Abstract

A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k0 (k0 is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

© 2015 Optical Society of America

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References

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    [Crossref]

2014 (1)

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

2013 (5)

X. Lu, J. Hu, and R. Tao, “Enhanced fractional Fourier lens with isotropic transformation media,” Opt. Eng. 52(6), 060501 (2013).
[Crossref]

K. Wu and G. P. Wang, “One-dimensional Fibonacci grating for far-field super-resolution imaging,” Opt. Lett. 38(12), 2032–2034 (2013).
[Crossref] [PubMed]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

2012 (5)

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
[Crossref] [PubMed]

2011 (3)

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

Y. J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express 19(24), 24411–24423 (2011).
[Crossref] [PubMed]

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscal plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

2010 (7)

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D Appl. Phys. 43(5), 055404 (2010).
[Crossref]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010).
[Crossref] [PubMed]

M. Zhang, J. Du, H. Shi, S. Yin, L. Xia, B. Jia, M. Gu, and C. Du, “Three-dimensional nanoscale far-field focusing of radially polarized light by scattering the SPPs with an annular groove,” Opt. Express 18(14), 14664–14670 (2010).
[Crossref] [PubMed]

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2007 (2)

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

2006 (2)

T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microw. Opt. Technol. Lett. 48(2), 363–367 (2006).
[Crossref]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

2005 (1)

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005).
[Crossref]

2003 (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

2002 (1)

J. B. Pendry and S. A. Ramakrishna, “Near-field lenses in two dimensions,” J. Phys. Condens. Matter 14(36), 8463–8479 (2002).
[Crossref]

2000 (1)

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85(14), 2933–2936 (2000).
[Crossref] [PubMed]

1994 (1)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

Alù, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Argyros, A.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Bai, J.

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D Appl. Phys. 43(5), 055404 (2010).
[Crossref]

Bartal, G.

Beigang, R.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010).
[Crossref] [PubMed]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

Cao, P.

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Chad, J. E.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Cheng, L.

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

Cheng, Q.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

Cui, T. J.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D Appl. Phys. 43(5), 055404 (2010).
[Crossref]

Dennis, M. R.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Depine, R. A.

T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microw. Opt. Technol. Lett. 48(2), 363–367 (2006).
[Crossref]

Du, C.

Du, J.

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Escarra, M. D.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Escobar, M. A.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Fischer, B. M.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Fleming, S. C.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Gmachl, C. F.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Gu, M.

Guo, C.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Han, S.

Han, T. C.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

He, Q.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Hoffman, A. J.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Hu, J.

X. Lu, J. Hu, and R. Tao, “Enhanced fractional Fourier lens with isotropic transformation media,” Opt. Eng. 52(6), 060501 (2013).
[Crossref]

Jia, B.

Jiang, W. X.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

Jokerst, N. M.

Kaltenecker, K. J.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Kino, G. S.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

Kong, W.

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

Kroll, N.

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85(14), 2933–2936 (2000).
[Crossref] [PubMed]

Krolla, B.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010).
[Crossref] [PubMed]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

Kuhlmey, B. T.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Kuhta, N. A.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Lakhtakia, A.

T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microw. Opt. Technol. Lett. 48(2), 363–367 (2006).
[Crossref]

Larouche, S.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Leonhardt, R.

Lester, M.

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
[Crossref]

Li, J.

Li, X.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Li, Y.

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

Lindberg, J.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Lipworth, G.

Liu, Q.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Liu, Z.

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
[Crossref] [PubMed]

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscal plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
[Crossref] [PubMed]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Lo, Y. H.

Lu, D.

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
[Crossref] [PubMed]

Lu, X.

X. Lu, J. Hu, and R. Tao, “Enhanced fractional Fourier lens with isotropic transformation media,” Opt. Eng. 52(6), 060501 (2013).
[Crossref]

Ma, C.

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscal plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
[Crossref] [PubMed]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

Ma, H. F.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

Mackay, T. G.

T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microw. Opt. Technol. Lett. 48(2), 363–367 (2006).
[Crossref]

Mamin, H. J.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

Mei, Z. L.

