Abstract

We study the directional far-field response of a spherical nanoantenna via engineering the plasmonic nanosphere’s distance, size, and material. A unified pattern synthesis approach based on the T-matrix method and the particle swarm optimization is proposed for the directional beamforming of the nanoantenna. The angular response of the directional nanoantenna is very sensitive to the material change but is immunized to the random error of the spatial position of each particle. The physical origin of the high directionality is attributed to the coherent near-field distribution with large correlation length. This work provides the fundamental theory and physics for future nanoantenna design.

© 2011 Optical Society of America

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L. Novotny and N. van Hulst, Nat. Photon. 5, 83 (2011).
[CrossRef]

2010

2009

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

2008

2007

J. J. Li, A. Salandrino, and N. Engheta, Phys. Rev. B 76, 245403 (2007).
[CrossRef]

2006

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

2005

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

2004

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

1999

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

1998

1977

Ahmadi, A.

Alu, A.

A. Alu and N. Engheta, Nat. Photon. 2, 307 (2008).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

Avlasevich, Y.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Burger, S.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Carter, W. H.

Ding, K. H.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

Djurisic, A. B.

Eisler, H. J.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Elazar, J. M.

Engheta, N.

A. Alu and N. Engheta, Nat. Photon. 2, 307 (2008).
[CrossRef]

J. J. Li, A. Salandrino, and N. Engheta, Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Fan, S. H.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Hakanson, U.

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Halas, N. J.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Hale, G. D.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Hecht, B.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Henkel, C.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Jackson, J. B.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Kalkbrenner, T.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Kinkhabwala, A.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

Kuhn, S.

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Li, J. J.

J. J. Li, A. Salandrino, and N. Engheta, Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Majewski, M. L.

Martin, O. J. F.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Moerner, W. E.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Mosallaei, H.

Muhlschlegel, P.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Mullen, K.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Novotny, L.

L. Novotny and N. van Hulst, Nat. Photon. 5, 83 (2011).
[CrossRef]

Oldenburg, S. J.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

Pohl, D. W.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Polman, A.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

Rahmat-Samii, Y.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Rakic, A. D.

Robinson, J.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Rogobete, L.

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Salandrino, A.

J. J. Li, A. Salandrino, and N. Engheta, Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Sandoghdar, V.

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Schadle, A.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Stefani, F. D.

Taminiau, T. H.

Tsang, L.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

van Hulst, N.

L. Novotny and N. van Hulst, Nat. Photon. 5, 83 (2011).
[CrossRef]

van Hulst, N. F.

Wolf, E.

Yu, Z. F.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys. Lett. 75, 1063 (1999).
[CrossRef]

IEEE Trans. Antennas Propag.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

J. Opt. Soc. Am.

Nat. Mater.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef] [PubMed]

Nat. Photon.

A. Alu and N. Engheta, Nat. Photon. 2, 307 (2008).
[CrossRef]

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

L. Novotny and N. van Hulst, Nat. Photon. 5, 83 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

J. J. Li, A. Salandrino, and N. Engheta, Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Phys. Rev. Lett.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkel, and V. Sandoghdar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

S. Kuhn, U. Hakanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Science

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Other

J. W. Goodman, Statistical Optics (Wiley, 2000).

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic design for the spherical NA. The wavelength of the incident light is 400 nm , and the diameter of each nanosphere is 15 nm .

Fig. 2
Fig. 2

(a) Normalized angular response of a metallic nanosphere compared to that of the dipole emitter sin θ . The maximum error is drawn as a function of the nanosphere diameter. The dashed curve denotes the error δ = 1 % . (b) Far-field scattering intensity of the directional NA as a function of the diameter of each nanosphere. The reference curves are calculated by using the Rayleigh approximation. (c) Uncertainty of the radiation pattern after introducing the random error of the spatial distribution of nanospheres. The red error bar indicates the standard deviation of the pattern. The space shift range from the center of each nanosphere is larger than their diameters. (d) Changed radiation pattern after replacing one of Au nanospheres by the Ag nanosphere. The red solid curve and the blue dashed curve represent the original radiation pattern and the changed radiation pattern, respectively.

Fig. 3
Fig. 3

(a), (f), and (b) Radiation patterns of the reference NA and the optimized ones with and without random fabrication errors, respectively; (c), (h), and (d) spatial correlation functions of the E z components for the reference NA and the optimized ones with and without random fabrication errors, respectively; (g), (e) near-field intensities of the optimized NAs with and without random fabrication errors, respectively.

Equations (6)

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E s = T 1 ( N ) 3 e i k r 2 i k r sin θ θ ^ = f ( θ ) θ ^ ,
E ( θ , ϕ ) = f ( θ ) n = 1 N e i k ( S n ) ,
S n = x n sin θ cos ϕ + y n sin θ sin ϕ + z n cos θ
min max | E ( θ , ϕ ) | subject to { | θ θ 0 | > w θ , | ϕ ϕ 0 | > w ϕ } ,
E ( k , ω ) E * ( k , ω ) = C ( θ ^ θ ^ + ϕ ^ ϕ ^ ) · W ¯ ( k ) · ( θ ^ θ ^ + ϕ ^ ϕ ^ ) W ¯ ( k ) = J ( r + r , ω ) J * ( r , ω ) exp ( i k · r ) d r ,
| E θ ( k , ω ) | 2 = C sin 2 θ J z ( r + r , ω ) , J z * ( r , ω ) exp ( i k · r ) d r .

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