## Sierpiński fractal plasmonic antenna: a fractal abstraction of the plasmonic bowtie antenna |

Optics Express, Vol. 19, Issue 11, pp. 10456-10461 (2011)

http://dx.doi.org/10.1364/OE.19.010456

Acrobat PDF (1528 KB)

### Abstract

A new class of bowtie antennas with Sierpiński fractal features is proposed for sensing molecular vibration modes in the near- to mid-infrared. These antennas offer a compact device footprint and an enhanced confinement factor compared to a bowtie antenna. Through extensive simulations, it is shown that these characteristics are related to the ability of this fractal geometry to become polarized. Simulation results demonstrate that these antennas may be tuned between 700nm ≤ λ ≤ 3.4µm and that electric field enhancement by 56 is possible at the center of the antenna gap.

© 2011 OSA

## 1. Introduction

4. C. Gaubert, L. Chusseau, A. Giani, D. Gasquet, F. Garet, F. Aquistapace, L. Duvillaret, J.-L. Coutaz, and W. Knap, “THz fractal antennas for electrical and optical semiconductor emitters and receptors,” Phys. Status Solidi **1**(6c), 1439–1444 (2004). [CrossRef]

7. A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. **102**(11), 113901 (2009). [CrossRef] [PubMed]

8. J. Matteo and L. Hesselink, “Fractal extensions of near-field aperture shapes for enhanced transmission and resolution,” Opt. Express **13**(2), 636–647 (2005). [CrossRef] [PubMed]

9. B. Hou, X. Q. Liao, and J. K. S. Poon, “Resonant infrared transmission and effective medium response of subwavelength H-fractal apertures,” Opt. Express **18**(4), 3946–3951 (2010). [CrossRef] [PubMed]

10. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. **98**(26), 266802 (2007). [CrossRef] [PubMed]

12. G. W. Hanson, “On the applicability of the surface impedance integral equation for optical and near infrared copper dipole antennas,” IEEE Trans. Antenn. Propag. **54**(12), 3677–3685 (2006). [CrossRef]

13. A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics **2**(5), 307–310 (2008). [CrossRef]

14. J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. **9**(5), 1897–1902 (2009). [CrossRef] [PubMed]

## 2. The Sierpiński fractal plasmonic antenna

## 3. Simulation technique and results

_{s}= 1.5. The antennas are given the properties of gold and the Drude model is used to represent the permittivity function of gold over a wide spectral range. Drude parameters of ε

_{∞}= 9.069, τ

_{c}= 8.669 fs, and ω

_{p}= 1.354 × 10

^{16}rad/s are based on an optimal fit to well-established experimental data and ensure that the optical properties of gold are well-represented for the wavelengths of interest [18

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

19. A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B **71**(8), 085416 (2005). [CrossRef]

20. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, ““Gap-Dependent Optical Coupling of Single “Bowtie” Nanoantennas Resonant in the Visible,” Nano Lett. **4**(5), 957–961 (2004). [CrossRef]

*λ*≤ 4.0µm. The antennas are excited from below the silica substrate and the electric fields are measured 3nm above the top surface of the antenna. The antenna gap is held constant at 30nm × 30nm for each structure and the gold film thickness is chosen to be 35nm. A spatial resolution of

*Δx*=

*Δy*=

*Δz*= 3nm is used to ensure that the electromagnetic fields in the antenna gap are accurately resolved. A time step of

*Δt*= 4.75as ensures stability at this resolution. Each triangle is connected to its neighbors by a thin strip to avoid geometric singularities, which also ensures excitation of a collective response from the entire structure (i.e. the triangles are all connected). The flare angle of the antenna is held constant at 90°, so that the length and width of the antenna are equal.

*L*= 475nm, is shown in Fig. 1(e). There are several observations that may be drawn from these spectral response plots. As the iteration of SFPA increases from zero to three, the wavelength of the main resonance is red-shifted from 1.40μm to 2.44μm and the enhancement factor increases from 37 to 49. In addition, there is a rearrangement of the minor resonances that occur at shorter wavelengths. As shown in Fig. 1(e), the bowtie antenna has a minor resonance at λ = 822nm, whereas the first iteration SFPA has minor resonances at λ = {660, 787} nm. It should be pointed out that these resonances are much weaker than the main resonance and do not effectively confine incident radiation to the gap. Therefore only the main resonance will be discussed in the remainder of this paper.

