## Light scattering, field localization and local density of states in co-axial plasmonic nanowires |

Optics Express, Vol. 18, Issue 15, pp. 16120-16132 (2010)

http://dx.doi.org/10.1364/OE.18.016120

Acrobat PDF (2223 KB)

### Abstract

Based on analytical scattering theory, we develop a multipolar expansion method to investigate systematically the near-field enhancement, far-field scattering and Local Density of States (LDOS) spectra in concentric metal-insulator-metal (MIM) cylindrical nanostructures, or coaxial plasmonic nanowires (CPNs). We demonstrate that these structures support distinctive plasmonic resonances with strongly reduced scattering in the far-field zone and significant electric field enhancement in deep sub-wavelength dielectric regions. Additionally, we study systematically the effects of geometrical parameters and dielectric index on the near-field and far-field plasmonic response of CPNs in the visible and near infrared spectral range. Finally, we demonstrate that CPNs provide a convenient approach for engineering strong (almost three orders of magnitude) LDOS enhancement in sub-wavelength dielectric gaps at multiple frequencies. These results enable the engineering of multiband optical detectors and CPNs-based light emitters with simultaneously enhanced excitation and emission rates for nanoplasmonics.

© 2010 OSA

## 1. Introduction

3. R. Zia, J.A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Materials Today **9****,**7–8 (2006). [CrossRef]

8. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science **302**(5644), 419–422 (2003). [CrossRef] [PubMed]

11. J. Hu, M. Ouyang, P. Yang, and C. M. Lieber, “Controlled growth and electrical properties of heterojunctions of carbon nanotubes and silicon nanowires,” Nature **399**(6731), 48–51 (1999). [CrossRef]

14. C. Colombo, M. Heiβ, M. Gratzel, and A. Fontcuberta i Morral, “Gallium arsenide p-i-n radial structures for photovoltaic applications,” Appl. Phys. Lett. **94**, 173108 (2009). [CrossRef]

15. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. **58**(20), 2059–2062 (1987). [CrossRef] [PubMed]

17. J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature **425**(6955), 268–271 (2003). [CrossRef] [PubMed]

18. Y. C. Jun, R. M. Briggs, H. A. Atwater, and M. L. Brongersma, “Broadband enhancement of light emission in silicon slot waveguides,” Opt. Express **17**(9), 7479–7490 (2009). [CrossRef] [PubMed]

20. Y. Gong, S. Yerci, R. Li, L. Dal Negro, and J. Vucković, “Enhanced light emission from erbium doped silicon nitride in plasmonic metal-insulator-metal structures,” Opt. Express **17**(23), 20642–20650 (2009). [CrossRef] [PubMed]

21. A. Gopinath, S. V. Boriskina, S. Selcuk, R. Li, and L. Dal Negro, “Enhancement of the 1.55mm Erbium^{3+} emission from quasi-periodic plasmonic arrays,” Appl. Phys. Lett. **96**(7), 071113 (2010). [CrossRef]

^{3}increase over free space) confined in sub-wavelength dielectric regions, making them very attractive for a variety of nanoscale device applications including light emitters, photodetectors, optical sensors, and nanowires-based solar cells [13

13. B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature **449**(7164), 885–889 (2007). [CrossRef] [PubMed]

14. C. Colombo, M. Heiβ, M. Gratzel, and A. Fontcuberta i Morral, “Gallium arsenide p-i-n radial structures for photovoltaic applications,” Appl. Phys. Lett. **94**, 173108 (2009). [CrossRef]

## 2. Computational method

23. A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. M. de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **63**(4), 046612 (2001). [CrossRef] [PubMed]

*m*concentric layers specified by

*m*values of radii and

*m +*1 permittivities.

