Abstract

The crescent nanostructure with gain medium inside is theoretically studied to analyze the characteristic of plasmonic emitting with wide bandwidth. An accurate analytical model is built based on the transformation optics. In this model, the poles of the electrostatic potential function are in the second and the fourth quadrant of the complex plane if the imaginary part of the relative permittivity of the gain medium is larger than the loss compensation threshold, and then the extinction cross section is to be negative by integrating the electrostatic potential over the half complex plane via an inverse Fourier transform. The positive extinction cross section corresponds to absorption, and the negative corresponds to emission. The proposed analytical model agrees well with the numerical simulation results based on the finite element method, to give a physical insight into the loss compensation property of the plasmonic nanostuctures. Results show that the negative extinction cross section is realizable by introducing the gain medium into a plasmonic crescent nanowire, which is equivalent to an emitting device with wide bandwidth.

© 2015 Optical Society of America

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References

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2014 (4)

H. Yang, W. Lee, T. Hwang, and D. Kim, “Probabilistic evaluation of surface-enhanced localized surface plasmon resonance biosensing,” Opt. Express 22(23), 28412–28426 (2014).
[Crossref] [PubMed]

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
[Crossref] [PubMed]

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light: Sci. Appl. 3(7), e191 (2014).
[Crossref]

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

2013 (2)

2012 (2)

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[Crossref]

2011 (2)

2010 (5)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Broadband plasmonic device concentrating the energy at the nanoscale: the crescent-shaped cylinder,” Phys. Rev. B 82(12), 125430 (2010).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Conformal transformation applied to plasmonics beyond the quasistatic limit,” Phys. Rev. B 82(20), 205109 (2010).
[Crossref]

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

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]

2006 (4)

K. Kim, S. J. Yoon, and D. Kim, “Nanowire-based enhancement of localized surface plasmon resonance for highly sensitive detection: a theoretical study,” Opt. Express 14(25), 12419–12431 (2006).
[Crossref] [PubMed]

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[Crossref] [PubMed]

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, L. Thio, and P. A. Wolff, “Extraordinary optical transmission through small apertures,” Nature 391(6668), 667–669 (1998).
[Crossref]

1997 (1)

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[Crossref] [PubMed]

1972 (1)

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

Andrianov, E. S.

Apalkov, V.

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light: Sci. Appl. 3(7), e191 (2014).
[Crossref]

Arias, R. E.

Aubry, A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Broadband plasmonic device concentrating the energy at the nanoscale: the crescent-shaped cylinder,” Phys. Rev. B 82(12), 125430 (2010).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Conformal transformation applied to plasmonics beyond the quasistatic limit,” Phys. Rev. B 82(20), 205109 (2010).
[Crossref]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chen, H.

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chen, L.

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
[Crossref] [PubMed]

Christy, R. W.

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

Davis, T. J.

Dorofeenko, A. V.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, L. Thio, and P. A. Wolff, “Extraordinary optical transmission through small apertures,” Nature 391(6668), 667–669 (1998).
[Crossref]

Emory, S. R.

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[Crossref] [PubMed]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[Crossref]

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

Gan, L.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, L. Thio, and P. A. Wolff, “Extraordinary optical transmission through small apertures,” Nature 391(6668), 667–669 (1998).
[Crossref]

Gómez, D. E.

Håkanson, U.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

Hwang, T.

Jin, J.

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]

Johnson, P. B.

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

Kim, D.

Kim, J.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[Crossref] [PubMed]

Kim, K.

Kim, S.

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]

Kim, S. W.

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]

Kim, Y.

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]

Kim, Y. J.

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]

Kühn, S.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

Lee, L. P.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[Crossref] [PubMed]

Lee, W.

Lei, D. Y.

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Conformal transformation applied to plasmonics beyond the quasistatic limit,” Phys. Rev. B 82(20), 205109 (2010).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Broadband plasmonic device concentrating the energy at the nanoscale: the crescent-shaped cylinder,” Phys. Rev. B 82(12), 125430 (2010).
[Crossref]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, L. Thio, and P. A. Wolff, “Extraordinary optical transmission through small apertures,” Nature 391(6668), 667–669 (1998).
[Crossref]

Li, J.

Li, Z. Y.

S.-Y. Liu, J. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
[PubMed]

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
[Crossref] [PubMed]

Lisyansky, A. A.

Liu, G. L.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[Crossref] [PubMed]

Liu, S.-Y.

Lu, Y.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[Crossref] [PubMed]

Maier, S. A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Broadband plasmonic device concentrating the energy at the nanoscale: the crescent-shaped cylinder,” Phys. Rev. B 82(12), 125430 (2010).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Conformal transformation applied to plasmonics beyond the quasistatic limit,” Phys. Rev. B 82(20), 205109 (2010).
[Crossref]

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

Maradudin, A. A.