## 4. Geometric investigation

## 5. Conclusion

## Acknowledgements

## References and links

1. | B. B. Mandelbrot, |

2. | K. J. Falconer, |

3. | D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Trans. Antennas Propag. |

4. | C. Gaubert, L. Chusseau, A. Giani, D. Gasquet, F. Garet, F. Aquistapace, L. Duvillaret, J.-L. Coutaz, and W. Knap, “THz fractal antennas for electrical and optical semiconductor emitters and receptors,” Phys. Status Solidi |

5. | Y.-J. Bao, B. Zhang, Z. Wu, J.-W. Si, M. Wang, R.-W. Peng, X. Lu, J. Shao, Z.-F. Li, X.-P. Hao, and N.-B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. |

6. | F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Teraherz electric response of fractal metamaterial structures,” Phys. Rev. B |

7. | A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. |

8. | J. Matteo and L. Hesselink, “Fractal extensions of near-field aperture shapes for enhanced transmission and resolution,” Opt. Express |

9. | B. Hou, X. Q. Liao, and J. K. S. Poon, “Resonant infrared transmission and effective medium response of subwavelength H-fractal apertures,” Opt. Express |

10. | L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. |

11. | A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. |

12. | G. W. Hanson, “On the applicability of the surface impedance integral equation for optical and near infrared copper dipole antennas,” IEEE Trans. Antenn. Propag. |

13. | A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics |

14. | J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. |

15. | S. A. Maier, |

16. | L. Wang and X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. |

17. | S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature |

18. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

19. | A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B |

20. | D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, ““Gap-Dependent Optical Coupling of Single “Bowtie” Nanoantennas Resonant in the Visible,” Nano Lett. |

**OCIS Codes**

(140.4780) Lasers and laser optics : Optical resonators

(260.3910) Physical optics : Metal optics

(260.5740) Physical optics : Resonance

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(250.5403) Optoelectronics : Plasmonics

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: March 14, 2011

Revised Manuscript: March 28, 2011

Manuscript Accepted: March 29, 2011

Published: May 12, 2011

**Citation**

Shawn Sederberg and A.Y. Elezzabi, "Sierpiński fractal plasmonic antenna: a fractal abstraction of the plasmonic bowtie antenna," Opt. Express **19**, 10456-10461 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10456

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### References

- B. B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freeman, 1982).
- K. J. Falconer, Fractal Geometry: Mathematical Foundations and Applications (Wiley, 2003).
- D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Trans. Antennas Propag. 45, 38–57 (2003).
- C. Gaubert, L. Chusseau, A. Giani, D. Gasquet, F. Garet, F. Aquistapace, L. Duvillaret, J.-L. Coutaz, and W. Knap, “THz fractal antennas for electrical and optical semiconductor emitters and receptors,” Phys. Status Solidi 1(6c), 1439–1444 (2004). [CrossRef]
- Y.-J. Bao, B. Zhang, Z. Wu, J.-W. Si, M. Wang, R.-W. Peng, X. Lu, J. Shao, Z.-F. Li, X.-P. Hao, and N.-B. Ming, “Surface-plasmon-enhanced transmission through metallic film perforated with fractal-featured aperture array,” Appl. Phys. Lett. 90(25), 251914 (2007). [CrossRef]
- F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Teraherz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008). [CrossRef]
- A. Agrawal, T. Matsui, W. Zhu, A. Nahata, and Z. V. Vardeny, “Terahertz spectroscopy of plasmonic fractals,” Phys. Rev. Lett. 102(11), 113901 (2009). [CrossRef] [PubMed]
- J. Matteo and L. Hesselink, “Fractal extensions of near-field aperture shapes for enhanced transmission and resolution,” Opt. Express 13(2), 636–647 (2005). [CrossRef] [PubMed]
- B. Hou, X. Q. Liao, and J. K. S. Poon, “Resonant infrared transmission and effective medium response of subwavelength H-fractal apertures,” Opt. Express 18(4), 3946–3951 (2010). [CrossRef] [PubMed]
- L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007). [CrossRef] [PubMed]
- A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101(4), 043901 (2008). [CrossRef] [PubMed]
- G. W. Hanson, “On the applicability of the surface impedance integral equation for optical and near infrared copper dipole antennas,” IEEE Trans. Antenn. Propag. 54(12), 3677–3685 (2006). [CrossRef]
- A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2(5), 307–310 (2008). [CrossRef]
- J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]
- S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
- L. Wang and X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. 90(26), 261105 (2007). [CrossRef]
- S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef] [PubMed]
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
- A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005). [CrossRef]
- D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, ““Gap-Dependent Optical Coupling of Single “Bowtie” Nanoantennas Resonant in the Visible,” Nano Lett. 4(5), 957–961 (2004). [CrossRef]

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