*A*,

^{l}*B*,

^{l}*C*, are uniquely associated to each layer and will be used to specify the fields within the

^{l}*l*

^{th}layer. Since the problem is 2D, it simplifies to a scalar problem specified by the z-component of the field, from which all the other field components can be derived using Maxwell’s equations. The field solution

*U*in the in the

^{l}*l*

^{th}layer, must satisfy the scalar Helmholtz equation in 2D, and can be expressed as a linear combination of Bessel functions in the radial variable and complex exponential functions in the azimuthal variable. Therefore, the field amplitude in the

*l*

^{th}layer can be expressed as:where

*U*is the field contribution due to the source within the

_{s}^{l}*l*

^{th}layer, which is nonzero only within the layer containing the source (in all other layers, there is no distinction between fields originating from the source and fields due to response of the structure). To determine the field solution in the rest of the structure we need to apply the boundary conditions by enforcing the continuity of the tangential field components across the layer interfaces. Since the field radiated by the source must also satisfy the Helmholtz equation, it will be represented as Bessel functions centered at the location of the source. However, in order to take advantage of the cylindrical symmetry of the problem, we first need to express the source term as an expansion of functions centered at the origin of our reference system (see Fig. 1), using the Graf’s addition theorem [24]. As a result, we obtain the following representation for the fields everywhere in the structure:where,and

*C*are the expansion coefficients of a source with an arbitrary field profile and

_{n}^{l}*r*is the amplitude of the position vector of the source. The function

_{s}*X*is a Bessel function in regions including the origin and becomes a Hankel function in unbounded regions in order to correctly handle singularities and to allow for power conservation in the system [24]. We can now use the general field expression in Eq. (2) to write the boundary condition equations at each interface resulting in a matrix equation which, for a three layer structure, is shown in the Appendix (Eq. (8)). It is worth noting that the contribution of the source has been separated from the matrix, which only depends on the geometry, materials and wavelength of the problem, but not on the source location or its intensity profile. Since the source intensity profile is yet unspecified, this matrix equation can be used to calculate the system’s response to a plane wave or, more generally, to localized point sources positioned at arbitrary locations specified by the source vector coefficients (right-hand side of Eq. (8)). The local density of states (LDOS),

_{n}^{l}23. A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. M. de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **63**(4), 046612 (2001). [CrossRef] [PubMed]

*U*(

_{s,a}*a = x,y,z)*is the source

*z*-component for an

*a*-oriented dipole in Eq. (1) and

27. P. Johnson and R. Christy, “Optical constants of Noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

## 3. Scattering and localized dark resonances in CPNs

*n*. The thickness of their internal dielectric regions is 50nm (Figs. 2(a) , and 2(c)) and 12nm (Figs. 2(b) and 2(d)), while its refractive index is n = 1.5. These structures simultaneously support strong plasmonic resonances in the visible and in the near-IR spectral regions, (a series of weak resonances are also observed at shorter wavelengths corresponding to higher order multipolar modes, and will not be discussed hereafter). The plots in Figs. 2(a) and 2(b) show the calculated wavelength spectra of the scattering (blue color lines) and absorption efficiencies (green color lines) of the structures. In Figs. 2(c) and 2(d) we plot the maxima of the electric field magnitudes inside the dielectric region. The structures are excited by a unit plane wave with a magnetic field vector H polarized along the wire axis (

_{air}= 1*z-*axis), corresponding to a transverse electric (TE) wave.

8. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science **302**(5644), 419–422 (2003). [CrossRef] [PubMed]

28. G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc A. **462**(2074), 3027–3059 (2006). [CrossRef]

29. N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express **15**(10), 6314–6323 (2007). [CrossRef] [PubMed]

8. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science **302**(5644), 419–422 (2003). [CrossRef] [PubMed]

30. Z. B. Wang, B. S. Luk’yanchuk, M. H. Hong, Y. Lin, and T. C. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B **70**(3), 035418 (2004). [CrossRef]

31. M. Bashevoy, V. Fedotov, and N. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express **13**(21), 8372–8379 (2005). [CrossRef] [PubMed]

30. Z. B. Wang, B. S. Luk’yanchuk, M. H. Hong, Y. Lin, and T. C. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B **70**(3), 035418 (2004). [CrossRef]

31. M. Bashevoy, V. Fedotov, and N. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express **13**(21), 8372–8379 (2005). [CrossRef] [PubMed]

32. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. **91**(23), 233901 (2003). [CrossRef] [PubMed]

## 4. Engineering resonances in CPNs

_{1}), the thickness of the dielectric layer (referred to as d

_{2}), and the thickness of the outer metal shell (referred to as d

_{3}). The results of our analysis, summarized in Fig. 6, show the formation of two main resonances observed in the scattering efficiency and in the internal field, corresponding to the dipolar and the quadrupolar modes of the structures. The intensities of these resonances are maximized within separate wavelength regions, depending solely on the geometrical parameters and the dielectric index of the structures.

