Abstract

We investigate the near-field focusing properties of three-dimensional phase antennas consisting of concentric rings designed to have source and image spots separated by several microns from the lens. Tight focal spots are obtained for silicon or gold rings patterned in a silica matrix. We analyze in detail the dependence of the performance of these lenses on geometrical parameters such as the number of rings, the ring thickness, and the focal distance. Subwavelength focal spots are found to form at distances of tens of wavelengths from the lens, thus suggesting applications to remote sensing and penlight microscopy and lithography.

© 2009 Optical Society of America

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  1. H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).
  2. 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, 508-511 (2006).
    [PubMed]
  3. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).
  4. S. Nie and S. R. Emory, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
    [PubMed]
  5. L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
    [PubMed]
  6. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
    [PubMed]
  7. F. M. Huang, N. Zheludev, Y. Chen, and F. J. García de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
  8. T. Xu, C. Du, C. Wang, and X. Luo, "Subwavelength imaging by metallic slab lens with nanoslits," Appl. Phys. Lett. 91, 201,501 (2007).
  9. M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, "The plasmon Talbot effect," Opt. Express 15, 9692- 9700 (2007).
    [PubMed]
  10. A. G. Curto and F. J. García de Abajo, "Near-field optical phase antennas for long-range plasmon coupling," Nano Lett. 8, 2479-2484 (2008).
    [PubMed]
  11. E. Schonbrun, C. Rinzler, and K. B. Crozier, "Microfabricated water immersion zone plate optical tweezer," Appl. Phys. Lett. 92, 071,112 (2008).
  12. L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, "Spatially shifted beam approach to subwavelength focusing," Phys. Rev. Lett. 101, 113,901 (2008).
  13. F. M. Huang and N. I. Zheludev, "Super-resolution without evanescent waves," Nano Lett. 9, 1249-1254 (2009).
    [PubMed]
  14. A. A. Maradudin and T. A. Leskova, "The Talbot effect for a surface plasmon polariton," New J. Phys. 11, 033,004 (2009).
  15. 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, 235-238 (2009).
  16. H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).
  17. M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).
  18. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
    [PubMed]
  19. F. J. García de Abajo and A. Howie, "Retarded field calculation of electron energy loss in inhomogeneous dielectrics," Phys. Rev. B 65, 115,418 (2002).
  20. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
  21. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
  22. F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205,105 (2003).
  23. M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

2009 (3)

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
[PubMed]

F. M. Huang and N. I. Zheludev, "Super-resolution without evanescent waves," Nano Lett. 9, 1249-1254 (2009).
[PubMed]

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, 235-238 (2009).

2008 (1)

A. G. Curto and F. J. García de Abajo, "Near-field optical phase antennas for long-range plasmon coupling," Nano Lett. 8, 2479-2484 (2008).
[PubMed]

2007 (1)

2006 (1)

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, 508-511 (2006).
[PubMed]

2005 (2)

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
[PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[PubMed]

1999 (2)

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).

1997 (2)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

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

1996 (1)

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).

1994 (1)

1973 (1)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).

1836 (1)

H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[PubMed]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[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, 235-238 (2009).

Berry, M. V.

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).

Bodenschatz, E.

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).

Bozhevolnyi, S. I.

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, 508-511 (2006).
[PubMed]

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, 235-238 (2009).

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, 235-238 (2009).

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[PubMed]

Chen, Y.

F. M. Huang, N. Zheludev, Y. Chen, and F. J. García de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).

Crozier, K. B.

E. Schonbrun, C. Rinzler, and K. B. Crozier, "Microfabricated water immersion zone plate optical tweezer," Appl. Phys. Lett. 92, 071,112 (2008).

Curto, A. G.

A. G. Curto and F. J. García de Abajo, "Near-field optical phase antennas for long-range plasmon coupling," Nano Lett. 8, 2479-2484 (2008).
[PubMed]

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

Dennis, M. R.

Devaux, E.

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, 508-511 (2006).
[PubMed]

Dong, X.

Draine, B. T.

Du, C.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
[PubMed]

T. Xu, C. Du, C. Wang, and X. Luo, "Subwavelength imaging by metallic slab lens with nanoslits," Appl. Phys. Lett. 91, 201,501 (2007).

Ebbesen, T. W.

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, 508-511 (2006).
[PubMed]

Echenique, P. M.

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205,105 (2003).

Eleftheriades, G. V.

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, "Spatially shifted beam approach to subwavelength focusing," Phys. Rev. Lett. 101, 113,901 (2008).

Emory, S. R.

S. Nie and S. R. Emory, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
[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, 235-238 (2009).

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

Flatau, P. J.

Gao, H.