Mejia, Y. X.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[Crossref] [PubMed]

Nie, S.

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[Crossref] [PubMed]

Niu, H.

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
[Crossref] [PubMed]

Park, I. Y.

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]

Pendry, J. B.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[Crossref]

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Conformal transformation applied to plasmonics beyond the quasistatic limit,” Phys. Rev. B 82(20), 205109 (2010).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Broadband plasmonic device concentrating the energy at the nanoscale: the crescent-shaped cylinder,” Phys. Rev. B 82(12), 125430 (2010).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Pukhov, A. A.

Qu, J.

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
[Crossref] [PubMed]

Rogobete, L.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

Sandoghdar, V.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Smith, D. R.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Song, J.

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
[Crossref] [PubMed]

Sonnefraud, Y.

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

Stockman, M. I.

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light: Sci. Appl. 3(7), e191 (2014).
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M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
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D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
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Thio, L.

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[Crossref]

Vernon, K. C.

Vinogradov, A. P.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, L. Thio, and P. A. Wolff, “Extraordinary optical transmission through small apertures,” Nature 391(6668), 667–669 (1998).
[Crossref]

Xia, Y.

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
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Xian, J.

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
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L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
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Light: Sci. Appl. (1)

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light: Sci. Appl. 3(7), e191 (2014).
[Crossref]

Nano Lett. (3)

A. Aubry, D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, S. A. Maier, and J. B. Pendry, “Plasmonic light-harvesting devices over the whole visible spectrum,” Nano Lett. 10(7), 2574–2579 (2010).
[Crossref] [PubMed]

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
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Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
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Nanoscale (1)

J. Xian, L. Chen, H. Niu, J. Qu, and J. Song, “Significant field enhancements in an individual silver nanoparticle near a substrate covered with a thin gain film,” Nanoscale 6(22), 13994–14001 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
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Nat. Photonics (1)

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

Nature (2)

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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).
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Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (4)

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Broadband plasmonic device concentrating the energy at the nanoscale: the crescent-shaped cylinder,” Phys. Rev. B 82(12), 125430 (2010).
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A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Conformal transformation applied to plasmonics beyond the quasistatic limit,” Phys. Rev. B 82(20), 205109 (2010).
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A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
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Phys. Rev. Lett. (3)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
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S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
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J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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Science (4)

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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
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J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
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Figures (7)

Fig. 1
Fig. 1 The 3D sketch (a) and the fabrication procedure (b).
Fig. 2
Fig. 2 (a) A thin layer of metal with air on the left domain and gain medium on the right domain. (b) The transformed crescent structure with air outside and gain medium inside. The dipole source is transformed into a uniform electric field. (c) The complex plane of the integration factor k . l 1 is the integration path along the real axis, which is from to + . l 2 is the integration path along a semicircle with the radius approaching + . is the area surrounded by the lines l 1 and l 2 .
Fig. 3
Fig. 3 The numerical (solid curves) and theoretical (dotted curves) extinction cross sections σ e x t / D o as a function of the wavelength λ 0 for different shapes of the crescents and different image parts of the relative permittivity of the gain medium. (I) (II) (III) (on the right side of the Fig. 3) are sketch maps of the normalized value of the electric field (blue) and of the x component value of the electric field (green) for the different ratios ρ = 0.4, 0.6, 0.8, respectively, at the same wavelength λ 0 = 380 nm.
Fig. 4
Fig. 4 The numerical (solid curves) and theoretical (dotted curves) extinction cross sections σ e x t / D o as a function of the wavelength λ 0 for the ratio ρ = 0.8 , the outer diameter D o = 20 nm, and different relative permittivities of the gain medium.
Fig. 5
Fig. 5 The sketch of the crescent structure (a). The numerical results of the polar plots of the intensities of near-field electric field (b), the far-field electric field (c), and the power flow (d), where the outer diameter D o = 20 nm, ρ = 0.8 , ε g = 2.09 0.2 i , and the wavelength λ 0 = 700 nm.
Fig. 6
Fig. 6 The numerical (solid curves) and theoretical (dotted curves) extinction cross section σ e x t / D o , E max and θ E max as a function of the imaginary part of the relative permittivity of the gain medium, ε g 2 .
Fig. 7
Fig. 7 The numerical (solid curves) and theoretical (dotted curves) threshold value of the loss compensation as a function of the wavelength λ 0 .

