## Cloaking and enhanced scattering of core-shell plasmonic nanowires |

Optics Express, Vol. 21, Issue 9, pp. 10454-10459 (2013)

http://dx.doi.org/10.1364/OE.21.010454

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### Abstract

We study scattering of light from multi-layer plasmonic nanowires and reveal that such structures can demonstrate both enhanced and suppressed scattering regimes. We employ the mode-expansion method and experimental data for material parameters and introduce an optimized core-shell nanowire design which exhibits simultaneously superscatter-ing and cloaking properties at different wavelengths in the visible spectrum.

© 2013 OSA

## 1. Introduction

*may exist for realistic parameters*and if these two dissimilar effects can be observed in one type of structure.

11. P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metalsemi-conductor photodetector,” Nat. Photonics **6**, 380–385 (2012) [CrossRef]

13. B. Edwards, A. Al, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. **103**, 153901 (2009) [CrossRef] [PubMed]

## 2. Model and parameters

**H**

*=*

^{Inc}**â**

_{z}H_{0}

*e*

^{−iωt+i2πλ−1rcos(φ)}with the structure, we use the multipole expansion method. In a

*L*-layered cylindrical structure, the total field in layer

*l*can be presented as where

*H*

_{0}is the incident wave amplitude,

*J*and

_{n}*n*-th order Bessel and Hankel functions of the first kind, respectively;

*n*is the mode number,

*ε*(

_{l}*λ*) is the dielectric constant of the

*l*-th layer at wavelength

*λ*,

*r*is the radius within the layer

*l*,

*n*-th mode expansion coefficients in the

*l*-th layer which are found by solving the boundary condition equations for the tangential components

*H*and

_{z}*E*. Additionally, we put

_{φ}*λ*/

*π*(taking into account

8. Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. **105**, 013901 (2010) [CrossRef] [PubMed] .

15. M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. **97**, 263902 (2006) [CrossRef] .

8. Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. **105**, 013901 (2010) [CrossRef] [PubMed] .

*λ*/

*π*introducing

*normalized scattering cross-section*(NSCS). Employing multi-layered structures with plasmonic materials, the value of SCS can be significantly enhanced by employing multiple scattering channels. To achieve this, we need to design a nanostructure with a significant contribution of different channels

*at a same frequency*by overlapping the frequencies of at least two different resonances [8

8. Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. **105**, 013901 (2010) [CrossRef] [PubMed] .

10. L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett. **108**, 083902 (2012) [CrossRef] [PubMed] .

**105**, 013901 (2010) [CrossRef] [PubMed] .

**105**, 013901 (2010) [CrossRef] [PubMed] .

*ε*= 12.96 is used as permittivity of the dielectric layer, as well as Drude’s model for the permittivity of silver,

_{d}*ε*

_{∞}= 1,

*ω*= 1.37 · 10

_{p}^{16}rad/sec and

*γ*= 2.74 · 10

^{13}rad/sec are plasma and bulk collision frequencies respectively (using additional surface damping as is followed). These dependences are shown by dashed lines in Fig. 2(a). The radii of the shells,

*r*

_{1,2,3}, are 47.9 nm, 77.3 nm, and 87.6 nm, respectively.

17. U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F: Metal Phys. **4**, 999–1014 (1974) [CrossRef] .

*γ*[17

17. U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F: Metal Phys. **4**, 999–1014 (1974) [CrossRef] .

*γ*=

_{small–particle}*γ*+

_{bulk}*AV*/

_{f}*d*, where

*A*= 1,

*V*= 1.388 · 10

_{f}^{6}m/s (the Fermi velocity in silver), and

*d*is the characteristic size of the metallic structure. Taking this additional surface damping into account, the calculated NSCS as well as contributions to scattering from the first three modes, is shown in Fig. 3(a), and these results coincide with those of Fig. 4(a) in [8

**105**, 013901 (2010) [CrossRef] [PubMed] .

*ε*

_{∞},

*γ*and

*ω*. This, however, still does not describe the parameters of silver well enough for higher frequencies, namely above the interband transition frequency [18]. To demonstrate the importance of using accurate values of

_{p}*ε*(

_{l}*λ*) in numerical simulations, below we study the light scattering by the same structure but using Palik’s data for

*ε*(

_{silver}*λ*) [16] and compare the results with those obtained using Drude’s approximation.

