Abstract

The plasmonic resonance effect on metasurfaces generates an abrupt phase change. We employ this phase modulation mechanism to design the longitudinal field distribution of an ultrathin terahertz (THz) lens for achieving the axial long-focal-depth (LFD) property. Phase distributions of the designed lens are obtained by the Yang-Gu iterative amplitude-phase retrieval algorithm. By depositing a 100 nm gold film on a 500 μm silicon substrate and etching arrayed V-shaped air holes through the gold film, the designed ultrathin THz lens is fabricated by the micro photolithography technology. Experimental measurements have demonstrated its LFD property, which basically agree with the theoretical simulations. In addition, the designed THz lens possesses a good LFD property with a bandwidth of 200 GHz. It is expected that the designed ultrathin LFD THz lens should have wide potential applications in broadband THz imaging and THz communication systems.

© 2013 Optical Society of America

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2013 (8)

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2,e72 (2013).
[Crossref]

D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

X. K. Wang, W. F. Sun, Y. Cui, J. S. Ye, S. F. Feng, and Y. Zhang, “Complete presentation of the Gouy phase shift with the THz digital holography,” Opt. Express 21, 2337–2346 (2013).
[Crossref] [PubMed]

J. W. He, X. K. Wang, D. Hu, J. S. Ye, S. F. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21, 20230–20239 (2013).
[Crossref] [PubMed]

2012 (7)

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

D. Hu, C. Q. Xie, M. Liu, and Y. Zhang, “High transmission of annular aperture arrays caused by symmetry breaking,” Phys. Rev. A 85,045801 (2012).
[Crossref]

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

X. Y. He, Q. J. Wang, and S. F. Yu, “Investigation of multilayer subwavelength metallic-dielectric stratified structures,” IEEE J. Quantum Electron. 48, 1554–1559 (2012).
[Crossref]

X. Y. He, Q. J. Wang, and S. F. Yu, “Analysis of dielectric loaded surface plasmon waveguide structures: transfer matrix method for plasmonic devices,” J. Appl. Phys. 111,073108 (2012).
[Crossref]

2011 (4)

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

L. Novotny and N. V. Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

2010 (4)

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, 1936–1940 (2010).
[Crossref] [PubMed]

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

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

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27, 2387–2393 (2010).
[Crossref]

1996 (1)

1994 (2)

1993 (1)

1992 (1)

1991 (1)

Abashin, M.

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

Agrawal, A.

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Bai, B. F.

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Bao, J. M.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Bao, K.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Bará, S.

Bardhan, R.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Beausoleil, R. G.

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

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

Capasso, F.

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Chang, M. P.

Chau, K. J.

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

Chen, X. Z.

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Choi, M.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Cui, Y.

Davidson, N.

Deng, Q. L.

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Dong, B. Z.

Dong, X. C.

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Du, C. L.

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Ersoy, O. K.

Fan, J. A.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Fattal, D.

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

Feng, S. F.

Fiorentino, M.

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

Friesem, A. A.

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

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, 1936–1940 (2010).
[Crossref] [PubMed]

Gu, B. Y.

Gu, J. Q.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Halas, N. J.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Han, J. G.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Hasman, E.

He, J. W.

He, X. Y.

X. Y. He, Q. J. Wang, and S. F. Yu, “Analysis of dielectric loaded surface plasmon waveguide structures: transfer matrix method for plasmonic devices,” J. Appl. Phys. 111,073108 (2012).
[Crossref]

X. Y. He, Q. J. Wang, and S. F. Yu, “Investigation of multilayer subwavelength metallic-dielectric stratified structures,” IEEE J. Quantum Electron. 48, 1554–1559 (2012).
[Crossref]

Hu, D.

D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

J. W. He, X. K. Wang, D. Hu, J. S. Ye, S. F. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21, 20230–20239 (2013).
[Crossref] [PubMed]

D. Hu, C. Q. Xie, M. Liu, and Y. Zhang, “High transmission of annular aperture arrays caused by symmetry breaking,” Phys. Rev. A 85,045801 (2012).
[Crossref]

Huang, L. L.