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D Appl. Phys. 43(5), 055404 (2010).
[Crossref]

Miao, J.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Misawa, H.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Monticone, F.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Neu, J.

Nomura, W.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005).
[Crossref]

Ohtsu, M.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005).
[Crossref]

Paul, O.

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010).
[Crossref] [PubMed]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

J. B. Pendry and S. A. Ramakrishna, “Near-field lenses in two dimensions,” J. Phys. Condens. Matter 14(36), 8463–8479 (2002).
[Crossref]

Podolskiy, V. A.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Qiu, C. W.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

Rahm, M.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010).
[Crossref] [PubMed]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna, “Near-field lenses in two dimensions,” J. Phys. Condens. Matter 14(36), 8463–8479 (2002).
[Crossref]

Reinhard, B.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010).
[Crossref] [PubMed]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

Rogers, E. T. F.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Roy, T.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

Savo, S.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Shi, H.

Silva, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Skigin, D. C.

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
[Crossref]

Smith, D. R.

Y. J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express 19(24), 24411–24423 (2011).
[Crossref] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85(14), 2933–2936 (2000).
[Crossref] [PubMed]

Studenmund, W. R.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Sun, S.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Tao, R.

X. Lu, J. Hu, and R. Tao, “Enhanced fractional Fourier lens with isotropic transformation media,” Opt. Eng. 52(6), 060501 (2013).
[Crossref]

Terris, B. D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

Thongrattanasiri, S.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

Tian, Y.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

Tsai, Y. J.

Tuniz, A.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Tyler, T.

Walther, M.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Wang, G. P.

Wang, Y.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

Wu, K.

Xia, L.

Xiao, S.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Xu, Q.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Yatsui, T.

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005).
[Crossref]

Yin, S.

Zhang, J.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Zhang, M.

Zhang, S.

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

J. Li, S. Han, S. Zhang, G. Bartal, and X. Zhang, “Designing the Fourier space with transformation optics,” Opt. Lett. 34(20), 3128–3130 (2009).
[Crossref] [PubMed]

Zhang, X.

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

J. Li, S. Han, S. Zhang, G. Bartal, and X. Zhang, “Designing the Fourier space with transformation optics,” Opt. Lett. 34(20), 3128–3130 (2009).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Zhao, X.

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

Zheludev, N. I.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Zhou, L.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Zhou, Z.

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

Adv. Mater. (1)

W. X. Jiang, C. W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, “Broadband all-dielectric magnifying lens for far-field high-resolution imaging,” Adv. Mater. 25(48), 6963–6968 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (6)

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97(10), 101103 (2010).
[Crossref]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterials based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010).
[Crossref]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994).
[Crossref]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

W. Nomura, M. Ohtsu, and T. Yatsui, “Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion,” Appl. Phys. Lett. 86(18), 181108 (2005).
[Crossref]

J. Nanophotonics (1)

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscal plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

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

M. Lester and D. C. Skigin, “Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays,” J. Opt. A, Pure Appl. Opt. 9(1), 81–87 (2007).
[Crossref]

J. Phys. Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna, “Near-field lenses in two dimensions,” J. Phys. Condens. Matter 14(36), 8463–8479 (2002).
[Crossref]

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

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D Appl. Phys. 43(5), 055404 (2010).
[Crossref]

Microw. Opt. Technol. Lett. (1)

T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microw. Opt. Technol. Lett. 48(2), 363–367 (2006).
[Crossref]

Nat. Commun. (2)

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
[Crossref] [PubMed]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Opt. Eng. (1)

X. Lu, J. Hu, and R. Tao, “Enhanced fractional Fourier lens with isotropic transformation media,” Opt. Eng. 52(6), 060501 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. B (2)

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

Phys. Rev. Lett. (3)

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85(14), 2933–2936 (2000).
[Crossref] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Plasmonics (2)

J. Miao, Y. Wang, C. Guo, Y. Tian, J. Zhang, Q. Liu, Z. Zhou, and H. Misawa, “Far-field focusing of spiral plasmonic lens,” Plasmonics 7(2), 377–381 (2012).
[Crossref]

