Abstract

An optimization method for design of SPP-based metallic nanoaperture optical elements is presented. The design process is separated into two steps: Firstly, derive the amplitude and phase modulation of isolating single slit with different width; Secondly, realize the optimal design of element by using an iteration procedure. The Yang-Gu algorithm is expanded to perform this design. Three kinds of lenses which can achieve various functions have been designed by using this method. The rigorous electromagnetical theory is employed to justify and appraise the performances of the designed elements. It has been found that the designed elements can achieve the preset functions well. This method may provide a convenient avenue to optimally design metallic diffractive optical elements with subwavelength scale.

© 2011 OSA

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  1. R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
    [CrossRef]
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
    [CrossRef] [PubMed]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  5. P. B. Catrysse, “Beaming light into the nanoworld,” Nat. Phys. 3, 839–840 (2007).
    [CrossRef]
  6. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyonds the diffractin limit,” Nat. Photonics 4, 83–91 (2010).
    [CrossRef]
  7. A. G. Curto, A. Manjavacas, and F. J. García de Abajo, “Near-field focusing with optical phase antennas,” Opt. Express 17, 17801–17811 (2009).
    [CrossRef] [PubMed]
  8. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clab optical waveguides: analytical and experimental study,” Appl. Opt. 13, 396–405 (1974).
    [CrossRef] [PubMed]
  9. H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
    [CrossRef]
  10. J. Lindberg, K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, “Spectral analysis of resonant transmission of light through a single sub-wavelength slit,” Opt. Express 12, 623–632 (2004).
    [CrossRef] [PubMed]
  11. P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
    [CrossRef]
  12. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
    [CrossRef] [PubMed]
  13. Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642–644 (2004).
    [CrossRef]
  14. T. Xu, C. T. Wang, C. L. Du, and X. G. Luo, “Plasmonic beam deflector,” Opt. Express 16, 4753–4759 (2008).
    [CrossRef] [PubMed]
  15. Z. J. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89, 261119 (2006).
    [CrossRef]
  16. 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. Express 13, 6815–6820 (2005).
    [CrossRef] [PubMed]
  17. 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, 235–238 (2009).
    [CrossRef]
  18. W. M. Saj, “Light focusing on a stack of metal-insulator-metal waveguides sharp edges,” Opt. Express 17, 13615–13623 (2009).
    [CrossRef] [PubMed]
  19. G. Z. Yang and B. Y. Gu, “On the amplitude-phase retrieval problem in optical system,” Acta Phys. Sin. 30, 410–413 (1981).
  20. B. Y. Gu, G. Z. Yang, and B. Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
    [CrossRef] [PubMed]
  21. T. Xu, C. L. Du, C. T. Wang, and X. G. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett. 91, 201501 (2007).
  22. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
    [CrossRef]
  23. B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
    [CrossRef]

2015 (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, 201501 (2007).

2010 (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyonds the diffractin limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

2009 (4)

A. G. Curto, A. Manjavacas, and F. J. García de Abajo, “Near-field focusing with optical phase antennas,” Opt. Express 17, 17801–17811 (2009).
[CrossRef] [PubMed]

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, 235–238 (2009).
[CrossRef]

W. M. Saj, “Light focusing on a stack of metal-insulator-metal waveguides sharp edges,” Opt. Express 17, 13615–13623 (2009).
[CrossRef] [PubMed]

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

2008 (2)

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

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

2007 (1)

P. B. Catrysse, “Beaming light into the nanoworld,” Nat. Phys. 3, 839–840 (2007).
[CrossRef]

2006 (1)

Z. J. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89, 261119 (2006).
[CrossRef]

2005 (2)

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. Express 13, 6815–6820 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

2004 (2)

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

J. Lindberg, K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, “Spectral analysis of resonant transmission of light through a single sub-wavelength slit,” Opt. Express 12, 623–632 (2004).
[CrossRef] [PubMed]

2003 (2)

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

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

2000 (1)

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1986 (1)

1981 (1)

G. Z. Yang and B. Y. Gu, “On the amplitude-phase retrieval problem in optical system,” Acta Phys. Sin. 30, 410–413 (1981).

1974 (1)

1957 (1)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

Astillean, S.

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

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, 235–238 (2009).
[CrossRef]

Barnes, W. L.

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

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyonds the diffractin limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

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, 235–238 (2009).
[CrossRef]

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, 235–238 (2009).
[CrossRef]

P. B. Catrysse, “Beaming light into the nanoworld,” Nat. Phys. 3, 839–840 (2007).
[CrossRef]

Curto, A. G.

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Dereux, A.

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

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Dong, B. Z.

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

B. Y. Gu, G. Z. Yang, and B. Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
[CrossRef] [PubMed]

Dong, X. C.

Du, C. L.

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

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

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

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, 235–238 (2009).
[CrossRef]

Friberg, A. T.

Gao, H. T.

García de Abajo, F. J.

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyonds the diffractin limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Gu, B. Y.

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

B. Y. Gu, G. Z. Yang, and B. Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
[CrossRef] [PubMed]

G. Z. Yang and B. Y. Gu, “On the amplitude-phase retrieval problem in optical system,” Acta Phys. Sin. 30, 410–413 (1981).

Hu, B.

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Kaivola, M.

Kaminow, I. P.

Kang, J. H.

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

Kihm, H. W.

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

Kim, D. S.

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

Kim, H. K.

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

Lalanne, P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Lee, K. G.

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Lindberg, J.

Lindfors, K.

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Liu, M.

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

Luo, X. G.

Mammel, W. L.

Manjavacas, A.

