## Optical horn antennas for efficiently transferring photons from a quantum emitter to a single-mode optical fiber |

Optics Express, Vol. 21, Issue 2, pp. 1762-1772 (2013)

http://dx.doi.org/10.1364/OE.21.001762

Acrobat PDF (803 KB)

### Abstract

We theoretically demonstrate highly efficient optical coupling between a single quantum emitter and a monomode optical fiber over remarkably broad spectral ranges by extending the concept of horn antenna to optics. The optical horn antenna directs the radiation from the emitter toward the optical fiber and efficiently phase-matches the photon emission with the fiber mode. Numerical results show that an optical horn antenna can funnel up to 85% of the radiation from a dipolar source within an emission cone semi-angle as small as 7 degrees (antenna directivity of 300). It is also shown that 50% of the emitted power from the dipolar source can be collected and coupled to an SMF-28 fiber mode over spectral ranges larger than 1000 nm, with a maximum energy transfer reaching 70 %. This approach may open new perspectives in quantum optics and sensing.

© 2013 OSA

## 1. Introduction

1. T. Miyazawa, K. Takemoto, Y. Sakuma, S. Hirose, T. Usuki, N. Yokoyama, M. Takatsu, and Y. Arakawa, “Single-photon generation in the 1.55-mum optical-fiber band from an inas/inp quantum dot,” Jpn. J. Appl. Phys. **44**, L620–L622 (2005). [CrossRef]

2. E. Moreau, I. Robert, JM Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. **79**, 2865–2867 (2001). [CrossRef]

9. X.W. Chen, S. Götzinger, and V. Sandoghdar, “99% efficiency in collecting photons from a single emitter,” Opt. lett. **36**, 3545–3547 (2011). [CrossRef] [PubMed]

10. D.E. Chang, A.S. Sørensen, P.R. Hemmer, and M.D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. **97**, 053002 (2006). [CrossRef] [PubMed]

11. M. Davanço and K. Srinivasan, “Fiber-coupled semiconductor waveguides as an efficient optical interface to a single quantum dipole,” Opt. lett. **34**, 2542–2544 (2009). [CrossRef] [PubMed]

11. M. Davanço and K. Srinivasan, “Fiber-coupled semiconductor waveguides as an efficient optical interface to a single quantum dipole,” Opt. lett. **34**, 2542–2544 (2009). [CrossRef] [PubMed]

## 2. Principle and optical antenna geometry

*λ*/4 where

_{g}*λ*is the effective wavelength of the waveguide mode. This optimum distance is defined precisely from a complex analysis of impedance matching between the coax and the waveguide and is found empirically as a function of the length of source wire [13

_{g}13. P. Wade, “Rectangular waveguide to coax transition design,” http://f1chf.free.fr/PDF/convertisseursWR90etWR75.pdf.

*λ*/4 protruding source wire placed within a waveguide of square section induces a maximum radiation in free space through the HA when it is set at

*λ*/4 from the reflector. The basic principle of the HA is that the back-reflected radiation along the closed channel interferes constructively with the radiation that propagates directly toward the open channel, leading to an overall radiation pattern directed outside of the waveguide. Then, the tapered horn provides a gradual transition structure to match the impedance of the waveguide to the vacuum. Note that high directivity and impedance-matching are achieved for tapered waveguides of aspect ratios (length/aperture size) that are high enough to induce output waves with nearly constant phase across the aperture (planar wavefronts).

_{g}5. D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B **26**, 1473–1478 (2009). [CrossRef]

14. W. Lukosz and R. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. ii. radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am. **67**, 1615–1619 (1977). [CrossRef]

*π*-plane in the following).

## 3. Simulation

*ω*[16

16. L. Novotny and B. Hecht, *Principle of nano-optics* (Cambridge University Press, 2006). [CrossRef]

*r*,

*θ*,

*z*) under the form

**f**(

*r,z*)exp[

*imθ*], where

*m*∈

*N*. Constant

*m*is the rotational symmetry order of the simulation defined by the electromagnetic spatial symmetry of the source. In our case, the excitation of the HA with an oscillating dipole oriented along the plane (

*r*,

*θ*) perpendicular to the symmetry axis (0

*z*) of the structure imposes

*m*= 1, leading to the simulation of linearly-polarized transverse fields. The flaring dielectric waveguide on which the QE is attached is placed at a distance

