Abstract

In order to realize super-resolution imaging of point source at any positions within a large object distance range, a graded-index equivalent medium (GEM) flat lens, which can break through the object distance limit d (d is the lens thickness), is analyzed by negative refraction. Based on this analysis, graded-index photonic crystal (GPC) flat lens with a large object distance is designed. Its imaging resolution can reach up to 0.4λ at the maximum object distance of 5d, which breaks through the diffraction limit.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (9)

C. X. Yue, W. Tan, and J. J. Liu, “Photonic band gap properties of one-dimensional Thue-Morse all-dielectric photonic quasicrystal,” Superlattices Microstruct. 117, 252–259 (2018).
[Crossref]

E. X. Liu, B. Yan, W. Tan, J. L. Xie, R. Ge, and J. J. Liu, “Guiding characteristics of Sunflower-type fiber,” Superlattices Microstruct. 115, 123–129 (2018).
[Crossref]

E. Liu, W. Tan, B. Yan, J. Xie, R. Ge, and J. Liu, “Broadband ultra-flattened dispersion, ultra-low confinement loss and large effective mode area in an octagonal photonic quasi-crystal fiber,” J. Opt. Soc. Am. A 35(3), 431–436 (2018).
[Crossref] [PubMed]

S. A. Lennon, F. S. F. Brossard, L. P. Nuttall, J. Wu, J. Griffiths, and R. A. Taylor, “Photonic molecules defined by SU-8 photoresist strips on a photonic crystal waveguide,” Opt. Express 26(24), 32332–32345 (2018).
[Crossref] [PubMed]

Z. W. Ziming Wang, K. S. Kang Su, B. F. Bo Feng, T. Z. Tianhua Zhang, W. H. Weiqing Huang, W. C. Weicheng Cai, W. X. Wei Xiao, H. L. Hongfei Liu, and J. L. Jianjun Liu, “Coupling length variation and multi-wavelength demultiplexing in photonic crystal waveguides,” Chin. Opt. Lett. 16(1), 011301 (2018).
[Crossref]

B. Yan, A. R. Wang, E. X. Liu, W. Tan, J. L. Xie, R. Ge, and J. J. Liu, “Polarization filtering in the visible wavelength range using surface plasmon resonance and a sunflower-type photonic quasi-crystal fiber,” J. Phys. D Appl. Phys. 51(15), 155105 (2018).
[Crossref]

R. Ge, J. Xie, B. Yan, E. Liu, W. Tan, and J. Liu, “Refractive index sensor with high sensitivity based on circular photonic crystal,” J. Opt. Soc. Am. A 35(6), 992–997 (2018).
[Crossref] [PubMed]

J. L. Xie, J. Z. Wang, R. Ge, B. Yan, E. X. Liu, W. Tan, and J. J. Liu, “Multiband super-resolution imaging of graded-index photonic crystal flat lens,” J. Phys. D Appl. Phys. 51(20), 205103 (2018).
[Crossref]

J. J. Liu and Z. G. Fan, “Size limits for focusing of two-dimensional photonic quasicrystal lenses,” IEEE Photonics Technol. Lett. 30(11), 1001–1004 (2018).
[Crossref]

2017 (3)

M. Turduev, E. Bor, and H. Kurt, “Photonic crystal based polarization insensitive flat lens,” J. Phys. D Appl. Phys. 50(27), 275105 (2017).
[Crossref]

F. Gaufillet, S. Marcellin, and E. Akmansoy, “Dielectric metamaterial-based gradient index lens in the terahertz frequency range,” IEEE J. Sel. Top. Quant. 23(4), 1 (2017).
[Crossref]

Y. F. Zhao, Z. M. Wang, J. J. Jiang, X. Chen, C. X. Yue, J. Z. Wang, and J. J. Liu, “Add-drop filter with compound structure of photonic crystal and photonic quasicrystal,” J. Infrared Millim. W. 36(3), 342–348 (2017).

2016 (4)

J. Liu, W. Tan, E. Liu, H. Hu, Z. Fan, T. Zhang, and X. Zhang, “Planar scanning method for detecting refraction characteristics of two-dimensional photonic quasi-crystal wedge-shaped prisms,” J. Opt. Soc. Am. A 33(5), 978–983 (2016).
[Crossref] [PubMed]

J. J. Liu, E. X. Liu, and Z. G. Fan, “Width dependence of two-dimensional photonic quasicrystal flat lens imaging characteristics,” J. Mod. Opt. 63(7), 692–696 (2016).
[Crossref]

B. Feng, E. X. Liu, Z. M. Wang, W. C. Cai, H. F. Liu, S. Wang, T. Y. Liang, W. Xiao, and J. J. Liu, “Generation of terahertz hollow beams by a photonic quasi-crystal flat lens,” Appl. Phys. Express 9(6), 062003 (2016).
[Crossref]

F. Monticone, C. A. Valagiannopoulos, and A. Alù, “Parity-time symmetric nonlocal metasurfaces: all-angle negative refraction and volumetric imaging,” Phys. Rev. X 6(4), 041018 (2016).
[Crossref]

2015 (2)

