Abstract

In this paper, systematical study on the focal shift phenomenon in planar lenses based on GaN high contrast gratings was performed using finite element method (FEM). Influence of parameters including device size, designed focal length, total phase difference on the focusing performance is presented. It shows that the focal shift is mainly determined by the Fresnel number of the lens, which is nearly equal to the total phase difference divided by π. The influence of the lens size and designed focal length can be attributed to the change of Fresnel number. Theoretical analysis based on diffraction theory is employed to predict the focal shift, which is in accordance with the numerical simulation.

© 2015 Optical Society of America

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References

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2014 (6)

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

J. H. Lee, J. W. Yoon, M. J. Jung, J. K. Hong, S. H. Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
[Crossref]

2013 (2)

A. B. Klemm, D. Stellinga, E. R. Martins, L. Lewis, G. Huyet, L. O’Faolain, and T. F. Krauss, “Experimental high numerical aperture focusing with high contrast gratings,” Opt. Lett. 38(17), 3410–3413 (2013).
[Crossref] [PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

2012 (5)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Y. Yu and H. Zappe, “Theory and implementation of focal shift of plasmonic lenses,” Opt. Lett. 37(9), 1592–1594 (2012).
[Crossref] [PubMed]

Y. Gao, J. Liu, X. Zhang, Y. Wang, Y. Song, S. Liu, and Y. Zhang, “Analysis of focal-shift effect in planar metallic nanoslit lenses,” Opt. Express 20(2), 1320–1329 (2012).
[Crossref] [PubMed]

B. Hu, Q. J. Wang, and Y. Zhang, “Systematic study of the focal shift effect in planar plasmonic slit lenses,” Nanotechnology 23(44), 444002 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (3)

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18(12), 12606–12614 (2010).
[Crossref] [PubMed]

2009 (1)

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(1), 235–238 (2009).
[Crossref] [PubMed]

2006 (1)

2004 (1)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[Crossref]

1991 (1)

Y. J. Li, “A High-accuracy formula for fast evaluation of the effect of focal shift,” J. Mod. Opt. 38(9), 1815–1819 (1991).
[Crossref]

1983 (1)

1982 (1)

Y. J. Li and E. Wolf, “Focal shift in focused truncated gaussian beam,” Opt. Commun. 42(3), 151–156 (1982).
[Crossref]

1981 (2)

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[Crossref]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981).
[Crossref]

Azad, A. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [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(1), 235–238 (2009).
[Crossref] [PubMed]

Barnes, W. L.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Beausoleil, R. G.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Briggs, D. P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [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(1), 235–238 (2009).
[Crossref] [PubMed]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Carletti, L.

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(1), 235–238 (2009).
[Crossref] [PubMed]

Chang-Hasnain, C. J.

Chase, C.

Chen, H. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Chen, Q.

Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6(1), 75–82 (2011).
[Crossref]

Chowdhury, D. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Chung, I. S.

Dalvit, D. A. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [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(1), 235–238 (2009).
[Crossref] [PubMed]

Fattal, D.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Fiorentino, M.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Gao, Y.

Gaylord, T. K.

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Grady, N. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Herzig, H. P.

Heyes, J. E.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Hong, J. K.

J. H. Lee, J. W. Yoon, M. J. Jung, J. K. Hong, S. H. Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

Hooper, I. R.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Hu, B.

B. Hu, Q. J. Wang, and Y. Zhang, “Systematic study of the focal shift effect in planar plasmonic slit lenses,” Nanotechnology 23(44), 444002 (2012).
[Crossref] [PubMed]

Huyet, G.

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Jung, M. J.

J. H. Lee, J. W. Yoon, M. J. Jung, J. K. Hong, S. H. Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

Karagodsky, V.

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[Crossref]

Klemm, A. B.

Krauss, T. F.

Kravchenko, I. I.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

Lee, J. H.

J. H. Lee, J. W. Yoon, M. J. Jung, J. K. Hong, S. H. Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

Lewis, L.

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Li, Y.

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[Crossref]

Li, Y. J.

Y. J. Li, “A High-accuracy formula for fast evaluation of the effect of focal shift,” J. Mod. Opt. 38(9), 1815–1819 (1991).
[Crossref]

Y. J. Li and E. Wolf, “Focal shift in focused truncated gaussian beam,” Opt. Commun. 42(3), 151–156 (1982).
[Crossref]

Lin, D.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Lin, L.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Liu, J.

Liu, S.

Lu, F.

Magnusson, R.

J. H. Lee, J. W. Yoon, M. J. Jung, J. K. Hong, S. H. Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

Malureanu, R.

Martins, E. R.

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Meinzer, N.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Moharam, M. G.

Moitra, P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

Mørk, J.

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

O’Faolain, L.

Peng, Z.