_{1}(i.e. core size) and wavelength. The other two geometrical parameters of the structure are kept constant equal to d

_{2}= 20nm and d

_{3}= 20nm, while the dielectric index is fixed to n = 1.5. We notice that strong dipolar and quadrupolar resonant peaks can be supported for a wide range of r

_{1}. As the size of the core increases in radius from 10nm to 100nm, both these resonances red-shift almost linearly, the dipolar resonance shifting at a higher rate across the entire visible and near-IR spectrum (up to 1650nm). This can be explained, in the weak plasmon mode coupling limit, by a simple azimuthal standing wave model where resonances are formed when half integer numbers of wavelengths close around the core of the structure. We found that the electric field amplitude of the dipolar mode in the dielectric gap is optimized for r

_{1}around 50nm while the scattering efficiency of this mode is optimized for a smaller core size around r

_{1}= 30nm. On the other hand, the scattering efficiency of the quadrupolar mode (Fig. 6(e)) remains very small across the entire parameter space while the intensity of the field inside the dielectric gap becomes significant for larger values of r

_{1}, as expected for higher order modes.

_{2}on the resonances of the structure, while the other parameters are fixed to r

_{1}= 60nm and d

_{3}= 20nm, n = 1.5. Both the scattering efficiency and field amplitude show two largely tunable resonance bands. However, when the thickness of the dielectric layer is increased, the frequency of the resonances blue-shifts in a non-linear way, varying very quickly at first and later approaching a plateau for thickness of about 40nm. This behavior is understood based on the established plasmon hybridization model [8

**302**(5644), 419–422 (2003). [CrossRef] [PubMed]

9. F. Hao, P. Nordlander, M. Burnett, and S. Maier, “Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B **76**(24), 245417 (2007). [CrossRef]

_{2}we decrease the coupling between these modes and shift the resonance of the coupled system to shorter wavelengths (larger energy). Moreover, we also notice that, as already discussed in section 3, the scattering efficiency of CPN systems (Fig. 6(f)) dramatically reduces by decreasing the dielectric gap thickness, since dark plasmon modes form inside the dielectric region. In Figs. 6(d) and 6(g) we show the tunability of the resonances with respect to the thickness of the outer metallic layer, while fixing r

_{1}= 60nm, n = 1.5, d

_{2}= 20nm in 6(d) and d

_{2}= 50nm in 6(g). Two distinct modes (dipolar and quadrupolar) can be clearly observed and their spectral positions blue-shift non linearly by increasing d

_{3}. This effect is due to the reduced coupling of the hybridized resonances [8

**302**(5644), 419–422 (2003). [CrossRef] [PubMed]

_{1}= 60nm, d

_{2}= 20nm, d

_{3}= 20nm and a real refractive index in the gap region varying in the n = 1.5-3 range. (The main conclusions of our analysis are robust with respect to the introduction of dielectric losses in the sub-wavelength layer). Due to the very small scattering values observed at small gaps (Fig. 6(e)), the scattering efficiency has been plotted for a structure with d

_{2}= 50nm. We can see from the results in Fig. 7(a) that the dipolar and quadrupolar resonances can be engineered across a wide range of refractive index values. However, we observe a significant decrease in the scattering efficiency and in the amplitude of the internal electric field values as the refractive index of the dielectric layer is increased from its minimum value. This general behavior has been observed in planar metal-insulator-metal slot waveguides [1–3

3. R. Zia, J.A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Materials Today **9****,**7–8 (2006). [CrossRef]

## 5. LDOS calculation

## 6. Conclusions

## Appendix

*A*coefficients (outermost layer) and

_{n}^{m + 1}*B*coefficients (innermost layer) have been set to zero and do not appear in the matrix equation for reasons detailed in [22,26]. The contribution of the source has been moved to the right hand side of the equation so the matrix is only dependent on the geometry, materials and wavelength of the problem, but not on the source location or profile. As mentioned in Section 2, the

_{n}^{1}*C*coefficients are non-zero only in the source layer; therefore most of the terms on the right hand side will vanish once the position of the source is determined. Since the source intensity profile is not yet specified, this matrix equation can be used to calculate the system’s response to a plane wave or, more generally, to localized point sources positioned at arbitrary locations as specified by source vector coefficients (right-hand side of Eq. (8)).