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Hulst, N. V.

L. Novotny and N. V. Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

Ishii, S.

X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2,e72 (2013).
[Crossref]

Jaroszewicz, Z.

Jin, G. F.

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Kan, Q.

J. W. He, X. K. Wang, D. Hu, J. S. Ye, S. F. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21, 20230–20239 (2013).
[Crossref] [PubMed]

D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Kang, K. Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Kang, S. B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Kats, M. A.

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Kildishev, A. V.

X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2,e72 (2013).
[Crossref]

Kim, Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Klar, P. J.

D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Kolodziejczyk, A.

Kwak, M. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Lee, S. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Lee, Y. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Lezec, H. J.

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

Li, G. X.

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Li, J.

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

Lin, J.

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

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, 1936–1940 (2010).
[Crossref] [PubMed]

Liu, M.

D. Hu, C. Q. Xie, M. Liu, and Y. Zhang, “High transmission of annular aperture arrays caused by symmetry breaking,” Phys. Rev. A 85,045801 (2012).
[Crossref]

Lu, Y. G.

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Manoharan, V. N.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

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, 1936–1940 (2010).
[Crossref] [PubMed]

Min, B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Mühlenbernd, H.

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Ni, X. J.

X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2,e72 (2013).
[Crossref]

Nordlander, P.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Novotny, L.

L. Novotny and N. V. Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

Park, N.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Peng, Z.

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

Qiu, C. W.

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Rho, J.

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (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, 1936–1940 (2010).
[Crossref] [PubMed]

Scully, M. O.

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

Shalaev, V. M.

X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2,e72 (2013).
[Crossref]

Shi, L. F.

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Shin, J.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Shvets, G.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Sochacki, J.

Staronski, L. R.

Sun, W. F.

Tan, Q. F.

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Tan, X.

Tetienne, J. P.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Tian, Z.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Wang, Q. J.

X. Y. He, Q. J. Wang, and S. F. Yu, “Analysis of dielectric loaded surface plasmon waveguide structures: transfer matrix method for plasmonic devices,” J. Appl. Phys. 111,073108 (2012).
[Crossref]

X. Y. He, Q. J. Wang, and S. F. Yu, “Investigation of multilayer subwavelength metallic-dielectric stratified structures,” IEEE J. Quantum Electron. 48, 1554–1559 (2012).
[Crossref]

Wang, X. K.

Wang, Y.

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

Wu, C. H.

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

Xie, C. Q.

D. Hu, C. Q. Xie, M. Liu, and Y. Zhang, “High transmission of annular aperture arrays caused by symmetry breaking,” Phys. Rev. A 85,045801 (2012).
[Crossref]

Xu, T.

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

Yang, G. Z.

Ye, J. S.

Ye, Y. T.

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Ye, Z. L.

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

Yin, X. B.

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

Yu, N. F.

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Yu, S. F.

X. Y. He, Q. J. Wang, and S. F. Yu, “Investigation of multilayer subwavelength metallic-dielectric stratified structures,” IEEE J. Quantum Electron. 48, 1554–1559 (2012).
[Crossref]

X. Y. He, Q. J. Wang, and S. F. Yu, “Analysis of dielectric loaded surface plasmon waveguide structures: transfer matrix method for plasmonic devices,” J. Appl. Phys. 111,073108 (2012).
[Crossref]

Yue, W. S.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Zentgraf, T.

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Zhang, S.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Zhang, W. L.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Zhang, X.

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

Zhang, X. Q.

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Zhang, Y.

Zhuang, J. Y.