J. J. Liu, E. X. Liu, T. H. Zhang, and Z. G. Fan, “Thickness dependence of two-dimensional photonic quasicrystal lens imaging characteristics,” Solid State Commun. 201, 68–71 (2015).
[Crossref]

J. J. Liu, E. X. Liu, Z. G. Fan, and X. Zhang, “Dielectric refractive index dependence of the focusing properties of a dielectric-cylinder-type decagonal photonic quasicrystal flat lens and its photon localization,” Appl. Phys. Express 8(11), 112003 (2015).
[Crossref]

2014 (1)

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
[Crossref] [PubMed]

2012 (1)

2011 (1)

2008 (1)

2005 (1)

C. D. Spataru, S. Ismail-Beigi, R. B. Capaz, and S. G. Louie, “Theory and ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes,” Phys. Rev. Lett. 95(24), 247402 (2005).
[Crossref] [PubMed]

2004 (4)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

X. D. Zhang, “Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. B Condens. Matter Mater. Phys. 70(19), 195110 (2004).
[Crossref]

X. D. Zhang, “Absolute negative refraction and imaging of unpolarized electromagnetic waves by two-dimensional photonic crystals,” Phys. Rev. B Condens. Matter Mater. Phys. 70(20), 205102 (2004).
[Crossref]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

2003 (6)

X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B Condens. Matter Mater. Phys. 68(11), 113103 (2003).
[Crossref]

A. Grbic and G. V. Eleftheriades, “Growing evanescent waves in negative-refractive-index transmission-line media,” Appl. Phys. Lett. 82(12), 1815–1817 (2003).
[Crossref]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91(20), 207401 (2003).
[Crossref] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
[Crossref] [PubMed]

J. B. Pendry, D. R. Smith, and A. P. Valanju, “Comment on wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 90(2), 029704 (2003).
[Crossref] [PubMed]

2002 (1)

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B Condens. Matter Mater. Phys. 65(20), 201104 (2002).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

2000 (4)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B Condens. Matter Mater. Phys. 62(16), 10696–10705 (2000).
[Crossref]

K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
[Crossref]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

1873 (1)

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv f. mikrosk. Anatomie 9(1), 413–418 (1873).

Abbe, E.

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv f. mikrosk. Anatomie 9(1), 413–418 (1873).

Akmansoy, E.

F. Gaufillet, S. Marcellin, and E. Akmansoy, “Dielectric metamaterial-based gradient index lens in the terahertz frequency range,” IEEE J. Sel. Top. Quant. 23(4), 1 (2017).
[Crossref]

Alù, A.

F. Monticone, C. A. Valagiannopoulos, and A. Alù, “Parity-time symmetric nonlocal metasurfaces: all-angle negative refraction and volumetric imaging,” Phys. Rev. X 6(4), 041018 (2016).
[Crossref]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Appel, J.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
[Crossref] [PubMed]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91(20), 207401 (2003).
[Crossref] [PubMed]

Bagci, T.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
[Crossref] [PubMed]

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Bo Feng, B. F.

Bor, E.

M. Turduev, E. Bor, and H. Kurt, “Photonic crystal based polarization insensitive flat lens,” J. Phys. D Appl. Phys. 50(27), 275105 (2017).
[Crossref]

Brossard, F. S. F.

Brown, T.

Cai, W. C.

B. Feng, E. X. Liu, Z. M. Wang, W. C. Cai, H. F. Liu, S. Wang, T. Y. Liang, W. Xiao, and J. J. Liu, “Generation of terahertz hollow beams by a photonic quasi-crystal flat lens,” Appl. Phys. Express 9(6), 062003 (2016).
[Crossref]

Capaz, R. B.

C. D. Spataru, S. Ismail-Beigi, R. B. Capaz, and S. G. Louie, “Theory and ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes,” Phys. Rev. Lett. 95(24), 247402 (2005).
[Crossref] [PubMed]

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
[Crossref]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
[Crossref]

Chen, X.

Y. F. Zhao, Z. M. Wang, J. J. Jiang, X. Chen, C. X. Yue, J. Z. Wang, and J. J. Liu, “Add-drop filter with compound structure of photonic crystal and photonic quasicrystal,” J. Infrared Millim. W. 36(3), 342–348 (2017).

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Subwavelength resolution in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. Lett. 91(20), 207401 (2003).
[Crossref] [PubMed]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Growing evanescent waves in negative-refractive-index transmission-line media,” Appl. Phys. Lett. 82(12), 1815–1817 (2003).
[Crossref]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Fan, Z.

Fan, Z. G.

J. J. Liu and Z. G. Fan, “Size limits for focusing of two-dimensional photonic quasicrystal lenses,” IEEE Photonics Technol. Lett. 30(11), 1001–1004 (2018).
[Crossref]

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Liu, J. J.

