Abstract

Planar lens based on nanoscale slits has been demonstrated theoretically and experimentally. In this paper, we propose a 2D model of a similar planar lens but with side-illumination. The lens consists of a main bus waveguide to transport plasmonic wave and grooves functioning as antennas. The shapes and filling materials of the waveguide and grooves are assumed to be invariant in the third direction. The phase retardation needed for wavefront shaping comes from the transverse propagation of the plasmonic wave in the waveguide and the well-designed groove positions. The concept is applied to the design of planar lenses and axicons. The simulation results demonstrate that such structures can work as good diffractive elements. The side-illumination property of such structure enables the potential integration of lens on chip.

© 2014 Optical Society of America

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References

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2013 (3)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

H. Pang, H. T. Gao, Q. L. Deng, S. Y. Yin, Q. Qiu, C. L. Du, “Multi-focus plasmonic lens design based on holography,” Opt. Express 21, 18689–18696 (2013).
[CrossRef] [PubMed]

2012 (2)

Y. Gao, J. L. Liu, X. R. Zhang, Y. X. Wang, Y. L. Song, S. T. Liu, Y. Zhang, “Analysis of focal-shift effect in planar metallic nanoslit lenses,” Opt. Express 20, 1320–1329 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

2011 (2)

2010 (1)

B. Yun, G. Hu, Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metalin-sulatormetal waveguide,” J. Phys. D: Appl. Phys. 43,385102 (2010).
[CrossRef]

2009 (2)

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

L. Verslegers, P. B. Catrysse, Z. Yu, S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95,071112 (2009).
[CrossRef]

2008 (1)

2007 (1)

T. Xu, C. L. Du, C. T. Wang, X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett. 91,201501 (2007).
[CrossRef]

2006 (3)

2005 (2)

2003 (1)

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Atwater, H.

J. Dionne, L. Sweatlock, H. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73,035407 (2006).
[CrossRef]

Barnard, E. S.

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

Barnes, W. L.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Brongersma, M. L.

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

Capasso, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Catrysse, P. B.

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

L. Verslegers, P. B. Catrysse, Z. Yu, S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95,071112 (2009).
[CrossRef]

Cheng, J. C.

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

Cho, W.

Cui, Y.

B. Yun, G. Hu, Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metalin-sulatormetal waveguide,” J. Phys. D: Appl. Phys. 43,385102 (2010).
[CrossRef]

Deng, Q. L.

Dereux, A.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Dionne, J.

J. Dionne, L. Sweatlock, H. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73,035407 (2006).
[CrossRef]

Dong, X. C.

Du, C. L.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95,071112 (2009).
[CrossRef]

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

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Gao, H. T.

Gao, Y.

Genevet, P.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Gessmann, T.

Gill, W. N.

Gu, B. Y.

Gu, Z. M.

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

Herzig, H. P.

Hosseini, A.

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

Hu, G.

B. Yun, G. Hu, Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metalin-sulatormetal waveguide,” J. Phys. D: Appl. Phys. 43,385102 (2010).
[CrossRef]

Kats, M. A.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Li, Y.

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

Liang, B.

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

Liu, J. L.

Liu, S. T.

Luo, X. G.

Massoud, Y.

Ojha, M.

Pang, H.

Plawsky, J. L.

Polman, A.

J. Dionne, L. Sweatlock, H. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73,035407 (2006).
[CrossRef]

Qiu, Q.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Ruffieux, P.

Scharf, T.

Schubert, E. F.

Shi, H. F.

Song, Y. L.

Sun, J.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

Sweatlock, L.

J. Dionne, L. Sweatlock, H. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73,035407 (2006).
[CrossRef]

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95,071112 (2009).
[CrossRef]

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

Volkel, R.

Wang, C. T.

Wang, D. Y.

Wang, Y. X.

Watts, M. R.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

Weible, K. J.

White, J. S.

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

Xi, J. Q.

