## Optimization of an optical wireless nanolink using directive nanoantennas |

Optics Express, Vol. 21, Issue 2, pp. 2369-2377 (2013)

http://dx.doi.org/10.1364/OE.21.002369

Acrobat PDF (1817 KB)

### Abstract

Optical connects will become a key point in the next generation of integrated circuits, namely the upcoming nanoscale optical chips. In this context, nano-optical wireless links using nanoantennas have been presented as a promising alternative to regular plasmonic waveguide links, whose main limitation is the range propagation due to the metal absorption losses. In this paper we present the complete design of a high-capability wireless nanolink using matched directive nanoantennas. It will be shown how the use of directive nanoantennas clearly enhances the capability of the link, improving its behavior with respect to non-directive nanoantennas and largely outperforming regular plasmonic waveguide connects.

© 2013 OSA

## 1. Introduction

1. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express **13**, 6645–6650 (2005). [CrossRef] [PubMed]

5. G. Veronis, Z. Yu, S. E. Kocabas, D. A. B. Miller, M. L. Brongersma, and S. Fan, “Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale,” Chin. Opt. Lett. **7**, 302–308 (2009). [CrossRef]

6. A. Alù and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett. **104**, 213902 (2010). [CrossRef] [PubMed]

8. 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**, 957–961 (2004). [CrossRef]

10. L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photon. **5**, 83–90 (2011). [CrossRef]

11. H. F. Hofmann, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical yagi-uda antenna,” New J. Phys. **9**, 207 (2007). [CrossRef]

6. A. Alù and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett. **104**, 213902 (2010). [CrossRef] [PubMed]

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

6. A. Alù and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett. **104**, 213902 (2010). [CrossRef] [PubMed]

## 2. Numerical results

13. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science **329**, 930–933 (2010). [CrossRef] [PubMed]

^{2}section separated by a 10 nm glass gap. The link frequency is set to 461.2185 THz, corresponding to a wavelength of

*λ*

_{0}= 650 nm in vacuum and

*λ*

_{g}= 447.97 nm in glass. We simulate a long enough piece of MIM waveguide (6

*μ*m, about 13.4

*λ*

_{g}) using the surface integral equation-method of moments (SIE-MoM) technique. The waveguide is terminated by a matched load to further avoid any end reflection. A detailed image of the matched load is shown in the upper-right inset of Fig. 1. It consists of a pyramid-shaped lossy material whose shape and constitutive parameters were selected to match the vacuum gap impedance; the values of

*ε*= (1 − 2

_{r}*j*)

*ε*

_{r}_{g}and

*μ*= 1 − 2

_{r}*j*are considered, with

*ε*

_{r}_{g}the relative permittivity of glass, providing a very small reflection coefficient amplitude of 0.0256 (below 0.066% in power reflection.) The surfaces of the waveguide and the matched load were modeled using 47898 Rao-Wilton-Glisson (RWG) [16

16. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. **30**, 409–418 (1982). [CrossRef]

*Z*

_{0}=

*V/I*, where

*V*is the voltage, obtained as the line integral of the electric field from the center of one arm to the other, and where

*I*is the displacement current, obtained according to Ampère’s law as the circulation of the magnetic field along a closed-loop enclosing one arm of the waveguide. The characteristic impedance obtained in this way is

*Z*

_{0}= 199.13 − 1.28

*j*Ω. We also calculate the propagation constant

*γ*=

*α*+

*jβ*, consisting of the attenuation constant

*α*and the wave vector

*β*. Figure 2(a) shows a line cut of the amplitude of the electric field along the center of the gap for the waveguide terminated by the matched load. The field profile obtained for the waveguide terminated by an open end is also shown for comparison. In the latter case, a standing wave pattern is observed close to the open end due to the wave reflection. Exploiting this pattern we determine the effective wavelength of the guided plasmon mode and the respective wave vector, leading to

*β*= 56.61 rad/

*μ*m. Owing to the virtual absence of power reflection, the standing wave pattern is almost negligible in the case of the matched terminated waveguide. From the exponential decay with distance for this profile we determine the attenuation constant as

*α*= 0.757 Np/

*μ*m, a strong attenuation which drastically limits the interconnect distance when using the MIM waveguide.

