Abstract

Multi-focus plasmonic lens with metallic nanoslits of variant widths have great potential applications in optical interconnection, integrated optics and nanophotonics. But the design method with simulated annealing algorithm or Yang-Gu algorithm requires complex calculation and multi focuses are limited to be set on the same output plane. In this paper, we propose a design method based on holography. The desired light field distribution and the incident plane wave can be treated as object wave and reference wave, respectively. So the calculation is relative simple and multi focuses can be located in different output plane. Numerical simulation of multi-focus lens design is performed through finite-difference time-domain (FDTD) method and the result confirms the feasibility of our method.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
    [CrossRef] [PubMed]
  3. R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express13(6), 1933–1938 (2005).
    [CrossRef] [PubMed]
  4. H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
    [CrossRef] [PubMed]
  5. L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
    [CrossRef] [PubMed]
  6. T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
    [CrossRef]
  7. Q. F. Zhu, D. Y. Wang, X. H. Zheng, and Y. Zhang, “Optical lens design based on metallic nanoslits with variant widths,” Appl. Opt.50(13), 1879–1883 (2011).
    [CrossRef] [PubMed]
  8. Q. F. Zhu, J. S. Ye, D. Y. Wang, B. Y. Gu, and Y. Zhang, “Optimal design of SPP-based metallic nanoaperture optical elements by using Yang-Gu algorithm,” Opt. Express19(10), 9512–9522 (2011).
    [CrossRef] [PubMed]
  9. J. J. Cowan, “Holography with standing surface plasma-waves,” Opt. Commun.12(4), 373–378 (1974).
    [CrossRef]
  10. S. Maruo, O. Nakamura, and S. Kawata, “Evanescent-wave holography by use of surface-plasmon resonance,” Appl. Opt.36(11), 2343–2346 (1997).
    [CrossRef] [PubMed]
  11. M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science332(6026), 218–220 (2011).
    [CrossRef] [PubMed]
  12. Y. H. Chen, J. X. Fu, and Z. Y. Li, “Surface wave holography on designing subwavelength metallic structures,” Opt. Express19(24), 23908–23920 (2011).
    [CrossRef] [PubMed]
  13. S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, and K. A. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Opt. Lett.19(6), 417–419 (1994).
    [PubMed]
  14. J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).
  15. Y. Yu and H. Zappe, “Effect of lens size on the focusing performance of plasmonic lenses and suggestions for the design,” Opt. Express19(10), 9434–9444 (2011).
    [CrossRef] [PubMed]
  16. Y. Gao, J. L. Liu, X. R. Zhang, Y. X. Wang, Y. L. Song, S. T. Liu, and Y. Zhang, “Analysis of focal-shift effect in planar metallic nanoslit lenses,” Opt. Express20(2), 1320–1329 (2012).
    [CrossRef] [PubMed]
  17. D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am.60(1), 15–17 (1970).
    [CrossRef]
  18. G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. Laczik, M. Padgett, and J. Courtial, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Opt. Express12(8), 1665–1670 (2004).
    [CrossRef] [PubMed]
  19. G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett.30(8), 833–835 (2005).
    [CrossRef] [PubMed]
  20. A. Anand and B. Javidi, “Three-dimensional microscopy with single-beam wavefront sensing and reconstruction from speckle fields,” Opt. Lett.35(5), 766–768 (2010).
    [CrossRef] [PubMed]

2012 (2)

J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).

Y. Gao, J. L. Liu, X. R. Zhang, Y. X. Wang, Y. L. Song, S. T. Liu, and Y. Zhang, “Analysis of focal-shift effect in planar metallic nanoslit lenses,” Opt. Express20(2), 1320–1329 (2012).
[CrossRef] [PubMed]

2011 (5)

2010 (1)

2009 (1)

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

2007 (1)

T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
[CrossRef]

2005 (3)

2004 (1)

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

1997 (1)

1994 (1)

1974 (1)

J. J. Cowan, “Holography with standing surface plasma-waves,” Opt. Commun.12(4), 373–378 (1974).
[CrossRef]

1970 (1)

Anand, A.

Barnard, E. S.

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

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Brolo, A. G.

Brongersma, M. L.

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

Catrysse, P. B.

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

Chen, Y. H.

Chuang, P.

J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).

Courtial, J.

Cowan, J. J.