*h*from the mirror (Fig. 1). Its refractive index (

*n*) and length (

*L*) are chosen to be equal to 1.52 and 42 microns, respectively. Its radius of curvature (

*R*) is chosen to be a few hundred nanometers large to efficiently outcouple photons from the dipole source into its tapered body. Dispersion within the dielectric horn is neglected whereas the dielectric constant of the metallic mirror is defined by a Drude model that fits the dielectric constant of gold at

*λ*= 1.55 microns given by Palik’s book [17]. Since the computation volume terminates at the end facet of the dielectric horn, the fields calculated at its upper limit can be directly used for the calculation of the mode coupling into a fiber. The second step, of the HA-to-fiber optical coupling, is simulated with the well-known overlap integral method [18]. Note that the reflection at the

*π*-plane is not included in our antenna model. Since the index difference between the dielectric horn and the optical fiber does not exceed 0.053, the reflectance at the

*π*-plane (of the order of 4 10

^{−4}) is small enough to be neglected.

*T*defined as : where

*q*is the quantum yield of the emitter,

*η*is the collection efficiency of the HA and

*C*is the coupling efficiency between the photons that leave the HA and the fiber mode. Factor

_{m}*T*represents the ratio of emitted photons that are collected by the HA and outcoupled into the fiber mode.

*q*is obtained from : where

*γ*and

_{r}*γ*are the radiative and non radiative decay rates of the QE. We have

_{nr}*γ*=

_{r}*P*/

_{r}*P*

_{0}and

*γ*=

_{nr}*P*/

_{nr}*P*

_{0}where

*P*is the power radiated in free space by the emitter coupled to the HA,

_{r}*P*is the power dissipated by the HA, and

_{nr}*P*

_{0}is the power radiated by the emitter in free space without the presence of the antenna.

*η*) of the HA is defined as the fraction of radiated power that is channeled within the body of the flaring dielectric waveguide. It is obtained from : where

*P*is the power collected by the HA.

_{i}*C*, defined as : where

_{m}*P*and

_{m}*P*are the powers carried by the fiber mode and the collected optical field that leaves the HA, respectively.

_{i}*P*and

_{m}*P*are obtained from Poynting vector integrations over specific areas in the

_{i}*π*-plane : Here the unit vector

*e⃗*defines the direction of the fiber axis, and the expressions of constants

_{z}*a*and

_{m}*b*are based on the overlap integrals between the collected fields that leave the HA (

_{m}*E⃗*,

_{i}*H⃗*) and the mode field distribution (

_{i}*E⃗*,

_{m}*H⃗*) : In these simulations, a SMF-28 optical fiber is considered (single mode at telecommunication wavelengths) whose core diameter is 8.2

_{m}*μ*m. Its core and cladding indices are deduced from the mode optical parameters given in the fiber datasheet. For accurate simulation of the HA optical properties, the lateral extent of the FDTD computation volume was chosen to be wide enough (15 microns along the radial coordinate) that the captured field distributions were significantly wider than the lateral extent of the fiber core.

*P*(

*β*,

*θ*) is the angular power radiated in the direction of polar angle

*β*and azimuthal angle

*θ*, and

*P*= ∬

_{r}*P*(

*β*,

*θ*)

*sinβdβdθ*is the integral over all angles. An isotropic source would have a directivity of 1, whereas for a dipolar emitter Dir=1.5.

## 4. Results and discussions

*P*(

_{out}*r*)/

*P*that crosses the output

_{r}*π*-plane of two different HA geometries, as a function of the bounding radial space coordinate

*r. P*(

_{out}*r*) is the power transmitted inside the circular area of radius

*r*contained in the

*π*-plane. The origin of coordinate

*r*is thus the intersection point between the

*π*-plane and the symmetry axis of the optical HA. The two HA geometries are given in the figure inset and the wavelength

*λ*is equal to 1450 nm. We see that the two HAs collect 80% and 85% of the total power radiated by the dipole source, respectively. The two vertical dotted lines represent the lateral limit in the

*π*-plane of the two dielectric horns considered here (lines positioned at

*D*/2). As a comparison, the green curve of Fig. 2(a) represents

*P*(

_{out}*r*)/

*P*achieved in the

_{r}*π*-plane without the presence of HA (free space dipole emission). The collection and emission properties of the optical HA are also revealed in Fig. 2(b) which plots the spatial distribution of the real part of the electric field that propagates along the longitudinal plane (

*r,z*) that contains the dipole source and the first 16 microns of the dielectric horn. The real part of the electric field is represented to show the amplitude and phase properties of the waves that are channeled within the dielectric horn. The configuration of optical HA under consideration here is detailed under the figure. We see that the propagating optical field within the flaring dielectric waveguide show planar wavefronts and its amplitude distribution is of gaussian-like shape. This is confirmed by Fig. 2(a) which show accumulated powers in the

*π*-plane as gaussian-like functions of the radial coordinate. Such field properties may insure highly directive propagations in free space or in optical fibers.