L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012).
[Crossref]

Science (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Dispersion and negative-refraction of the uniform hyperbolic metamaterial. (a) Dispersion curve of the hyperbolic metamaterial. (b) Negative-refraction at the interface of the hyperbolic metamaterial and air. The transverse momentum ky of the incident wave is equal to 0.3k0. The amplitude of the incident beam fulfills the Gaussian distribution with the beam radius being 2.5λ. The relative permittivity of the metamaterial is ε = (−1, 1).
Fig. 2
Fig. 2 Analysis and results of the ray tracing. (a) The model and light rays in the first two unit layer. The red and black solid lines with arrows represent the directions of energy flow and phase velocity, respectively. (b) Ray tracing in the hyperbolic GRIN lens. (c) Double focusing inside and outside the hyperbolic GRIN lens for ky /k0 = 0, 0.5, 1.5, −2.
Fig. 3
Fig. 3 Full-wave simulating verification for the double focusing. (a) simulation parameters. (b) ky = 0k0. (c) ky = 0.5k0. (d) ky = 1.5k0. (e) ky = −2k0. Both the amplitude of the incident beams fulfills the Gaussian distribution with the beam radius being 3λ, as shown in (a).
Fig. 4
Fig. 4 y-direction internal and external focal positions with the transverse momentums ky being from 0 to 2.7k0, predicted by the ray tracing and full-wave simulation.
Fig. 5
Fig. 5 Verification of the extraordinary spatial FT and the super-resolution imaging. (a) The simulating (red line) and theoretical (blue dashed line) results of the spatial spectrum of a single rectangular pulse. The width of the pulse is 2λ/3. The magnetic field pattern and the observation path are given inset. (b) The post-processing results of the super-resolution imaging, with the red line being the reconstructed image and the blue dashed line being the sources. The width and separation of the two rectangular pulses are λ/15 and λ/5, respectively. The amplitude distribution of the magnetic field is also given inset.
Fig. 6
Fig. 6 Double-lenses long-distance super-resolution imaging. (a) The schematic of the imaging configuration. (b) The normalized amplitude distribution of the images, with the red solid and blue dashed lines being the simulating and theoretical results, respectively. According to the Rayleigh criterion, the two separated objects can be clearly resolved. The amplitude pattern of the magnetic field and the enlarged view of the images are also given inset.
Fig. 7
Fig. 7 Simulating results of the constructed lens. (a) The filling ratio of the negative material and the effective relative permittivity of ε2 as a function of y. The inset is the unit layer of the combined metamaterial. (b), (c) and (d) are amplitude distribution of the magnetic field for different incidences, (b) ky /k0 = 0, (c) ky /k0 = 0.5, (d) ky /k0 = 1.5.
Fig. 8
Fig. 8 Simulating verification for the super-resolution imaging of the constructed lens. The amplitude distribution of the magnetic field and the enlarged view of the images are also given inset.

Equations (9)

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k y 2 ε x + k x 2 ε y = k 0 2 ,
P y P x = ε y k y 2 ε x k x 2 ,
1 ε y 1 1 ε y 1 2 tan 2 ( θ 1 ) = 1 ε y 2 1 ε y 2 2 tan 2 ( θ 2 ) ,
k x 1 2 = ε y i n [ k 0 2 + ( k y i n ) 2 ] , k x n 2 = ε y o u t [ k 0 2 + ( k y o u t ) 2 ] ,
| k y o u t | = ε y i n ε y o u t [ k 0 2 + ( k y i n ) 2 ] k 0 2 .
S ( k y ) = λ / 3 λ / 3 p ( y ) e j k y y d y = A sin c ( k y λ / 3 ) ,
p ( y ) = 2.7 k 0 2.7 k 0 ρ ( k y ) S ( k y ) e j k y y d k y ,
ε x = ε 1 f 0 + ε 2 ( 1 f 0 ) ,
ε y = ε 1 ε 2 ε 1 ( 1 f 0 ) + ε 2 f 0 ,

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