Abstract

We have designed and characterized three different types of plasmonic lenses that cannot only focus, but can also bend electromagnetic (EM) waves. The bending effect is achieved by constructing an asymmetric phase front caused by varying phase retardations in EM waves as they pass through a plasmonic lens. With an incident wave normal to the lens surface, light bends up to 8° off the axial direction. The optical wave propagation was numerically investigated using the finite-difference time-domain (FDTD) method. Simulation results show that the proposed plasmonic lenses allow effective beam bending under both normal and tilted incidence. With their relatively large bending range and capability to perform in the far field, the plamsonic lenses described in this article could be valuable in applications such as photonic communication and plasmonic circuits.

© 2010 OSA

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2010

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer,” Nano Lett. 10(6), 2075–2079 (2010).
[CrossRef] [PubMed]

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

Y. Fu, Y. Liu, X. Zhou, Z. Xu, and F. Fang, “Experimental investigation of superfocusing of plasmonic lens with chirped circular nanoslits,” Opt. Express 18(4), 3438–3443 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-4-3438 .
[CrossRef] [PubMed]

2009

C. K. Chang, Y. Y. Yu, M. W. Lai, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Recording Bessel-like beam shapes generated by plasmonics lens,” Opt. Express 17(16), 13946–13952 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-16-13946 .
[CrossRef] [PubMed]

S. Yang, W. Chen, R. L. Nelson, and Q. Zhan, “Miniature circular polarization analyzer with spiral plasmonic lens,” Opt. Lett. 34(20), 3047–3049 (2009),
 http://www.opticsinfobase.org/abstract.cfm?URI=ol-34-20-3047 .
[CrossRef] [PubMed]

L. Martin-Moreno, “Plasmonic circuits: Detecting unseen light,” Nat. Phys. 5(7), 457–458 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

J. A. Shackleford, R. Grote, M. Currie, J. E. Spanier, and B. Nabet, “Integrated plasmonic lens photodetector,” Appl. Phys. Lett. 94(8), 083501 (2009).
[CrossRef]

2008

W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008).
[CrossRef] [PubMed]

E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express 16(1), 45–57 (2008),
 http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-45 .
[CrossRef] [PubMed]

2007

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–62 (2007).
[CrossRef] [PubMed]

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength meatl slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90(5), 051113 (2007).
[CrossRef]

2006

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88(17), 171108 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

2005

2004

1983

1972

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Abeysinghe, D. C.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer,” Nano Lett. 10(6), 2075–2079 (2010).
[CrossRef] [PubMed]

Atwater, H. A.

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296(4), 56–62 (2007).
[CrossRef] [PubMed]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Beermann, J.

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

Bogy, D. B.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Brolo, A. G.

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Chang, C. K.

Chen, W.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer,” Nano Lett. 10(6), 2075–2079 (2010).
[CrossRef] [PubMed]

S. Yang, W. Chen, R. L. Nelson, and Q. Zhan, “Miniature circular polarization analyzer with spiral plasmonic lens,” Opt. Lett. 34(20), 3047–3049 (2009),
 http://www.opticsinfobase.org/abstract.cfm?URI=ol-34-20-3047 .
[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]

Currie, M.

J. A. Shackleford, R. Grote, M. Currie, J. E. Spanier, and B. Nabet, “Integrated plasmonic lens photodetector,” Appl. Phys. Lett. 94(8), 083501 (2009).
[CrossRef]

Devaux, E.

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Du, C.

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

Du, C. L.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Ebbesen, T. W.

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Fang, F.

Fu, Y.

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Gordon, R.

Gramotnev, D. K.

Grote, R.

J. A. Shackleford, R. Grote, M. Currie, J. E. Spanier, and B. Nabet, “Integrated plasmonic lens photodetector,” Appl. Phys. Lett. 94(8), 083501 (2009).
[CrossRef]

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, H.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength meatl slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90(5), 051113 (2007).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano- optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Kim, S.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength meatl slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90(5), 051113 (2007).
[CrossRef]

Kuipers, L. K.

Lai, M. W.

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Lee, B.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength meatl slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90(5), 051113 (2007).
[CrossRef]

Lee, C. K.

Lee, H.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88(17), 171108 (2006).
[CrossRef]

Lerman, G. M.