García de Abajo, F. J.

A. G. Curto and F. J. García de Abajo, "Near-field optical phase antennas for long-range plasmon coupling," Nano Lett. 8, 2479-2484 (2008).
[PubMed]

M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, "The plasmon Talbot effect," Opt. Express 15, 9692- 9700 (2007).
[PubMed]

F. M. Huang, N. Zheludev, Y. Chen, and F. J. García de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205,105 (2003).

F. J. García de Abajo and A. Howie, "Retarded field calculation of electron energy loss in inhomogeneous dielectrics," Phys. Rev. B 65, 115,418 (2002).

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[PubMed]

Howie, A.

F. J. García de Abajo and A. Howie, "Retarded field calculation of electron energy loss in inhomogeneous dielectrics," Phys. Rev. B 65, 115,418 (2002).

Huang, F. M.

F. M. Huang and N. I. Zheludev, "Super-resolution without evanescent waves," Nano Lett. 9, 1249-1254 (2009).
[PubMed]

F. M. Huang, N. Zheludev, Y. Chen, and F. J. García de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

Käll, M.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).

Klein, S.

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

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, 508-511 (2006).
[PubMed]

Leskova, T. A.

A. A. Maradudin and T. A. Leskova, "The Talbot effect for a surface plasmon polariton," New J. Phys. 11, 033,004 (2009).

Liddle, J. A.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[PubMed]

Luo, X.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
[PubMed]

T. Xu, C. Du, C. Wang, and X. Luo, "Subwavelength imaging by metallic slab lens with nanoslits," Appl. Phys. Lett. 91, 201,501 (2007).

Maradudin, A. A.

A. A. Maradudin and T. A. Leskova, "The Talbot effect for a surface plasmon polariton," New J. Phys. 11, 033,004 (2009).

Markley, L.

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, "Spatially shifted beam approach to subwavelength focusing," Phys. Rev. Lett. 101, 113,901 (2008).

Nie, S.

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

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).

Rinzler, C.

E. Schonbrun, C. Rinzler, and K. B. Crozier, "Microfabricated water immersion zone plate optical tweezer," Appl. Phys. Lett. 92, 071,112 (2008).

Rivacoba, A.

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205,105 (2003).

Rodríguez-Lorenzo, L.

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
[PubMed]

Schonbrun, E.

E. Schonbrun, C. Rinzler, and K. B. Crozier, "Microfabricated water immersion zone plate optical tweezer," Appl. Phys. Lett. 92, 071,112 (2008).

Shi, H.

Talbot, H. F.

H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

Verslegers, 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, 235-238 (2009).

Volkov, V. S.

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, 508-511 (2006).
[PubMed]

Wang, C.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
[PubMed]

T. Xu, C. Du, C. Wang, and X. Luo, "Subwavelength imaging by metallic slab lens with nanoslits," Appl. Phys. Lett. 91, 201,501 (2007).

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, "Single molecule detection using surface-enhanced Raman scattering (SERS)," Phys. Rev. Lett. 78, 1667-1670 (1997).

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, "Spatially shifted beam approach to subwavelength focusing," Phys. Rev. Lett. 101, 113,901 (2008).

White, J. 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, 235-238 (2009).

Wong, A. M. H.

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, "Spatially shifted beam approach to subwavelength focusing," Phys. Rev. Lett. 101, 113,901 (2008).

Xu, H.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, "Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering," Phys. Rev. Lett. 83, 4357-4360 (1999).

Xu, T.

T. Xu, C. Du, C. Wang, and X. Luo, "Subwavelength imaging by metallic slab lens with nanoslits," Appl. Phys. Lett. 91, 201,501 (2007).

Yu, Z.

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, 235-238 (2009).

Zabala, N.

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205,105 (2003).

Zheludev, N.

F. M. Huang, N. Zheludev, Y. Chen, and F. J. García de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).

Zheludev, N. I.

F. M. Huang and N. I. Zheludev, "Super-resolution without evanescent waves," Nano Lett. 9, 1249-1254 (2009).
[PubMed]

M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, "The plasmon Talbot effect," Opt. Express 15, 9692- 9700 (2007).
[PubMed]

Astrophys. J. (1)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).

J. Am. Chem. Soc. (1)

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, I. Pastoriza-Santos, S. Mazzucco, O. Stéphan, M. Kociak, L. M. Liz-Marzán, and F. J. García de Abajo, "Zeptomol Detection through controlled ultrasensitive surface-enhanced Raman scattering," J. Am. Chem. Soc. 131, 4616-4618 (2009).
[PubMed]

J. Mod. Opt. (2)

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

J. Opt. Soc. Am. A (1)

Nano Lett. (3)

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, 235-238 (2009).