*D*

_{0}[19]. The range of possible values was set from 0.1 to 0.5

*λ*

_{g}both for lengths and distances. The SIE-MoM analysis technique was applied for the accurate evaluation of

*D*

_{0}(which constitutes the GA fitness function) for each of the individuals in each generation of the GA. The final design achieved after 82 generations (starting with a random population of 64 individuals and considering mutation and crossover probabilities of 0.01 and 0.6 respectively) is shown in Fig. 1(a) and Fig. 1(b) for the transmitting and receiving sides. Through reciprocity, the same design is used for the transmit and the receive antenna. The length of the feed element is 96.4 nm, and the lengths of the successive directors are 51.2 nm, 50.9 nm, and 51.9 nm (0.215

*λ*

_{g}, 0.114

*λ*

_{g}, 0.114

*λ*

_{g}, and 0.116

*λ*

_{g}respectively). The distance between the feed element and the first director is 64.3 nm and the successive distances between directors are 81.4 nm and 121.4 nm (0.144

*λ*

_{g}, 0.182

*λ*

_{g}, and 0.271

*λ*

_{g}respectively.) The attained directivity with this design is

*D*

_{0}= 3.471 n.u. or 5.4 dBi (dB with respect to an isotropic theoretical antenna).

11. H. F. Hofmann, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical yagi-uda antenna,” New J. Phys. **9**, 207 (2007). [CrossRef]

13. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science **329**, 930–933 (2010). [CrossRef] [PubMed]

12. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical yagi-uda antenna,” Nat. Photon. **4**, 312–315 (2010). [CrossRef]

*Z*

_{0}, which can be achieved by means of a properly designed matching network. For this, we first calculate the reflection coefficient for fields at the antenna connection point, Γ = |Γ|

*e*. Figure 2(b) shows the standing wave pattern of the electric field on a linear path along the gap of the transmitting waveguide. The reflection coefficient can be determined by curve fitting of this standing wave pattern. We only consider the fundamental mode for the fitting procedure, since other higher order modes are negligible in comparison with the fundamental one. The field amplitude for this mode at position

^{jϕ}*x*in the waveguide can be described as

*E*=

*E*

_{0}

*e*

^{−γx}(1 + Γ

*e*

^{2γx}), with the reflection plane (antenna connection point) located at

*x*= 0.

*E*

_{0}is the field amplitude of the wave in the forward direction (direction from the source to the antenna) and

*γ*is the propagation constant. The reflection coefficient so determined for the nanoantenna alone, without matching network, is Γ = 0.6362

*e*

^{j1.4343}, meaning that 40.5% of the power available on the waveguide is reflected and only 59.5% is accepted by the antenna. Similarly as done in [6

**104**, 213902 (2010). [CrossRef] [PubMed]

*ε*of this nanoparticle the impedance matching can be achieved, obtaining the point of minimum reflection (maximum transmission) for

_{r}*ε*= 3.1, with Γ = 0.1919

_{r}*e*

^{−j0.3473}. This means a reflection below 3.7 % of the available power and 96.3 % of power accepted by the nanoantenna. The input impedance of the nanoantenna with the matching network can be obtained from the reflection coefficient and the waveguide characteristic impedance as

*Z*=

_{in}*Z*

_{0}(1 + Γ)/(1 − Γ), leading to

*Z*= 283.5 − 40.306

_{in}*j*Ω. The standing wave pattern and the best fit for this case are also collected in Fig. 2(b). Now, by computing a line integral over the electric field from one arm to the other at each point along the waveguide, we obtain a standing wave pattern for the voltage (not shown since it is analogous to the electric field pattern of Fig. 2(b)). Applying the fitting procedure described above to this voltage pattern we determine the amplitude of the voltage wave flowing in the forward direction. Taking the value of this voltage at the antenna connection point,

*V*, and the characteristic impedance,

*Z*

_{0}, we can calculate the power available at the antenna feeding point as

*P*= (1 − |Γ|

_{in}^{2})

*P*. On the other hand, the power being effectively radiated by the nanoantenna,

_{tx}*P*, can be calculated by computing the flux of the Poynting vector across a closed surface containing both the antenna and the waveguide [19]. The efficiency of the transmit antenna can then be obtained as the ratio

_{rad}*η*=

*P*/

_{rad}*P*, leading to

_{in}*η*= 0.412, which, by reciprocity, will be also the efficiency of the receiving antenna.

*d*= 17.92

*μ*m (40

*λ*

_{g}); the sketch is depicted in the lower inset of Fig. 1. Figures 3(a) and 3(b) illustrate the electric near field amplitude on transverse planes to the transmit and receive nanoantennas respectively. Looking at Fig. 3(a) and the respective line cut in Fig. 2(b), we can observe that the amplitude of the field is almost constant on the gap of the transmitting waveguide, showing a smooth standing wave pattern. This is due to the good impedance match between the antenna and the waveguide. Similarly, we observe in Fig. 3(b) that the amplitude of the field is almost constant in the gap of the receiving waveguide. In this case, this is due to the effect of the matched load termination, absorbing almost all the energy. The power balance (ratio of the received power at the output of the Rx nanoantenna,

*P*, to the available power at the feeding point of the Tx nanoantenna,

_{rx}*P*) obtained from this full-wave simulation is

_{tx}*P*/

_{rx}*P*= 6.9948 · 10

_{tx}^{−6}(−51.55 dB).