_{n}^{l}## Acknowledgments

## References and links

1. | S. Maier, |

2. | R. Zia, M. Selker, P. Catrysse, and M. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. |

3. | R. Zia, J.A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Materials Today |

4. | P. B. Catrysse and S. Fan, “Understanding the dispersion of coaxial plasmonic structures though a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. |

5. | J. Rybczynski, K. Kempa, A. Herczynski, Y. Wang, M. J. Naughton, Z. F. Ren, Z. P. Huang, D. Cai, and M. Giersig, “Subwavelength waveguide for visible light,” Appl. Phys. Lett. |

6. | M. Kushwaha and B. Djafari-Rouhani, “Green-funciton theory of confined plasmons in coaxial cylindrical geometries: Zero magnetic field,” Phys. Rev. Lett. B |

7. | M. L. Brongersma, and P. G. Kik, |

8. | E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science |

9. | F. Hao, P. Nordlander, M. Burnett, and S. Maier, “Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B |

10. | E. Prodan and P. Nordlander, “Structural Tunability of the plasmon resonances in metallic nanoshells,” Nanoletters |

11. | J. Hu, M. Ouyang, P. Yang, and C. M. Lieber, “Controlled growth and electrical properties of heterojunctions of carbon nanotubes and silicon nanowires,” Nature |

12. | X. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature |

13. | B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature |

14. | C. Colombo, M. Heiβ, M. Gratzel, and A. Fontcuberta i Morral, “Gallium arsenide p-i-n radial structures for photovoltaic applications,” Appl. Phys. Lett. |

15. | E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. |

16. | D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. |

17. | J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature |

18. | Y. C. Jun, R. M. Briggs, H. A. Atwater, and M. L. Brongersma, “Broadband enhancement of light emission in silicon slot waveguides,” Opt. Express |

19. | Y. Kurokawa and H. Miyazaki, “Metal-insulator-metal plasmon nanocavities: Analysis of optical properties,” Phys. Rev. B |

20. | Y. Gong, S. Yerci, R. Li, L. Dal Negro, and J. Vucković, “Enhanced light emission from erbium doped silicon nitride in plasmonic metal-insulator-metal structures,” Opt. Express |

21. | A. Gopinath, S. V. Boriskina, S. Selcuk, R. Li, and L. Dal Negro, “Enhancement of the 1.55mm Erbium |

22. | A. Boriskin, and A. Nosich, “Whispering-Gallery and Luneberg-Lens Effects in a Beam-Fed Circularly Layered Dielectric Cylinder,” IEEE Trans. on Antennas and Propagation, Vol. |

23. | A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. M. de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

24. | P. A. Martin, |

25. | L. Novotny, and B. Hecht, |

26. | C. F. Bohren, and D. R. Huffman, |

27. | P. Johnson and R. Christy, “Optical constants of Noble metals,” Phys. Rev. B |

28. | G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc A. |

29. | N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express |

30. | Z. B. Wang, B. S. Luk’yanchuk, M. H. Hong, Y. Lin, and T. C. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B |

31. | M. Bashevoy, V. Fedotov, and N. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express |

32. | R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(290.4020) Scattering : Mie theory

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: May 26, 2010

Revised Manuscript: June 17, 2010

Manuscript Accepted: June 17, 2010

Published: July 15, 2010

**Citation**

Nate Lawrence and Luca Dal Negro, "Light scattering, field localization and local density of states in co-axial plasmonic nanowires," Opt. Express **18**, 16120-16132 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-16120