J. J. Cowan, “Holography with standing surface plasma-waves,” Opt. Commun.12(4), 373–378 (1974).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Dixit, S. N.

Dong, X. C.

Du, C. L.

T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
[CrossRef]

H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Fan, S. H.

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

Fu, J. X.

Gao, H. T.

Gao, Y.

Gibson, G.

Gordon, R.

Gu, B. Y.

Javidi, B.

Jordan, P.

Kato, J.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science332(6026), 218–220 (2011).
[CrossRef] [PubMed]

Kawata, S.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science332(6026), 218–220 (2011).
[CrossRef] [PubMed]

S. Maruo, O. Nakamura, and S. Kawata, “Evanescent-wave holography by use of surface-plasmon resonance,” Appl. Opt.36(11), 2343–2346 (1997).
[CrossRef] [PubMed]

Kermisch, D.

Laczik, Z.

Lawson, J. K.

Leach, J.

Li, Z. Y.

Liu, J. L.

Liu, S. T.

Luo, X. G.

T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
[CrossRef]

H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Manes, K. R.

Maruo, S.

Nakamura, O.

Nugent, K. A.

Osten, W.

Ozaki, M.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science332(6026), 218–220 (2011).
[CrossRef] [PubMed]

Padgett, M.

Pedrini, G.

Powell, H. T.

Shi, H. F.

Sinclair, G.

Song, Y. L.

Tao, Z. Y.

J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).

Verslegers, L.

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

Wang, C. T.

T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
[CrossRef]

H. F. Shi, C. T. Wang, C. L. Du, X. G. Luo, X. C. Dong, and H. T. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Wang, D. Y.

Wang, Y. X.

White, J. S.

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

Xi, W.

J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).

Xu, T.

T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
[CrossRef]

Yao, E.

Ye, J. S.

Yu, J. X.

J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).

Yu, Y.

Yu, Z. F.

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

Zappe, H.

Zhang, X. R.

Zhang, Y.

Zheng, X. H.

Zhu, Q. F.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett.91(20), 201501 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

Nano Lett. (1)

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

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. J. Cowan, “Holography with standing surface plasma-waves,” Opt. Commun.12(4), 373–378 (1974).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Proc. SPIE (1)

J. X. Yu, P. Chuang, W. Xi, and Z. Y. Tao, “A novel iterative computation algorithm for Kinoform of 3D object,” Proc. SPIE8556, 88561H (2012).

Science (1)

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science332(6026), 218–220 (2011).
[CrossRef] [PubMed]

Other (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Principle of multi-focus plasmonic lens design. (a) Multi focuses are considered as multi point light source and then the interference light field with reference wave is calculated. (b) Schematic of a plasmonic lens based on nanoslit array with different width perforated in thin metallic Ag film surrounded by air. The thickness of the plasmonic lens is d. When a TM polarized plane wave is incident on the upside, multi focuses can be generated.

Fig. 2
Fig. 2

Design result of plasmonic lens with two focuses by our method. (a) Calculated Hz amplitude distribution by the FDTD method. (b) Phase distribution of Hz. (c) Cross section of the focus. (d) Calculated distribution of slit width at different positions perforated in the Ag film.

Fig. 3
Fig. 3

Design result of plasmonic lens with three tilted focuses by our method. (a) Calculated Hz amplitude distribution by the FDTD method. (b) Phase distribution of Hz. (c) Calculated distribution of slit width at different positions perforated in the Ag film.

Fig. 4
Fig. 4

Comparison of two-focus plasmonic lens design with two methods. (a) Amplitude distribution of Hz of the designed structure by our method. (b) Phase distribution of Hz of the designed structure by our method. (c) Amplitude distribution of Hz of the designed structure by the equal optical path length principle. (d) Phase distribution of Hz of the designed structure by the equal optical path length principle.

Equations (6)

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

U( x=0,y )= j=1 n A j r j exp( i k 0 r j ),
r j = x j 2 + ( y y j ) 2 .
ϕ(y)=2πmod(angle(U),2π),
tanh( β 2 k 0 2 ε d w/2 )= ε d β 2 k 0 2 ε m ε m β 2 k 0 2 ε d ,
ΔφRe( βd ).
I=AS π 4 [ I 0 + 1 8 I 0 ( I 0 I 0 )+ 3 64 I 0 ( I 0 I 0 )( I 0 I 0 )+ ],

Metrics