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A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
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T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
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J. B. Pendry, D. R. Smith, and A. P. Valanju, “Comment on wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 90(2), 029704 (2003).
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T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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C. D. Spataru, S. Ismail-Beigi, R. B. Capaz, and S. G. Louie, “Theory and ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes,” Phys. Rev. Lett. 95(24), 247402 (2005).
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Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
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A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
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A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
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B. Yan, A. R. Wang, E. X. Liu, W. Tan, J. L. Xie, R. Ge, and J. J. Liu, “Polarization filtering in the visible wavelength range using surface plasmon resonance and a sunflower-type photonic quasi-crystal fiber,” J. Phys. D Appl. Phys. 51(15), 155105 (2018).
[Crossref]

R. Ge, J. Xie, B. Yan, E. Liu, W. Tan, and J. Liu, “Refractive index sensor with high sensitivity based on circular photonic crystal,” J. Opt. Soc. Am. A 35(6), 992–997 (2018).
[Crossref] [PubMed]

J. L. Xie, J. Z. Wang, R. Ge, B. Yan, E. X. Liu, W. Tan, and J. J. Liu, “Multiband super-resolution imaging of graded-index photonic crystal flat lens,” J. Phys. D Appl. Phys. 51(20), 205103 (2018).
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E. Liu, W. Tan, B. Yan, J. Xie, R. Ge, and J. Liu, “Broadband ultra-flattened dispersion, ultra-low confinement loss and large effective mode area in an octagonal photonic quasi-crystal fiber,” J. Opt. Soc. Am. A 35(3), 431–436 (2018).
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[Crossref]

C. X. Yue, W. Tan, and J. J. Liu, “Photonic band gap properties of one-dimensional Thue-Morse all-dielectric photonic quasicrystal,” Superlattices Microstruct. 117, 252–259 (2018).
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Taylor, R. A.

Thylén, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
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Tianhua Zhang, T. Z.

Turduev, M.

M. Turduev, E. Bor, and H. Kurt, “Photonic crystal based polarization insensitive flat lens,” J. Phys. D Appl. Phys. 50(27), 275105 (2017).
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T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
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F. Monticone, C. A. Valagiannopoulos, and A. Alù, “Parity-time symmetric nonlocal metasurfaces: all-angle negative refraction and volumetric imaging,” Phys. Rev. X 6(4), 041018 (2016).
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J. B. Pendry, D. R. Smith, and A. P. Valanju, “Comment on wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 90(2), 029704 (2003).
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T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507(7490), 81–85 (2014).
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P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426(6965), 404 (2003).
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B. Yan, A. R. Wang, E. X. Liu, W. Tan, J. L. Xie, R. Ge, and J. J. Liu, “Polarization filtering in the visible wavelength range using surface plasmon resonance and a sunflower-type photonic quasi-crystal fiber,” J. Phys. D Appl. Phys. 51(15), 155105 (2018).
[Crossref]

Wang, J. Z.

J. L. Xie, J. Z. Wang, R. Ge, B. Yan, E. X. Liu, W. Tan, and J. J. Liu, “Multiband super-resolution imaging of graded-index photonic crystal flat lens,” J. Phys. D Appl. Phys. 51(20), 205103 (2018).
[Crossref]

Y. F. Zhao, Z. M. Wang, J. J. Jiang, X. Chen, C. X. Yue, J. Z. Wang, and J. J. Liu, “Add-drop filter with compound structure of photonic crystal and photonic quasicrystal,” J. Infrared Millim. W. 36(3), 342–348 (2017).

Wang, S.

B. Feng, E. X. Liu, Z. M. Wang, W. C. Cai, H. F. Liu, S. Wang, T. Y. Liang, W. Xiao, and J. J. Liu, “Generation of terahertz hollow beams by a photonic quasi-crystal flat lens,” Appl. Phys. Express 9(6), 062003 (2016).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Imaging model of CPC flat lens: (a) ERI is −1; (b) ERI is −0.7.
Fig. 2
Fig. 2 (a) GEM flat lens; (b) Segmental refractive indices distribution of GEM flat lens.
Fig. 3
Fig. 3 Imaging effect of the HEM flat lens with refractive index n = −1 for the incident point source at different positions: (a) u = 0.5d; (b) u = 2d; (c) u = 5d. Imaging effect of the GEM flat lens for the incident point source at different positions: (d) u = 0.5d; (e) u = 2d; (f) u = 5d.
Fig. 4
Fig. 4 Theoretical model of GPC flat lens with large object distance for point source.
Fig. 5
Fig. 5 (a) Analysis of beam propagation direction using EFL; (b) Partial GPC band structures diagram.
Fig. 6
Fig. 6 Imaging effect of the CPC flat lens with a refractive index n = 3 for the incident point source at different positions: (a) u = 0.5d; (b) u = 2d; (c) u = 5d. Imaging effect of the GPC flat lens for the incident point source at different positions: (d) u = 0.5d; (e) u = 2d; (f) u = 5d.
Fig. 7
Fig. 7 The relationship between the imaging characteristics of the GPC flat lens and the object distance: (a) the intensity ratio between the image intensity and point source intensity; (b) the image distance and the FWHM.
Fig. 8
Fig. 8 The off-axis point source imaging with large object distance: (a) GEM flat lens; (b) GPC flat lens.

Equations (3)

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v g = k ω ( k ) .
N A = n sin θ
N A = n w / 2 u 1 2 + ( w / 2 ) 2

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