Xu, T.

T. Xu, C. T. Wang, C. L. Du, X. G. Luo, “Plasmonic beam deflector,” Opt. Express 16, 4753–4759 (2008).
[CrossRef] [PubMed]

T. Xu, C. L. Du, C. T. Wang, X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett. 91,201501 (2007).
[CrossRef]

Yaacobi, A.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

Ye, J. S.

Yin, S. Y.

Yu, N.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95,071112 (2009).
[CrossRef]

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

Yun, B.

B. Yun, G. Hu, Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metalin-sulatormetal waveguide,” J. Phys. D: Appl. Phys. 43,385102 (2010).
[CrossRef]

Zhang, X. R.

Zhang, Y.

Zheng, X. H.

Zhu, Q. F.

Zou, X. Y.

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

T. Xu, C. L. Du, C. T. Wang, X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett. 91,201501 (2007).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95,071112 (2009).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

B. Yun, G. Hu, Y. Cui, “Theoretical analysis of a nanoscale plasmonic filter based on a rectangular metalin-sulatormetal waveguide,” J. Phys. D: Appl. Phys. 43,385102 (2010).
[CrossRef]

Nano Lett. (2)

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

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[CrossRef] [PubMed]

Nature (2)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express (7)

Opt. Lett. (1)

Phys. Rev. B (1)

J. Dionne, L. Sweatlock, H. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73,035407 (2006).
[CrossRef]

Sci. Rep. (1)

Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, J. C. Cheng, “Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3,2546 (2013).
[PubMed]

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic illustration of a MIM waveguide-antenna system. (b) The simulated field distribution (Hy) out of a single groove based on finite-element method. The width of the waveguide is w = 100 nm and the metal barrier thickness is set as t = 50 nm. (c) Dependence of the energy transmission through a single groove upon the barrier thickness t.

Fig. 2
Fig. 2

Schematic illustration of a side-illuminated plasmonic diffractive element. The incident energy in the main waveguide is coupled partly to the side-grooves and then diffracts into free space.

Fig. 3
Fig. 3

(a) Magnetic field intensity (|Hy|2) of the designed side-illuminated lens obtained by finite-element method. (b) A transient phase distribution of Hy. (c) The extracted intensity distribution along the axis (x = 0). (d) The intensity distribution at the real focal plane (z = 3.9 μm).

Fig. 4
Fig. 4

The intensity and phase distribution of the designed side-illuminated lens obtained by finite-element method. The barrier thickness is t = 0 nm ((a), (d)), 20 nm ((b), (e)) and 80 nm ((c), (f)), respectively. Other parameters remain unchanged as those in Fig. 3(a).

Fig. 5
Fig. 5

Real focal position zm as a function of the preset focal length f. The red circles represents the simulation results of the peak position of the field intensity along the axis. The black dotted line represents the ideal focal position which is equal to the preset focal length. The red dashed line shows the upper limit (34.3 μm) of the focal length for a planar lens with aperture size 2a = 8 μm.

Fig. 6
Fig. 6

(a) Magnetic field intensity (|Hy|2) of the designed side-illuminated axicon obtained by finite-element method. (b) A transient phase distribution of Hy. (c) The extracted intensity distribution along the axis (x = 0). (d) The intensity distribution at the peak irradiance (z = 11.18μm) and other two positions (z = 8.38μm and z = 14.13μm) where the intensity is 80.0% of the maximal intensity. The FWHM at these positions is 0.82 μm, 0.89 μm and 0.95 μm, respectively.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

tanh ( k 1 w 2 ) = ε d k 2 ε m k 1
ϕ 0 + k f + 2 π m = β x m + ϕ m + k f 2 + x m 2
I ( x = 0 , z ) = 2 A 2 [ C 2 ( ξ ) + S 2 ( ξ ) ]
ϕ 0 + 2 π m = β x m + ϕ m + k | x m | sin ( α )

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