Martin-Merono, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Merono, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Möller, K. D.

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Palamaru, M.

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Park, Q.

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Saj, W. M.

Setälä, T.

Shi, H. F.

Sun, Z. J.

Z. J. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89, 261119 (2006).
[CrossRef]

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

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

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, 235–238 (2009).
[CrossRef]

Wang, C. T.

Weber, H. P.

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, 235–238 (2009).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

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, 201501 (2007).

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

Yang, G. Z.

B. Y. Gu, G. Z. Yang, and B. Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
[CrossRef] [PubMed]

G. Z. Yang and B. Y. Gu, “On the amplitude-phase retrieval problem in optical system,” Acta Phys. Sin. 30, 410–413 (1981).

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, 235–238 (2009).
[CrossRef]

Zhang, Y.

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

Acta Phys. Sin. (1)

G. Z. Yang and B. Y. Gu, “On the amplitude-phase retrieval problem in optical system,” Acta Phys. Sin. 30, 410–413 (1981).

Appl. Opt. (2)

Appl. Phys. Lett. (4)

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q. Park, “Control of surface plamson generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008).
[CrossRef]

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

Z. J. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89, 261119 (2006).
[CrossRef]

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

Cent. Eur. J. Phys. (1)

B. Hu, B. Y. Gu, B. Z. Dong, Y. Zhang, and M. Liu, “Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits,” Cent. Eur. J. Phys. 8, 448–454 (2009).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

P. Lalanne, J. P. Hugonin, S. Astillean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Nano Lett. (1)

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Figures (7)

Fig. 1
Fig. 1

Structural diagram of a SPPs lens formed on a thin metallic film.

Fig. 2
Fig. 2

SPPs lens with one focal spot designed by the Yang-Gu algorithm. (a) Objective and designed intensity distributions. (b) Distributions of the slit widths. (c) Normalized intensity distribution of |Hy| for the designed lens calculated using the FDTD method. (d) Cross section of the focal spot along the z direction.

Fig. 3
Fig. 3

Chromatic dispersion of the SPPs lens with one focal spot, optimally designed for λ = 650nm, but operating at different wavelength, as indicated in each plot. The dashed line indicates the real focal plane for λ = 650nm.

Fig. 4
Fig. 4

Lens with two focal spots designed by the Yang-Gu algorithm. (a) Objective and designed normalized intensity distributions. (b) Distribution of the slit widths. (c) Normalized intensity distribution of |Hy | for the designed lens calculated using the FDTD method. (d) Cross sections of the focal spots along the z direction.

Fig. 5
Fig. 5

Chromatic dispersion of the SPPs lens with two focal spots, optimally designed for λ = 650nm, but operating at different wavelengths, as indicated in each plot. The dashed line indicates the focal plane for λ = 650nm.

Fig. 6
Fig. 6

Lens with three focal spots designed by the Yang-Gu algorithm. (a) Objective and designed intensity distributions. (b) Distribution of the slit widths. (c) Normalized intensity distribution of |Hy | for the designed lens calculated using the FDTD method. (d) Cross sections of focal spots along the z direction.

Fig. 7
Fig. 7

Chromatic dispersion of the SPPs lens with three focal spots, optimally designed for λ = 650nm, but operating at different wavelength, as indicated in each plot. The dashed line indicates the real focal plane for λ = 650nm.

Equations (25)

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p m ε d k d ε m = 1 e k w 1 + e k w ,
k d = k 0 ( β k 0 ) 2 ε d ;
p m = k 0 ( β k 0 ) 2 ε m ,
Δ ϕ R e ( β h ) .
| H y | sin ( k spp w / 2 ) k spp ,
H y ( r ) = P 0 H y0 ( r 0 ) G ˜ ( r 0 , r ) n ^ d x 0 ,
G ˜ ( r 0 , r ) n ^ = j k 0 2 z z 0 | r r 0 | H 1 ( k 0 | r r 0 | ) ,
H y ( r ) = j k 0 2 P 0 H y0 ( r 0 ) H 1 ( k 0 | r r 0 | ) cos θ d x 0 ,
cos θ = z z 0 | r r 0 | .
H y ( r ) = G ^ H y0 ( r 0 ) = P 0 G ( r 0 , r ) H y0 ( r 0 ) d x 0 ,
G ( r 0 , r ) = j k 0 2 H 1 ( k 0 | r r 0 | ) cos θ .
H y0 = ρ 0 exp ( i ϕ 0 ) ,
H y = ρ exp ( i ϕ ) ,
H y = G ^ H y0 .
D 2 = | | H y G ^ H y0 | | 2 .
δ w ( ρ 0 ) = ρ 0 ( w ( x 0 ) ) = p ( w ) ,
δ w ( ϕ 0 ) = ϕ 0 ( w ( x 0 ) ) = q ( w ) ,
δ ρ 0 δ w = p ( w ) ,
δ ϕ 0 δ w = q ( w ) .
δ w ( D 2 ) = δ ρ 0 ( D 2 ) δ w ( ρ 0 ) + δ ϕ 0 ( D 2 ) δ w ( ϕ 0 ) = 0 ,
δ ϕ ( D 2 ) = 0 ,
H y0 = ( A ^ D + q ) 1 ( i e i arg ( H y0 ) p + G ^ + H y A ^ ND H y0 ) ,
ϕ 0 = arg [ ( A ^ D + q ) 1 ( i e i arg ( H y0 ) p + G ^ + H y A ^ ND H y0 ) ] ,
A ^ = G ^ + G ^ ,
A ^ = A ^ D + A ^ ND ,

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