*ε*) and imaginary (

_{r}*ε*) parts of bulk material dielectric permittivity from [16] to achieve

_{i}*γ*and

_{bulk}*ω*by using the Drude formula as follows (here we use

_{p}*γ*we recover the value of

_{small–particle}*ε*using Drude’s model (one also can use the approximation

## 3. Superscattering and cloaking

*Is it still possible to observe enhanced scattering with layered nanowires for realistic materials?*Or, what is the realistic variation of the SCS of layered nanowires? To answer these questions we analyse the scattering properties of a simpler core-shell metal-dielectric structure shown in Fig. 1(b), which has silver core and silicon outer shell. In Fig. 4 we plot maximum and minimum NSCS within the frequency range of interest as a function of radii

*r*

_{1}and

*r*

_{2}. We observe that the maximum NSCS close to 1.4 can be achieved in this structure. Moreover, if we take the values

*r*

_{1}= 18 nm and

*r*

_{2}= 73 nm, then both enhanced and suppressed scattering can be observed simultaneously. In particular, for such a choice of parameters, the NSCS is 0.135 at 426.9 nm and 1.284 at 733.2 nm. Corresponding NSCS is shown in Fig. 5(a) as a function of wavelength. The suppressed scattering is associated with the cloaking phenomenon, where the scattering of all modes is simultaneously and significantly reduced [2

2. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E **72**, 016623 (2005) [CrossRef] .

3. A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. **100**, 113901 (2008) [CrossRef] [PubMed] .

## 4. Conclusions

## Acknowledgments

## References and links

1. | N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. |

2. | A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E |

3. | A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. |

4. | A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (nano)particles,” Bull. Russ. Acad. Sci.: Physics |

5. | D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings form plasmonic cloaking,” Phys. Status Solidi RRL |

6. | P. Y. Chen, J. Soric, and A. Alu, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater. |

7. | Z. Ruan and S. Fan, “Temporal coupled-mode theory for fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C , |

8. | Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. |

9. | Z. Ruan and S. Fan, “Design of subwavelength superscattering nanospheres,” Appl. Phys. Lett. |

10. | L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett. |

11. | P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metalsemi-conductor photodetector,” Nat. Photonics |

12. | D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Al, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. |

13. | B. Edwards, A. Al, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. |

14. | C. A. Balanis, |

15. | M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. |

16. | E. Palik, |

17. | U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F: Metal Phys. |

18. | S. A. Maier, |

**OCIS Codes**

(240.3695) Optics at surfaces : Linear and nonlinear light scattering from surfaces

(250.5403) Optoelectronics : Plasmonics

(230.3205) Optical devices : Invisibility cloaks

**ToC Category:**

Optics at Surfaces

**Citation**

Ali Mirzaei, Ilya V. Shadrivov, Andrey E. Miroshnichenko, and Yuri S. Kivshar, "Cloaking and enhanced scattering of core-shell plasmonic nanowires," Opt. Express **21**, 10454-10459 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10454

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### References

- N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater.11, 917–924 (2012). [CrossRef] [PubMed]
- A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E72, 016623 (2005). [CrossRef]
- A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett.100, 113901 (2008). [CrossRef] [PubMed]
- A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (nano)particles,” Bull. Russ. Acad. Sci.: Physics74, 89–92 (2010). [CrossRef]
- D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings form plasmonic cloaking,” Phys. Status Solidi RRL6, 46–48 (2012). [CrossRef]
- P. Y. Chen, J. Soric, and A. Alu, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24, OP281–304 (2012). [CrossRef] [PubMed]
- Z. Ruan and S. Fan, “Temporal coupled-mode theory for fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C, 114, 7324–7329 (2010). [CrossRef]
- Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett.105, 013901 (2010). [CrossRef] [PubMed]
- Z. Ruan and S. Fan, “Design of subwavelength superscattering nanospheres,” Appl. Phys. Lett.98, 043101 (2011). [CrossRef]
- L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett.108, 083902 (2012). [CrossRef] [PubMed]
- P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metalsemi-conductor photodetector,” Nat. Photonics6, 380–385 (2012) [CrossRef]
- D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Al, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys.14, 013054 (2012) [CrossRef]
- B. Edwards, A. Al, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett.103, 153901 (2009) [CrossRef] [PubMed]
- C. A. Balanis, Advanced engineering electromagnetics (Wiley, 1989).
- M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett.97, 263902 (2006). [CrossRef]
- E. Palik, Handbook of optical constants of solids (Academic Press, 1997).
- U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F: Metal Phys.4, 999–1014 (1974). [CrossRef]
- S. A. Maier, Plasmonics: fundamentals and applications (Springer, 2007).

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