Equations (26)

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ϕ Δ ( r ) = 1 2 π ε 0 Δ r r 2 = 1 2 π d k ϕ Δ ( k ) e i k y ,
ϕ Δ ( k ) = ϕ Δ ( x , y ) e i k y d y = a ( k ) e | k | | x | ,
a ( k ) = sgn ( x ) Δ x + i sgn ( k ) Δ y 2 ε 0 .
ϕ ( k ) = { b ( k ) e | k | x , c ( k ) e | k | x + d ( k ) e | k | x , e ( k ) e | k | x , x < a a < x < a + d x > a + d .
a ( k ) e | k | a + b ( k ) e | k | a = c ( k ) e | k | a + d ( k ) e | k | a ,
c ( k ) e | k | ( a + d ) + d ( k ) e | k | ( a + d ) = e ( k ) e | k | ( a + d ) ,
a ( k ) e | k | a + b ( k ) e | k | a = ε m [ c ( k ) e | k | a + d ( k ) e | k | a ] ,
ε m [ c ( k ) e | k | ( a + d ) + d ( k ) e | k | ( a + d ) ] = ε g e ( k ) e | k | ( a + d ) .
b ( k ) = [ ε m ε g ε m + ε g ε m 1 ε m + 1 e 2 | k | d ] e 2 | k | a e 2 | k | d e 2 α a ( k ) ,
c ( k ) = 2 ε m + 1 e 2 | k | d e 2 | k | d e 2 α a ( k ) ,
d ( k ) = 2 ( ε m ε g ) ( ε m + 1 ) ( ε m + ε g ) e 2 | k | a e 2 | k | d e 2 α a ( k ) ,
e ( k ) = 4 ε m ( ε m + 1 ) ( ε m + ε g ) e 2 | k | d e 2 | k | d e 2 α a ( k ) .
ϕ ( x , y ) = 1 2 π { b ( k ) e i k y + | k | x d k , [ c ( k ) e | k | x + d ( k ) e | k | x ] e i k y d k , e ( k ) e i k y | k | x d k , x < a a < x < a + d x > a + d .
ϕ ( x < a ) = 1 4 π ε 0 + [ Δ x i sgn ( k ) Δ y ] [ ε m ε g ε m + ε g ε m 1 ε m + 1 e 2 | k | d ] e 2 | k | a e 2 | k | d e 2 α e i k y + | k | x d k ,
| k d | = α = 1 2 ln ( ε m 1 ) ( ε m ε g ) ( ε m + 1 ) ( ε m + ε g ) , ( for ε m 1 < ε g 1 < 1 )
f o r α 2 > 0 ϕ ( x < a ) = 1 ε 0 d ε m ε m 2 1 ( i Δ x + sgn ( y ) Δ y ) e α d ( x 2 a ) e i α d | y | ,
f o r α 2 < 0 ϕ ( x < a ) = 1 ε 0 d ε m ε m 2 1 ( i Δ x + sgn ( y ) Δ y ) e α d ( x 2 a ) e i α d | y | .
f o r α 2 > 0 , E ( z = 0 ) = i α ε 0 d ε m ε m 2 1 e 2 α a d Δ ,
f o r α 2 < 0 , E ( z = 0 ) = i α ε 0 d ε m ε m 2 1 e 2 α a d Δ ,
z = g 2 z ,
σ e x t = 4 π 2 k 0 ( ρ 1 ρ ) 2 D o 2 Re { α ε m 1 ε m 2 e 2 α ρ 1 ρ } , ( α 2 > 0 )
σ e x t = 4 π 2 k 0 ( ρ 1 ρ ) 2 D o 2 Re { α ε m 1 ε m 2 e 2 α ρ 1 ρ } , ( α 2 < 0 )
| E E 0 | = 2 π ( ρ 1 ρ ) 2 | ln ( ε m 1 ) ( ε m ε g ) ( ε m + 1 ) ( ε m + ε g ) ε m ε m 2 1 [ ( ε m 1 ) ( ε m ε g ) ( ε m + 1 ) ( ε m + ε g ) ] ρ 2 ( 1 ρ ) | exp ( ρ 1 ρ α 2 | tan ( θ 2 ) | ) cos 2 ( θ 2 ) , ( α 2 > 0 )
| E E 0 | = 2 π ( ρ 1 ρ ) 2 | ln ( ε m 1 ) ( ε m ε g ) ( ε m + 1 ) ( ε m + ε g ) ε m ε m 2 1 [ ( ε m 1 ) ( ε m ε g ) ( ε m + 1 ) ( ε m + ε g ) ] ρ 2 ( 1 ρ ) | exp ( ρ 1 ρ α 2 | tan ( θ 2 ) | ) cos 2 ( θ 2 ) , ( α 2 < 0 )
θ E max = π | arc sin ( ρ 1 ρ α 2 ) | .
α 2 ε m 2 ε m 1 2 1 + ε m 2 ε g 1 ε m 1 ε g 2 ε m 1 2 ε g 1 2 .

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