*P*/

_{rx}*P*= [

_{tx}*λ*

_{g}/(4

*πd*)]

^{2}(1−|Γ

*|*

_{tx}^{2})(1 − |Γ

*|*

_{rx}^{2})

*η*. The first term on the second hand of Friis equation accounts for free space path losses in the external (glass) region with the link distance

_{tx}η_{rx}D_{tx}D_{rx}*d*, second and third account for impedance mismatch between nanoantennas and their respective optical waveguides,

*η*and

_{tx}*η*are the radiation efficiencies of the nanoantennas, and

_{rx}*D*and

_{tx}*D*are the directivities of the two nanoantennas facing each other. We are assuming that the transmit and receive nanoantennas are perfectly aligned, so there are no polarization losses. The result provided by the Friis formula with Γ

_{rx}*= Γ*

_{tx}*= Γ,*

_{rx}*η*=

_{tx}*η*=

_{rx}*η*, and

*D*=

_{tx}*D*=

_{rx}*D*

_{0}, where Γ,

*η*and

*D*

_{0}have been calculated previously, is

*P*/

_{rx}*P*= 7.5024 · 10

_{tx}^{−6}(−51.25 dB), which is in perfect agreement with the full wave simulation.

*d*for three different connects: (i) MIM plasmonic waveguide, (ii) broadcast wireless connect using matched dipole nanoantennas, and (iii) the proposed wireless connect using matched directive Yagi-Uda nanoantennas. The curves have been obtained using the Friis equation for the wireless links, and using the exponential decay with the attenuation constant

*α*for the plasmonic waveguide. Full wave simulations of the complete Tx/Rx directive link have also been carried out for a number of distances (between 1.5

*μ*m and 32.5

*μ*m) and represented with marks. Looking at Fig. 4, it can be seen that for distances larger than about 6 to 8

*μ*m, the wireless connects clearly outperform the plasmonic waveguide connect. The reason is that the power density decays as 1/

*d*

^{2}for wireless links, while it drops exponentially as exp(−2

*αd*) for the waveguide connect. This slope change means that the wireless link will always outperform the waveguide connect after a certain distance. In the particular case of plasmonic waveguides, this distance is moderately short due to high metal absorption. Otherwise, the directive link always provides a better power balance than the broadcast link. The received power is almost 7 dB higher due to the higher directivity of the Yagi-Uda nanoantennas. An additional advantage of this higher directivity is a better field confinement compared with the broadcast link, reducing interference and increasing the density of connections with minimal footprint, which indeed is a key point for miniaturization.

21. B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: Molding, printing, and other techniques,” Chem. Rev. **105**, 1171–1196 (2005). [CrossRef] [PubMed]

22. J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method of moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A **28**, 1341–1348 (2011). [CrossRef]

24. L. Landesa, M. G. Araújo, J. M. Taboada, L. Bote, and F. Obelleiro, “Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies,” Opt. Express **20**, 17237–17249 (2012). [CrossRef]

25. S. M. Rao and D. R. Wilton, “E-field, h-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromagnetics **10**, 407–421 (1990). [CrossRef]

27. P. Yla-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. **53**, 1168–1173 (2005). [CrossRef]

22. J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method of moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A **28**, 1341–1348 (2011). [CrossRef]

24. L. Landesa, M. G. Araújo, J. M. Taboada, L. Bote, and F. Obelleiro, “Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies,” Opt. Express **20**, 17237–17249 (2012). [CrossRef]

28. A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3d simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A **26**, 732–740 (2009). [CrossRef]

29. J. Song, C.-C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. **45**, 1488–1493 (1997). [CrossRef]

33. M. G. Araújo, J. M. Taboada, J. Rivero, D. M. Solís, and F. Obelleiro, “Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm,” Opt. Lett. **37**, 416–418 (2012). [CrossRef] [PubMed]

## 3. Conclusions

**104**, 213902 (2010). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express |

2. | G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. |

3. | G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. |

4. | J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B |

5. | G. Veronis, Z. Yu, S. E. Kocabas, D. A. B. Miller, M. L. Brongersma, and S. Fan, “Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale,” Chin. Opt. Lett. |

6. | A. Alù and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett. |

7. | S. A. Maier, |

8. | 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. |

9. | P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science |

10. | L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photon. |

11. | H. F. Hofmann, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical yagi-uda antenna,” New J. Phys. |

12. | T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical yagi-uda antenna,” Nat. Photon. |

13. | A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science |

14. | M. Klemm, “Directional plasmonic nanoantennas for wireless links at the nanoscale,” in |

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

16. | S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. |

17. | M. G. Araújo, D. M. Solís, J. Rivero, J. M. Taboada, F. Obelleiro, and L. Landesa, “Design of optical nanoantennas with the surface integral equation method of moments,” in |

