantage of our design, resulting in a very compact structure. More accurately speaking, the tapering also induces energy coupling between the two supermodes. In other words, the ratio of energy stored in the two modes will change at different locations along the metal taper, and only the H

_{TM,0}mode becomes localized as the metallic tip. In our analysis based on a simplified model, we consider that the two supermodes have constant mode effective indices which are calculated using the average width of the taper.

*L*of the Au triangle, while the radius of curvature

*a*is fixed at 20nm. The wavelength

*λ*is 800nm. The two curves correspond to two cases of the maximum width

*W*of the triangular taper: the blue solid one is for the case

*W*= 300nm, and the red dashed one is for the case

*W*= 400nm. Two oscillatory behaviors can be seen in Fig. 7: the slow variations corresponding to the mode-beat effect and the ripples with high oscillation frequency corresponding to the weak resonance effect.

*w*, we can use it to estimate the beat length of the tapered structure by using the average metallic width over the tapered length for

*w*. For a triangular taper, this corresponds to about 1/2 of the maximum width

*W*of the taper. Using this approach, we can find

*n*

_{eff}for the hybrid H

_{TM,0}and H

_{TM,1}modes, and then compute the beat lengths for the two cases (

*W*= 300nm and

*W*= 400nm) shown in Fig. 7. For the narrower taper (

*W*= 300nm and

*w*=

*W*/2 = 150nm), we obtain Real(

*n*

_{eff}(H

_{TM,0}(150nm))) = 1.9694, Real(

*n*

_{eff}(H

_{TM,1}(150nm))) = 1.5475 and BL(150nm) = 1896nm. For the wider taper (

*W*= 400nm and

*w*=

*W*/2 = 200nm), we obtain Real(

*n*

_{eff}(H

_{TM,0}(200nm))) = 1.9216, Real(

*n*

_{eff}(H

_{TM,1}(200nm))) = 1.5413 and BL(200nm) = 2104nm. We can see that the computed beat length for the wider taper is a little larger than that for the narrower one.

*μ*m and for the wider taper is 2.0

*μ*m, agreeing well with the computations based on Equation (1).

*L*is about half of the beat length (e.g.

*L*⋍ 1.0

*μ*m for the wider taper with

*W*= 400nm), the light energy transfers from the dielectric region to the metal region most efficiently, which results in a higher FCF, as shown in Fig. 7.

*n*

_{eff}(H

_{TM,0}(

*w*)) with

*w*being the average width of the triangular taper, we can calculate the free spectral range (FSR) of these fast oscillation using For example, in the case of wider taper (

*W*= 400nm and

*w*= 200nm) in Fig. 7, we have Real(

*n*

_{eff}(H

_{TM,0}(200nm))) = 1.9216, and FSR(200nm) = 208nm. This corresponds to about 15 peaks for the red curve, matching well with an actual counting on the figure.

*L*is chosen to be at a resonance peak close to half the beat length. In an actual design, we might choose

*L*smaller than its optimal value to reduce the device dimension while keeping

*FCF*high. For example, by choosing

*L*= 500nm, an FCF of about 10 can be obtained as seen from Fig. 7.

## 5. Analysis of the transmission, reflection and FCF spectra

*T*, reflection

*R*, and

*T*+

*R*spectra for (a)

*L*= 1

*μ*m and (b)

*L*= 2

*μ*m for the triangular taper with

*W*= 400nm and

*a*= 20nm. The wavelength range is 600 – 1100nm.

*L*= 1

*μ*m case first. As we have computed, when

*W*= 400nm, the beat length is about 2.1

*μ*m at the wavelength of 800nm. For wavelengths in a range around 800nm, the beat length does not change much. Therefore, 1

*μ*m is around half the beat length, when the PLC is expected to be most efficient. The term 1 −

*T*−

*R*indicates the power consumption on the metal structure due to the internal material absorption and the radiative loss.

*T*and the overall

*T*+

*R*, while inducing a larger reflection

*R*. It is noticeable that the reflection part contributes less significantly to the overall

*T*+

*R*than the transmission part, and therefore the profile of the

*T*+

*R*spectrum is basically determined by the transmission spectrum. When the structure is off resonance, we have

*T*+

*R*about 0.8, which means a certain amount of power is still coupled to the metal region. This is quite different from the typical spectrum of a plasmonic resonator, for which

*T*+

*R*is very close to 1 when the structure is off resonance.

*L*= 2

*μ*m case. The spacing between two successive drops in the transmission spectrum is clearly less than that of the

*L*= 1

*μ*m case. Moreover, since 2

*μ*m is close to the beat length, the PLC is expected to be less efficient. As a result, the overall reflection is considerably smaller than that in the

*L*= 1

*μ*m case.

