Abstract

Gradient index structures are gaining increased importance with the constant development of Transformation Optics and metamaterials. Our ability to fabricate such devices, while limited, has already demonstrated the extensive capabilities of those designs, in the forms of invisibility devices, as well as illusion optics and super-lensing. In this paper we present a low loss, high index contrast lens that is integrated with conventional nanophotonic waveguides to provide improved tolerance in fiber-to-chip optical links for future communication networks. This demonstration represents a positive step in making the extraordinary capabilities of gradient index devices available for integrated optics.

© 2011 OSA

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  1. D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
    [CrossRef]
  2. R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
    [CrossRef]
  3. T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
    [CrossRef]
  4. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
    [CrossRef]
  5. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef] [PubMed]
  6. R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
    [CrossRef]
  7. K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.
  8. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).
  9. U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).
  10. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
    [CrossRef]
  11. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302 (2003).
    [CrossRef] [PubMed]
  12. K. K. Lee, D. R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L. C. Kimerling, K. P. Yap, and M. T. Doan, “Mode transformer for miniaturized optical circuits,” Opt. Lett. 30, 498 (2005).
    [CrossRef] [PubMed]
  13. G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
    [CrossRef]
  14. A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19, 5156 (2011).
    [CrossRef] [PubMed]
  15. F. Zernike, “Luneburg lens for optical waveguide use,” Opt. Commun. 12, 379–381 (1974).
    [CrossRef]
  16. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–32 (2010).
    [CrossRef]
  17. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
    [CrossRef] [PubMed]
  18. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
    [CrossRef]
  19. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17, 4752 (2009).
    [CrossRef] [PubMed]

2011 (2)

A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19, 5156 (2011).
[CrossRef] [PubMed]

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

2010 (2)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–32 (2010).
[CrossRef]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

2009 (4)

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17, 4752 (2009).
[CrossRef] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

2006 (1)

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

2005 (4)

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

K. K. Lee, D. R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L. C. Kimerling, K. P. Yap, and M. T. Doan, “Mode transformer for miniaturized optical circuits,” Opt. Lett. 30, 498 (2005).
[CrossRef] [PubMed]

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

2003 (1)

2002 (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

1974 (1)

F. Zernike, “Luneburg lens for optical waveguide use,” Opt. Commun. 12, 379–381 (1974).
[CrossRef]

Almeida, V. R.

Baets, R.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Basov, D. N.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Bogaerts, W.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[CrossRef]

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17, 4752 (2009).
[CrossRef] [PubMed]

Chen, L.

Cui, T. J.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Di Falco, A.

Doan, M. T.

Driscoll, T.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Dumon, P.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[CrossRef]

Gollub, J. G.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Greegor, R. B.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Hoepfner, C.

Kehr, S. C.

Kimerling, L. C.

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–32 (2010).
[CrossRef]

Lee, K. K.

Leonhardt, U.

A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19, 5156 (2011).
[CrossRef] [PubMed]

U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).

Levi, J. S.

K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Lim, D. R.

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[CrossRef]

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17, 4752 (2009).
[CrossRef] [PubMed]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302 (2003).
[CrossRef] [PubMed]

K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.

Lira, H. L. R.

K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.

Liu, R.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Liu, Y.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

Mikkelsen, M. H.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Mock, J.

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Mock, J. J.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Morita, H.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Nielsen, J. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Oh, W.-Y.

Pan, D.

Panepucci, R. R.

Parazzoli, C. G.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Philbin, T.

U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[CrossRef]

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17, 4752 (2009).
[CrossRef] [PubMed]

Preston, K.

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17, 4752 (2009).
[CrossRef] [PubMed]

K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.

Robinson, J. T.

Roelkens, G.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

Rye, P. M.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Schurig, D.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Sherwood-Droz, N.

K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.

Shoji, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

Smith, D.

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–32 (2010).
[CrossRef]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Starr, A.

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Starr, A. F.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Tanielian, M. H.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Thompson, M. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Tsuchizawa, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

Valentine, J.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Van Thourhout, D.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

Wada, K.

Watanabe, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

Yamada, K.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

Yang, X. M.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Yap, K. P.

Zentgraf, T.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Zernike, F.

F. Zernike, “Luneburg lens for optical waveguide use,” Opt. Commun. 12, 379–381 (1974).
[CrossRef]

Zhang, X.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Electron. Lett. (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38, 1669 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17, 2613–2615 (2005).
[CrossRef]

Nat. Commun. (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

Nat. Mater. (2)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–32 (2010).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Nat. Photonics (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[CrossRef]

Opt. Commun. (1)

F. Zernike, “Luneburg lens for optical waveguide use,” Opt. Commun. 12, 379–381 (1974).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[CrossRef]

Other (3)

K. Preston, N. Sherwood-Droz, J. S. Levi, H. L. R. Lira, and M. Lipson, “Design rules for WDM optical interconnects using silicon microring resonators,” (2011), submitted to Opt. Express.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).

U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2010).

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Figures (4)

Fig. 1
Fig. 1

(Color online) Comparison between a Luneburg and a standard lens. (a) The conventional lens creates a Fourier transform of the input image at its focal plane, distorted by aberrations. (b) The Luneburg lens does the same over a focal circumference without aberrations. (c) Instead of a constant refractive index, the Luneburg lens shows a refractive index that decreases radially.

Fig. 2
Fig. 2

(Color online) Characterization of the FIB patterning process. (a) AFM scan from a Luneburg lens patterned via FIB with thickness varying from 0 to 82nm. (b) Comparison between the fabricated (circles) and the required (continuous line) lens profiles. The measured RMS surface roughness is around 2nm for most of the surface, with exception of approximately 1μm around the edge, where imperfections are due to the abrupt change in the silicon depth.

Fig. 3
Fig. 3

(Color online) Fiber-to-chip coupler based on the Luneburg lens. (a) A lensed fiber is used to couple light into the silicon waveguide. (b) Zoomed-in illustration of the coupling region. We add a Luneburg lens to the conventional inverse taper design to minimize losses induced by the misalignment Δ. (c) Optical microscope image of the fabricated device. The trenches defining the waveguide and taper are due to the use of positive resist. The variation of the silicon layer thickness in the lens can be clearly seen by the interference pattern (colors) in the image. Note that the dark area on the left edge of the image is due to face polishing, i.e., the lens has not been damaged.

Fig. 4
Fig. 4

(Color online) Experimental results for the alignment sensitivity of the coupler devices. Two Luneburg-based devices (blue) and 2 bare taper couplers (red) are measured. One can clearly see that the introduction of the Luneburg lens improves the robustness to misalignment. Full 3-d simulations (continuous lines) match the experimental results very well.

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