18. | D. Goldberg, |

19. | C. A. Balanis, |

20. | Z. Cui, |

21. | B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: Molding, printing, and other techniques,” Chem. Rev. |

22. | J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method of moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A |

23. | M. G. Araújo, J. M. Taboada, D. M. Solís, J. Rivero, L. Landesa, and F. Obelleiro, “Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers,” Opt. Express |

24. | L. Landesa, M. G. Araújo, J. M. Taboada, L. Bote, and F. Obelleiro, “Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies,” Opt. Express |

25. | S. M. Rao and D. R. Wilton, “E-field, h-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromagnetics |

26. | P. Yla-Oijala, M. Taskinen, and S. Jarvenpaa, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. |

27. | P. Yla-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. |

28. | A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3d simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A |

29. | J. Song, C.-C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. |

30. | O. Ergul and L. Gurel, “A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. |

31. | J. Taboada, M. Araújo, J. Bértolo, L. Landesa, F. Obelleiro, and J. Rodríguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. |

32. | J. Taboada, M. Araújo, F. Obelleiro, J. Rodríguez, and L. Landesa, “MLFMA-FFT parallel algorithm for the solution of extremely large problems in electromagnetics,” Proceedings of the IEEE |

33. | M. G. Araújo, J. M. Taboada, J. Rivero, D. M. Solís, and F. Obelleiro, “Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm,” Opt. Lett. |

**OCIS Codes**

(200.4650) Optics in computing : Optical interconnects

(240.6680) Optics at surfaces : Surface plasmons

(250.5300) Optoelectronics : Photonic integrated circuits

(260.2110) Physical optics : Electromagnetic optics

(260.3910) Physical optics : Metal optics

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: December 20, 2012

Manuscript Accepted: January 4, 2013

Published: January 23, 2013

**Citation**

Diego M. Solís, José M. Taboada, Fernando Obelleiro, and Luis Landesa, "Optimization of an optical wireless nanolink using directive nanoantennas," Opt. Express **21**, 2369-2377 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-2369

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### References

- L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13, 6645–6650 (2005). [CrossRef] [PubMed]
- G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett.30, 3359–3361 (2005). [CrossRef]
- G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett.87, 131102 (2005). [CrossRef]
- J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73, 035407 (2006). [CrossRef]
- G. Veronis, Z. Yu, S. E. Kocabas, D. A. B. Miller, M. L. Brongersma, and S. Fan, “Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale,” Chin. Opt. Lett.7, 302–308 (2009). [CrossRef]
- A. Alù and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett.104, 213902 (2010). [CrossRef] [PubMed]
- S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
- 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, 957–961 (2004). [CrossRef]
- P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308, 1607–1608 (2005). [CrossRef] [PubMed]
- L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photon.5, 83–90 (2011). [CrossRef]
- H. F. Hofmann, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical yagi-uda antenna,” New J. Phys.9, 207 (2007). [CrossRef]
- T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical yagi-uda antenna,” Nat. Photon.4, 312–315 (2010). [CrossRef]
- A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science329, 930–933 (2010). [CrossRef] [PubMed]
- M. Klemm, “Directional plasmonic nanoantennas for wireless links at the nanoscale,” in Proceedings of Antennas and Propagation Conference, (Loughborough, 2011).
- J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett.9, 1897–1902 (2009). [CrossRef] [PubMed]
- S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag.30, 409–418 (1982). [CrossRef]
- M. G. Araújo, D. M. Solís, J. Rivero, J. M. Taboada, F. Obelleiro, and L. Landesa, “Design of optical nanoantennas with the surface integral equation method of moments,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications, (Cape Town, 2012).
- D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, MA, 1989).
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- Z. Cui, Nanofabrication: Principles, Capabilities and Limits (Springer, New York, 2008).
- B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: Molding, printing, and other techniques,” Chem. Rev.105, 1171–1196 (2005). [CrossRef] [PubMed]
- J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method of moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28, 1341–1348 (2011). [CrossRef]
- M. G. Araújo, J. M. Taboada, D. M. Solís, J. Rivero, L. Landesa, and F. Obelleiro, “Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers,” Opt. Express20, 9161–9171 (2012). [CrossRef] [PubMed]
- L. Landesa, M. G. Araújo, J. M. Taboada, L. Bote, and F. Obelleiro, “Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies,” Opt. Express20, 17237–17249 (2012). [CrossRef]
- S. M. Rao and D. R. Wilton, “E-field, h-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromagnetics10, 407–421 (1990). [CrossRef]
- P. Yla-Oijala, M. Taskinen, and S. Jarvenpaa, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40, RS6002 (2005). [CrossRef]
- P. Yla-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag.53, 1168–1173 (2005). [CrossRef]
- A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3d simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A26, 732–740 (2009). [CrossRef]
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