*μ*m, 0.425

*μ*m and 0.45

*μ*m, those in the second group (Fig. 9(b)) are 1

*μ*m, 1.025

*μ*m and 1.05

*μ*m, and those in the third group (Fig. 9(c)) are 2

*μ*m, 2.025

*μ*m and 2.05

*μ*m. We use

*W*= 400nm and

*a*= 20nm for all structures. Recall that by definition, the FCF(

*a*= 20nm) is the normalized norm of the electric field at the point (0, 320nm, 20nm) in the coordinate system. When the wavelength is less than 700nm, the bare photonic waveguide supports higher order TM modes and the hybrid structure supports more modes in addition to H

_{TM,0}and H

_{TM,1}. Thus our analytic model using two supermodes is no longer valid in this case. The simulations show that the field concentration effect is tremendously suppressed in this case. For wavelengths larger than 700nm, the vertical dashed lines indicate that a local minima of the transmission corresponds almost exactly to a local maxima of the FCF, and correspondingly the plasmonic structure is at resonance.

## 6. Conclusion

_{3}N

_{4}waveguide. We use the fundamental TM-like mode for the incident light from a photonic waveguide to excite two supermodes in the hybrid structure. We have shown that three major effects (mode beat, nanofocusing, and weak resonance) interplay to generate the light concentration phenomenon and govern the performance of the device. By proper combination of these three effects, the overall structure can be optimized to obtain very large field concentration. In particular, we have demonstrated that after an optimization of the size parameters, a field concentration factor (FCF) of about 13 can be achieved with the length of the device less than 1

*μ*m for a moderate tip radius of 20nm. Such a field concentration efficiency is about twice better than all reported results of on-chip plasmonic light concentrators in literature with much larger device sizes and an assumption of smaller tip radii. In addition, the dimensions of the device can be reduced further while maintaining a high concentration efficiency (a FCF of 5 – 10 is achievable with the length of triangle about 400nm).

25. R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficiently squeezing near infrared light into a 21nm-by-24nm nanospot,” Opt. Express **16**, 20142–20148 (2008). [CrossRef] [PubMed]

28. B. Desiatov, I. Goykhman, and U. Levy, “Plasmonic nanofocusing of light in an integrated silicon photonics platform,” Opt. Express **19**, 13150–13157 (2011). [CrossRef] [PubMed]

30. X. He, L Yang, and T. Yang, “Optical nanofocusing by tapering coupled photonic-plasmonic waveguides,” Opt. Express **19**, 12865–12872 (2011). [CrossRef] [PubMed]

## Acknowledgment

## References and links

1. | J. A. Schuller, E. S. Barnard, W. Cai, Y. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Materials |

2. | Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. |

3. | W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. |

4. | L Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Sub-wavelength focusing and guiding of surface plasmons,” Nano Lett. |

5. | A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express |

6. | L. Novotny, R. X. Bian, and X.S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. |

7. | K. V. Nerkararyan, “Superfocusing on a surface polariton in a wedge-like structure,” Phys. Lett. A |

8. | A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. |

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20. | E. Verhagen, A. Polman, and L. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express |

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24. | M. Malerba, A. Alabastri, G. Cojoc, M. Francardi, M. P. Donnorso, R. P. Zaccaria, F. De Angelis, and E. Di Fabrizio, “Optimization of surface plasmon polariton generation in a nanocone through linearly polarized laser beams,” Microelectron. Eng. |

25. | R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficiently squeezing near infrared light into a 21nm-by-24nm nanospot,” Opt. Express |

26. | B. Desiatov, I. Goykhman, and U. Levy, “On-chip focusing of light by metallic nanotip,” |

27. | B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale mode selector in silicon waveguide for on-chip nanofocusing applications,” Nano Lett. |

28. | B. Desiatov, I. Goykhman, and U. Levy, “Plasmonic nanofocusing of light in an integrated silicon photonics platform,” Opt. Express |

29. | Y. Luo, M. Chamanzar, A. A. Eftekhar, and A. Adibi, “On-chip nanofocusing using a hybrid plasmonic-dieletric tapered waveguide,” |

30. | X. He, L Yang, and T. Yang, “Optical nanofocusing by tapering coupled photonic-plasmonic waveguides,” Opt. Express |

31. | P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width Bound modes of asymmetric structures,” Phys. Rev. B |

32. | R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. |

33. | D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express |

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35. | M. Chamanzar, M. Soltani, B. Momeni, S. Yegnanarayanan, and A. Adibi, “Hybrid photonic surface-plasmon-polariton ring resonators for sensing applications,” Appl. Phys. B |

36. | M. Chamanzar and A. Adibi, “Hybrid nanoplasmonic-photonic resonators for efficient coupling of light to single plasmonic nanoresonators,” Opt. Express |

37. | A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: November 5, 2012

Revised Manuscript: December 30, 2012

Manuscript Accepted: January 9, 2013

Published: January 17, 2013

**Citation**

Ye Luo, Maysamreza Chamanzar, and Ali Adibi, "Compact on-chip plasmonic light concentration based on a hybrid photonic-plasmonic structure," Opt. Express **21**, 1898-1910 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1898

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### References

- J. A. Schuller, E. S. Barnard, W. Cai, Y. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Materials9, 193–204 (2010). [CrossRef]
- Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett.5, 1726–1729 (2005). [CrossRef] [PubMed]
- W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett.9, 4320–4325 (2009). [CrossRef] [PubMed]
- L Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Sub-wavelength focusing and guiding of surface plasmons,” Nano Lett.5, 1399–1402 (2005). [CrossRef] [PubMed]
- A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express17, 13150–13157 (2009). [CrossRef]
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