*η*(Eq. (3)) will be defined as

*P*(

_{out}*r*=

*D*/2)/

*P*, ie.

_{r}*P*(Eq. (3)) will be calculated by Poynting vector integration through the microtip output cross-section. Coefficient

_{i}*η*is reported in Figs. 3(a,b) as a function of the dipole-to-mirror spacing (

*h*) for two HA geometries defined in the figure insets. The wavelength range spans in the near-infrared domain from 1000 nm to 2000 nm and the spacing

*h*ranges from 30 nm to 1270 nm. The collection efficiencies of both HA geometries are oscillating functions of

*h*and their local maxima and minima are linear functions of

*λ*. The spacing

*h*that induces maximum collection efficiency (called

*h*) is close to

_{opt}*λ*/4 for both HA geometries, which is consistent with the empirical rules of microwave HA design (the spacing

*h*=

*λ*/4 is represented in the figures with white dashed lines). The little mismatch between the optimum

*h*values achieved for the two HA configurations is the result of the complex optical mechanism between the dipolar source and the optical HA that is strongly dependent on the HA geometrical parameters. Note that the free space propagation phenomenon between the dipole and the mirror explains why the local maxima of

*η*are decreasing functions of

*h*and increasing functions of the ratio

*R*/

*λ*and why the mismatch |

*h*−

_{opt}*λ*/4| is a increasing function

*R*/

*λ*. It also explains why the optical HA has a spectrally broadband operation compared to the microwave HA for which waveguiding occurs between the feed and the reflector. We see from Fig. 3(b) that the collection efficiency

*η*can stay above 78% over the spectral domain 1000 nm–2000 nm with a maximum value larger than 88% at

*λ*= 1000 nm. By comparing Figs. 2(d) and 3, we see that the optical HA is capable of radiating in free space more than 85 % of the energy from a dipole source within an emission cone semi-angle of 7° (corresponds to an antenna directivity of 300).

*ηC*(see section 3), which represents the fraction of radiated power from the dipole source that is collected by the HA and guided within the optical fiber. Figs. 4(a) and (b) show

_{m}*ηC*as a function of

_{m}*λ*and

*h*, for the two different HA geometries shown previously (see figure insets). Our calculation does not take into account the free space propagating photons that are projected onto the entrance facet of the fiber and coupled to the fiber mode. Simulations that include this dipole-to-fiber coupling channel show discrepancies in the energy transfer which do not exceed 1%. Therefore,

*ηC*is a very good approximation of the probability that a photon radiated in free space by a QE coupled with the optical HA is guided into the fiber.

_{m}*λ*= 1450 nm) for the two particular HA geometries studied here.

*ηC*remains slightly higher for the larger radius of curvature of the microtip (R=750 nm). Such energy transfers are made possible by the ability of the HA to direct the dipole emission and to project field distributions onto the fiber entrance facet that tightly overlap the fiber mode (gaussian-like profile of the proper size and plane wavefronts). For both HA geometries, the maximum dipole-to-fiber energy transfer is achieved for dipole-to-mirror spacings

_{m}*h*close to

*λ*/4, which is consistent with the operating principle of HAs.

*γ*and the quantum yield

_{tot}*q*of the HA for the two HAs considered here (see figure insets). Since the energy transfer does not rely on the interaction of the nano-emitter with a high quality factor and/or small mode volume resonator, the emitter’s decay rate is not strongly enhanced (dashed curves) and is rather a slowly increasing function of

*h*/

*λ*(result consistent with Ref. [19

19. C. Vion, P. Spinicelli, L. Coolen, C. Schwob, J.M. Frigerio, J.P. Hermier, and A. Maître, “Controlled modification of single colloidal cdse/zns nanocrystal fluorescence through interactions with a gold surface,” Opt. express **18**, 7440–7455 (2010). [CrossRef] [PubMed]

*h*/

*λ*becomes too small. Figure 5(a) shows for example that

*γ*< 1 when

_{tot}*λ*> 1550nm, for the HA geometry with

*R*= 500nm and

*h*= 290nm (blue dashed curve). Therefore, the radius of curvature at the microtip apex has to be chosen in a way that the optimum spacing

*h*is as large as possible to avoid weak emission configurations. For example, the HA geometry with

_{opt}*R*= 750nm does not hinder the emission rate of the QE over the spectral range considered in this study. The quantum yield (solid curves) of the structure is however almost unaffected (in opposition to metallic nano-antennas which dissipate optical energy) and the HA radiation process remains efficient over unprecedented spectral bandwidths of several hundreds nanometers.