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Polman, A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Reiten, M. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Roberts, A.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Ruffieux, P.

Scharf, T.

Sedgwick, F. G.

Song, S. H.

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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
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S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
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Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
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P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
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S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
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B. Hu, Q. J. Wang, and Y. Zhang, “Systematic study of the focal shift effect in planar plasmonic slit lenses,” Nanotechnology 23(44), 444002 (2012).
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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(1), 235–238 (2009).
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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(1), 235–238 (2009).
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Zeng, Y.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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J. H. Lee, J. W. Yoon, M. J. Jung, J. K. Hong, S. H. Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: A polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[Crossref]

IEEE Photonics Technol. Lett. (1)

S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, R. G. Beausoleil, and M. Fiorentino, “Sub-wavelength grating lenses with a twist,” IEEE Photonics Technol. Lett. 26(13), 1375–1378 (2014).
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Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [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(1), 235–238 (2009).
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Nanotechnology (1)

B. Hu, Q. J. Wang, and Y. Zhang, “Systematic study of the focal shift effect in planar plasmonic slit lenses,” Nanotechnology 23(44), 444002 (2012).
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Nat. Commun. (1)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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Nat. Photonics (2)

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
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D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
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Opt. Commun. (2)

Y. J. Li and E. Wolf, “Focal shift in focused truncated gaussian beam,” Opt. Commun. 42(3), 151–156 (1982).
[Crossref]

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Plasmonics (1)

Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6(1), 75–82 (2011).
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Science (3)

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Other (1)

Z. H. Wang, S. M. He, Q. F. Liu, W. Wang, Y. J. Wang, and H. B. Zhu, “Metasurfaces based on gallium nitride high contrast gratings at visible range,” presented at the APS March Meeting 2015, San Antonio, Texas, USA, 2–6 Mar. 2015.

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Figures (7)

Fig. 1
Fig. 1 Schematic geometry of a lens based on non-periodic GaN HCGs. The grating period and thickness are denoted by P and T, respectively. The width of the lens, which is defined as the distance between the center of the two outermost slits, is denoted by 2a. The point F is the geometrical focus, and the designed focal length is f. The actual focus locates at point F’ with an actual focal length of f’. The focal shift is defined as Δf/f = (f-f’)/f.
Fig. 2
Fig. 2 (a) Fill factor-period-dependent TM-transmissitity spectrum and (b) transmission phase shift spectrum (unit: π) of a strictly periodic GaN grating with T = 410 nm at λ = 460 nm.
Fig. 3
Fig. 3 Phase distribution of non-periodic HCG focusing lenses. The solid lines are the desired phase distribution determined by Eq. (1). Blue triangles, red circles, and black squares are the phases of each HCG bar for lenses with focal length f = 4 μm, 10 μm and 15 μm, respectively.
Fig. 4
Fig. 4 Effect of the lens width on the focusing performance. The designed focal length is set as f = 10 μm. (a) Intensity distribution of the transmitted field for lenses with widths of 2a = 3.16, 4.98, and 16.05 µm, respectively. The white lines indicate the designed focal plane. (b) Beam intensity profile at the focal plane for lenses with different widths. (c) Field intensity distribution along y direction at x = 0 of the transmitted wave.
Fig. 5
Fig. 5 Effect of the designed focal length on the focus of the lens. The lens width is set as about 8 μm. (a) Intensity distribution of the transmitted field for lenses with f = 4, 6, and 10 μm. The white lines indicate the designed focal plane. (b) Beam intensity profile at the focal plane for lenses with f = 4, 6, 10 and 15 μm, and that of the incident light (black line); (c) Field intensity distribution along y direction at x = 0 of the transmitted wave.
Fig. 6
Fig. 6 Effect of the total phase difference on the focusing performance. The designed focal length of the lenses is f = 10 μm. (a) Intensity distribution of the transmitted field. The total phase differences are π, 2π, 8π and 12π, respectively. The white lines indicate the designed focal plane. (b) Simulated focal shift and (c) FWHM and DOF as a function of the total phase difference.
Fig. 7
Fig. 7 Focal shift of HCG lenses with f = 10 μm calculated using Eq. (3), and that simulated by FEM.

Tables (3)

Tables Icon

Table 1 Deviation of the focal length between the design, numerical simulation, and experimental measurement

Tables Icon

Table 2 Dependence of performance parameters on lens size for lenses with designed focal length of f = 10 μm.

Tables Icon

Table 3 Dependence of performance parameters on the designed focal length for lenses with size of about 8 μm.

Equations (3)

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Δ φ ( x ) = φ ( x ) φ ( 0 ) = 2 π λ ( f 2 + x 2 f )
N = a 2 λ f
Δ f f = ( 1 + N × 1 + ( π 2 12 N ) c c ) 1

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