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### References

- S. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007)
- R. Zia, M. Selker, P. Catrysse, and M. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. 21(12), 2442 (2004). [CrossRef]
- R. Zia, J.A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9,7–8 (2006). [CrossRef]
- P. B. Catrysse and S. Fan, “Understanding the dispersion of coaxial plasmonic structures though a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett. 94(23), 231111 (2009). [CrossRef]
- J. Rybczynski, K. Kempa, A. Herczynski, Y. Wang, M. J. Naughton, Z. F. Ren, Z. P. Huang, D. Cai, and M. Giersig, “Subwavelength waveguide for visible light,” Appl. Phys. Lett. 90(2), 021104 (2007). [CrossRef]
- M. Kushwaha and B. Djafari-Rouhani, “Green-funciton theory of confined plasmons in coaxial cylindrical geometries: Zero magnetic field,” Phys. Rev. Lett. B 67, 245320 (2003).
- M. L. Brongersma, and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007)
- E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]
- F. Hao, P. Nordlander, M. Burnett, and S. Maier, “Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B 76(24), 245417 (2007). [CrossRef]
- E. Prodan and P. Nordlander, “Structural Tunability of the plasmon resonances in metallic nanoshells,” Nanoletters 3(4), 543–547 (2003).
- J. Hu, M. Ouyang, P. Yang, and C. M. Lieber, “Controlled growth and electrical properties of heterojunctions of carbon nanotubes and silicon nanowires,” Nature 399(6731), 48–51 (1999). [CrossRef]
- X. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421(6920), 241–245 (2003). [CrossRef] [PubMed]
- B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007). [CrossRef] [PubMed]
- C. Colombo, M. Heiβ, M. Gratzel, and A. Fontcuberta i Morral, “Gallium arsenide p-i-n radial structures for photovoltaic applications,” Appl. Phys. Lett. 94, 173108 (2009). [CrossRef]
- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]
- D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]
- J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425(6955), 268–271 (2003). [CrossRef] [PubMed]
- Y. C. Jun, R. M. Briggs, H. A. Atwater, and M. L. Brongersma, “Broadband enhancement of light emission in silicon slot waveguides,” Opt. Express 17(9), 7479–7490 (2009). [CrossRef] [PubMed]
- Y. Kurokawa and H. Miyazaki, “Metal-insulator-metal plasmon nanocavities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007). [CrossRef]
- Y. Gong, S. Yerci, R. Li, L. Dal Negro, and J. Vucković, “Enhanced light emission from erbium doped silicon nitride in plasmonic metal-insulator-metal structures,” Opt. Express 17(23), 20642–20650 (2009). [CrossRef] [PubMed]
- A. Gopinath, S. V. Boriskina, S. Selcuk, R. Li, and L. Dal Negro, “Enhancement of the 1.55mm Erbium3+ emission from quasi-periodic plasmonic arrays,” Appl. Phys. Lett. 96(7), 071113 (2010). [CrossRef]
- A. Boriskin and A. Nosich, “Whispering-Gallery and Luneberg-Lens Effects in a Beam-Fed Circularly Layered Dielectric Cylinder,” IEEE Trans. on Antennas and Propagation, Vol. 50, No. 9; (2002).
- A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. M. de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4), 046612 (2001). [CrossRef] [PubMed]
- P. A. Martin, Multiple Scattering, (Cambridge University Press, 2006)
- L. Novotny, and B. Hecht, Principles of nano-optics, (Cambridge University Press, 2006)
- C. F. Bohren, and D. R. Huffman, Absorption and scattering of light by small particles, (John Wiley, 1983)
- P. Johnson and R. Christy, “Optical constants of Noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
- G. W. Milton and N. A. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc A. 462(2074), 3027–3059 (2006). [CrossRef]
- N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15(10), 6314–6323 (2007). [CrossRef] [PubMed]
- Z. B. Wang, B. S. Luk’yanchuk, M. H. Hong, Y. Lin, and T. C. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B 70(3), 035418 (2004). [CrossRef]
- M. Bashevoy, V. Fedotov, and N. Zheludev, “Optical whirlpool on an absorbing metallic nanoparticle,” Opt. Express 13(21), 8372–8379 (2005). [CrossRef] [PubMed]
- R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003). [CrossRef] [PubMed]

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