*T*, ie. the probability that a photon emitted by the QE is collected and guided within the optical fiber (see Eq. (1)), for two different pairs (

*R,h*) given in the figure insets, respectively. For each pair (

*R,h*), the diameter

*D*of the output interface of the flaring dielectric waveguide is varied from 9

*μ*m to 12

*μ*m by steps of 1

*μ*m.

*D*has to be chosen to match the width of the field distribution that leaves the optical HA to the width of the fiber mode. We see that the influence of

*D*, ie. the flare angle of the microtip, onto parameter

*T*is important. However,

*D*is not a predominant parameter in the HA-to-fiber coupling since the relationship between

*D*and

*T*is strongly dependant on the other geometrical

*R*and

*h*. Therefore, a trade-off has to be found between the geometrical parameters

*R*,

*L*and

*D*of the flaring dielectric waveguide to optimize the photon transmission in the optical fiber. When

*R*=500nm,

*h*=290nm and

*D*=10

*μ*m,

*T*remains above 50% for wavelengths spanning between 1000 nm and 2000 nm and with a maximum value of about 65% at

*λ*=1400 nm (Fig. 5(b)). When

*R*=750nm,

*h*=390nm and

*D*=11

*μ*m,

*T*is larger than 50% for wavelengths ranging between 1000 nm and 2000 nm and reaches a maximum value of about 70% at

*λ*=1220 nm. The HA configuration involving

*R*=750nm and

*D*=12

*μ*m (gray curve of Fig. 5(c)) is of particular interest for applications in telecommunications since it insures a ratio of guided photons into the fiber larger than 60% over the spectral range 1280 nm–1750 nm with a maximum of 67% at

*λ*= 1430nm.

## 5. Conclusion

20. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale : A yagi-uda nanoantenna in the optical domain,” Phys. Rev. B **76**, 245403 (2007). [CrossRef]

22. T.H. Taminiau, F.D. Stefani, and N.F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express **16**, 10858–10866 (2008). [CrossRef] [PubMed]

## Acknowledgments

## Références

1. | T. Miyazawa, K. Takemoto, Y. Sakuma, S. Hirose, T. Usuki, N. Yokoyama, M. Takatsu, and Y. Arakawa, “Single-photon generation in the 1.55-mum optical-fiber band from an inas/inp quantum dot,” Jpn. J. Appl. Phys. |

2. | E. Moreau, I. Robert, JM Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett. |

3. | M. Pelton, C. Santori, J. Vuc̆ković, B. Zhang, G.S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons : a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. |

4. | J. Claudon, J. Bleuse, N.S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photon. |

5. | D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B |

6. | A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” Nano Lett. |

7. | 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 |

8. | KG Lee, XW Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon. |

9. | X.W. Chen, S. Götzinger, and V. Sandoghdar, “99% efficiency in collecting photons from a single emitter,” Opt. lett. |

10. | D.E. Chang, A.S. Sørensen, P.R. Hemmer, and M.D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. |

11. | M. Davanço and K. Srinivasan, “Fiber-coupled semiconductor waveguides as an efficient optical interface to a single quantum dipole,” Opt. lett. |

12. | C.A. Balanis, |

13. | P. Wade, “Rectangular waveguide to coax transition design,” http://f1chf.free.fr/PDF/convertisseursWR90etWR75.pdf. |

14. | W. Lukosz and R. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. ii. radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am. |

15. | A. Taflove and S.C. Hagness, |

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

17. | E.D. Palik, |

18. | CSF Thomson, |

19. | C. Vion, P. Spinicelli, L. Coolen, C. Schwob, J.M. Frigerio, J.P. Hermier, and A. Maître, “Controlled modification of single colloidal cdse/zns nanocrystal fluorescence through interactions with a gold surface,” Opt. express |