Adv. Mater. (1)

X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013).
[Crossref]

Adv. Opt. Mater. (1)

D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100,013101 (2012).
[Crossref]

IEEE J. Quantum Electron. (1)

X. Y. He, Q. J. Wang, and S. F. Yu, “Investigation of multilayer subwavelength metallic-dielectric stratified structures,” IEEE J. Quantum Electron. 48, 1554–1559 (2012).
[Crossref]

J. Appl. Phys. (1)

X. Y. He, Q. J. Wang, and S. F. Yu, “Analysis of dielectric loaded surface plasmon waveguide structures: transfer matrix method for plasmonic devices,” J. Appl. Phys. 111,073108 (2012).
[Crossref]

J. Opt. Soc. Am. A (3)

Light: Sci. Appl. (2)

L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2,e70 (2013).
[Crossref]

X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2,e72 (2013).
[Crossref]

Nano Lett. (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, 1936–1940 (2010).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref] [PubMed]

N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref] [PubMed]

Nat. Commun. (1)

X. Z. Chen, L. L. Huang, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3,1198 (2012).
[Crossref] [PubMed]

Nat. Photon. (2)

L. Novotny and N. V. Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[Crossref]

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

Nature (2)

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013).
[Crossref] [PubMed]

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref] [PubMed]

Opt. Eng. (1)

L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50,063001 (2011).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

D. Hu, C. Q. Xie, M. Liu, and Y. Zhang, “High transmission of annular aperture arrays caused by symmetry breaking,” Phys. Rev. A 85,045801 (2012).
[Crossref]

Science (3)

J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) A focusing geometry of the ultrathin LFD THz lens. (b) Eight-level quantized phase distributions of the designed ultrathin LFD THz lens.

Fig. 2
Fig. 2

(a) A schematic of the metasurface in a unit cell. (b) An optical microscopy of the central part of the fabricated ultrathin LFD THz lens. (c) Experimental intensity distributions in the xz plane. (d) The blue and red curves represent the theoretical and experimental intensity distributions of the LFD THz lens along the z-axis. The black curve plots the axial intensity distributions of a conventional THz lens. The dashed lines mark the three focal depths.

Fig. 3
Fig. 3

(a) Experimental intensity profiles |Ey|2 along the x-axis on the three lateral planes at zα = 9 mm (blue solid curve), 11 mm (red dashed curve), and 13 mm (black solid curve). (b) is the same as (a) except for the theoretical simulations. (c), (d), and (e) are regional intensity patterns on the three lateral planes at zα = 9, 11, and 13 mm, respectively.

Fig. 4
Fig. 4

(a), (b) and (c) represent the experimental intensity patterns |Ey|2 of the fabricated ultrathin LFD THz lens on the xz-plane at frequencies of 0.617, 0.706, and 0.794 THz, respectively. (d) The blue, green, and red curves represent the The experimental axial intensity profiles. The dashed lines illustrate the LFD regions. (e) is the same as (d) except for theoretical simulations.

Tables (2)

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Table1 Structure units and their parameters for eight quantized phases

Tables Icon

Table 2 Experimental dispersive LFD properties of the fabricated ultrathin LFD THz lens

Equations (9)

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U 1 = U 1 ( X 1 ) = ρ 1 ( X 1 ) exp [ i ϕ 1 ( X 1 ) ] ,
U 2 α = U 2 α ( X 2 α , z α ) = ρ 2 α ( X 2 α , z α ) exp [ i ϕ 2 α ( X 2 α , z α ) ] ,
U 2 α ( X 2 α , z α ) = G ( X 2 α , X 1 , z α ) U 1 ( X 1 ) d X 1 ,
G ( X 2 α , X 1 , z α ) = 2 π i λ z α exp [ i 2 π z α λ + i π ( X 2 α X 1 ) 2 λ z α ] .
U 2 α ( X 2 α , z α ) = G ^ α U 1 ( X 1 ) .
Δ = α ( U 2 α 0 U 2 α ) 2 ,
exp [ i ϕ 1 ( X 1 ) ] = Q * / | Q | ,
exp [ i ϕ 2 α ( X 2 α , z α ) ] = G ^ α ρ 1 ( X 1 ) exp [ i ϕ 1 ( X 1 ) ] | G ^ α ρ 1 ( X 1 ) exp [ i ϕ 1 ( X 1 ) ] | ,
Q = α ρ 1 ( X 1 ) exp [ i ϕ 1 ( X 1 ) ] A ^ α ρ 2 α ( X 2 α ) exp [ i ϕ 2 α ( X 2 α , z α ) G ^ α ] ,

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