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Supplementary Material (1)

» Media 1: AVI (2578 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Near-field lens and example of focusing. The lens is formed by N=15 coplanar, concentric silicon nanowires embedded in silica (n=1.45), and it is designed to focus a point source S on an image spot I. For simplicity we consider both image and source to be equally separated at a distance a=10λ from the plane of the rings. The free-space wavelength is λ 0=1550 nm. The rings have inner radius R=100 nm and external radii bn determined by the condition of constructive interference (see Eq. (1)). The bar scale in the figure is given relative to the wavelength inside the silica, λ=λ 0=n. The source is an electric dipole of magnitude P ext=x̂+iŷ.

Fig. 2.
Fig. 2.

Comparison between (a) a semi-analytical model (see Sec. 2) and (b) the full solution of Maxwell’s equations using BEM under the same conditions as in Fig. 1 (i.e., N=15 silicon rings of radius R=100 nm embedded in silica and a free-space wavelength λ 0=1550 nm). The plane of representation and the source dipole are the same as in Fig. 1 and the rings are shown as pink solid circles. The strength of the induced-polarization components along radial (|PR |), azimuthal (out-of-plane, |Pφ |), and rotational-axis (|Pz |) directions is shown in (c) for each of the rings (1=innermost, 15=outermost). The evolution of the position and field intensity at the image spot maximum with the number of rings is shown in (d). Both (c) and (d) are calculated with the analytical model.

Fig. 3.
Fig. 3.

Variation of the lens performance with geometrical and compositional parameters calculated from BEM. The default parameters given in (a) are the same as in Fig. 1, and each of the panels (b)–(f) shows the field intensity when one of these parameters is varied, as indicated by text insets. (b),(c): Variation with ring inner radius R. (d): Variation with focal distance a. (e) Variation with number of rings N. (f) Variation with material in the rings. The source is an electric dipole P ext=x̂, as shown by black arrows, and the free-space wavelength is λ 0=1550 nm. The plane of representation is the same as in Fig. 1 in all cases.

Fig. 4.
Fig. 4.

Dependence of the lens focusing properties on (a) the inner radius of the rings R (for a=10λ) and (b) the focal distance a (for R=100 nm), calculated using BEM. The lens is made of N=15 silicon rings in a silica matrix, except the lower-right plot, calculated for 30 rings. The plots are close-ups of the image spot intensity in the same plane of representation as in Fig. 1, but the source is a dipole P ext=x̂. The intensity is given in linear scale and normalized to its maximum in each plot. The contour of half-maximum intensity is shown as solid lines. The geometrical focus is indicated by dashed lines.

Fig. 5.
Fig. 5.

Chromatic dispersion of the antenna of Fig. 1, designed for a free-space wavelength λ 0,ref =1550 nm, but operating at different vacuum wavelengths λ 0, as indicated in each plot. The dashed line indicates the geometrical focus position z=a. The intensity is calculated using BEM, normalized to the maximum for λ 0=λ 0,re f , and represented in linear scale. The plane of representation is the same as in Fig. 1, but the source is a dipole P ext=x̂.

Fig. 6.
Fig. 6.

Focusing of off-axis spots. The lower images (b) show different source spots, laterally displaced away from the axis of the lens by a distance Δx as indicated by labels. The upper images (a) show the corresponding image spots. The vertical dashed lines indicate the lens axis. The antenna has 30 silicon rings embedded in silica and a focal distance of 10λ. The free-space light wavelength is λ 0=1550nm. The external dipole is like in Eq. (5).

Fig. 7.
Fig. 7.

Lens focusing for different source and image focal distances. The source focal distance is fixed at a 1=10λ. The near-field distribution is represented in (a) for two different values of the image focal distance a 2. Some basic parameters describing the image spot are represented in (b) as a function of a 2: the actual position of the image spot maximum relative to a 2 (black curve), the FWHM of the spot along the lens axis direction (red curve), and the electric field intensity maximum (blue curve). The number of rings (silicon on silica) is maintained fixed at N=15. The light wavelength is λ 0=1550nm. The external dipole is like in Eq. (5). A video showing the evolution of the near field intensity as the image focal distance is varied is available at Media 1.

Equations (6)

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bi=(iλ2)2a2 (i2aλ) ,
ibi(iλ2)2log(N)
Pi=αi[Eiext+jiGijPj],
Gij,ab=bjdφ[k2ûa0·ûbφ+(ûa0·)(ûbφ·)] eikri0rjφri0rjφ eiφ ,
Pext=x̂+iŷ=(R̂+iφ̂)eiφ,
n1 a12+bi2 + n2 a22+bi2 = 0 .

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