20. | J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale : A yagi-uda nanoantenna in the optical domain,” Phys. Rev. B |

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

22. | T.H. Taminiau, F.D. Stefani, and N.F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express |

**OCIS Codes**

(060.2430) Fiber optics and optical communications : Fibers, single-mode

(230.3990) Optical devices : Micro-optical devices

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

(180.4243) Microscopy : Near-field microscopy

**ToC Category:**

Optical Devices

**History**

Original Manuscript: November 1, 2012

Revised Manuscript: January 7, 2013

Manuscript Accepted: January 9, 2013

Published: January 16, 2013

**Citation**

T. Grosjean, M. Mivelle, G.W. Burr, and F.I. Baida, "Optical horn antennas for efficiently transferring photons from a quantum emitter to a single-mode optical fiber," Opt. Express **21**, 1762-1772 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1762

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### References

- T. Miyazawa, K. Takemoto, Y. Sakuma, S. Hirose, T. Usuki, N. Yokoyama, M. Takatsu, and Y. Arakawa, “Single-photon generation in the 1.55-mum optical-fiber band from an inas/inp quantum dot,” Jpn. J. Appl. Phys.44, L620–L622 (2005). [CrossRef]
- E. Moreau, I. Robert, JM Gérard, I. Abram, L. Manin, and V. Thierry-Mieg, “Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities,” Appl. Phys. Lett.79, 2865–2867 (2001). [CrossRef]
- M. Pelton, C. Santori, J. Vuc̆ković, B. Zhang, G.S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons : a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89, 233602 (2002). [CrossRef] [PubMed]
- J. Claudon, J. Bleuse, N.S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photon.4, 174–177 (2010). [CrossRef]
- D. Gérard, A. Devilez, H. Aouani, B. Stout, N. Bonod, J. Wenger, E. Popov, and H. Rigneault, “Efficient excitation and collection of single-molecule fluorescence close to a dielectric microsphere,” J. Opt. Soc. Am. B26, 1473–1478 (2009). [CrossRef]
- A. Devilez, B. Stout, and N. Bonod, “Compact metallo-dielectric optical antenna for ultra directional and enhanced radiative emission,” Nano Lett.4, 3390–3396 (2010).
- 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]
- KG Lee, XW Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photon.5, 166–169 (2011). [CrossRef]
- X.W. Chen, S. Götzinger, and V. Sandoghdar, “99% efficiency in collecting photons from a single emitter,” Opt. lett.36, 3545–3547 (2011). [CrossRef] [PubMed]
- D.E. Chang, A.S. Sørensen, P.R. Hemmer, and M.D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006). [CrossRef] [PubMed]
- M. Davanço and K. Srinivasan, “Fiber-coupled semiconductor waveguides as an efficient optical interface to a single quantum dipole,” Opt. lett.34, 2542–2544 (2009). [CrossRef] [PubMed]
- C.A. Balanis, Antenna Theory : Analysis and Design (John Wiley & Sons, New-York, 1997).
- P. Wade, “Rectangular waveguide to coax transition design,” http://f1chf.free.fr/PDF/convertisseursWR90etWR75.pdf .
- W. Lukosz and R. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. ii. radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am.67, 1615–1619 (1977). [CrossRef]
- A. Taflove and S.C. Hagness, Computational Electrodynamics : The Finite-Difference Time-Domain Method, Third Edition (Artech House, Boston, 2005).
- L. Novotny and B. Hecht, Principle of nano-optics (Cambridge University Press, 2006). [CrossRef]
- E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
- CSF Thomson, L’optique Guidée Monomode et ses Applications, 15 (Masson, 1983).
- C. Vion, P. Spinicelli, L. Coolen, C. Schwob, J.M. Frigerio, J.P. Hermier, and A. Maître, “Controlled modification of single colloidal cdse/zns nanocrystal fluorescence through interactions with a gold surface,” Opt. express18, 7440–7455 (2010). [CrossRef] [PubMed]
- J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale : A yagi-uda nanoantenna in the optical domain,” Phys. Rev. B76, 245403 (2007). [CrossRef]
- H.F. Hofmann, T. Kosako, and Y. Kadoya, “Design parameters for a nano-optical yagi–uda antenna,” New J. Phys.9, 217 (2007). [CrossRef]
- T.H. Taminiau, F.D. Stefani, and N.F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express16, 10858–10866 (2008). [CrossRef] [PubMed]

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