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

Levy, U.

G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9(5), 2139–2143 (2009).
[CrossRef] [PubMed]

Lim, L. E. N.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Lim, Y.

B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010).
[CrossRef]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength meatl slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett. 90(5), 051113 (2007).
[CrossRef]

Lin, L.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Liu, J. M.

Liu, Y.

Liu, Z.

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88(17), 171108 (2006).
[CrossRef]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Luo, X.

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

Luo, X. G.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Maradudin, A. A.

Martin-Moreno, L.

L. Martin-Moreno, “Plasmonic circuits: Detecting unseen light,” Nat. Phys. 5(7), 457–458 (2009).
[CrossRef]

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Nabet, B.

J. A. Shackleford, R. Grote, M. Currie, J. E. Spanier, and B. Nabet, “Integrated plasmonic lens photodetector,” Appl. Phys. Lett. 94(8), 083501 (2009).
[CrossRef]

Nelson, R. L.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer,” Nano Lett. 10(6), 2075–2079 (2010).
[CrossRef] [PubMed]

S. Yang, W. Chen, R. L. Nelson, and Q. Zhan, “Miniature circular polarization analyzer with spiral plasmonic lens,” Opt. Lett. 34(20), 3047–3049 (2009),
 http://www.opticsinfobase.org/abstract.cfm?URI=ol-34-20-3047 .
[CrossRef] [PubMed]

Novikov, S. M.

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

Pan, L.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008).
[CrossRef] [PubMed]

Pikus, Y.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005).
[CrossRef] [PubMed]

Pile, D. F. P.

Polman, A.

Roberts, A.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Shackleford, J. A.

J. A. Shackleford, R. Grote, M. Currie, J. E. Spanier, and B. Nabet, “Integrated plasmonic lens photodetector,” Appl. Phys. Lett. 94(8), 083501 (2009).
[CrossRef]

Shi, H.

H. Shi, C. Du, and X. Luo, “Focal length modulation based on a metallic slit surrounded with grooves in curved depths,” Appl. Phys. Lett. 91(9), 093111 (2007).
[CrossRef]

Søndergaard, T.

T. Søndergaard, S. I. Bozhevolnyi, S. M. Novikov, J. Beermann, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission enhanced by nanofocusing,” Nano Lett. 10(8), 3123–3128 (2010).
[CrossRef] [PubMed]

Spanier, J. E.

J. A. Shackleford, R. Grote, M. Currie, J. E. Spanier, and B. Nabet, “Integrated plasmonic lens photodetector,” Appl. Phys. Lett. 94(8), 083501 (2009).
[CrossRef]

Srituravanich, W.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008).
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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of a plasmonic lens that can bend a light beam or focal point in transverse direction; (b), (c) and (d) are the isometric views of three proposed designs of the plasmonic lens, termed as Lens I, Lens II, and Lens III.

Fig. 2
Fig. 2

(a) Relative phase change caused by varying the width of a rectangular slit w. (b) Relative phase difference caused by varying the length of the slit d. (c) Relative phase difference of a tapered slit. The input aperture w1 is varying, while the output aperture w2 is fixed at 50 nm.

Fig. 3
Fig. 3

(a), (c) and (e) are three representative designs of plasmonic lenses (Lens I, Lens II, Lens III), corresponding to Fig. 1(b), (c) and (d). The constructed phase differences are 1.5π, 0.96π, and 1.45π, respectively. (b), (d) and (f) the corresponding simulation results. All the simulations show the bending of light off the optical axis.

Fig. 4
Fig. 4

Influence of different incident angles on the bending effects of Lens III. The red dashed lines denote the phase front change caused by both incident light and plasmonic lenses. (a) Schematic of light incidence at an angle of −10° to the optical axis; (b) Simulation results corresponding to (a). (c) Schematic of light incidence at an angle of 10° to the optical axis. (d) Simulation results corresponding to (c).

Tables (1)

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Table 1 Efficiency calculation of the proposed plasmonic lenses.

Equations (2)

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tan h ( w β 2 ε d k 0 2 / 2 ) = ε d β 2 ε m k 0 2 ε m β 2 ε d k 0 2 ,
φ ( m ) = 2 n π + 2 π f λ 2 π f 2 + m 2 λ ,

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