Abstract

A new structure is reported, which realizes the flat focusing by introducing the silicon subwavelength slits into the waveguide. The subwavelength silicon-air slits, with variable widths to match the phase compensation, makes possible to focus a plane wave. The flat lens proposed here demonstrates relatively high power gain at the focal point or two focal points. By using such a design, we demonstrate a grating coupler with an ultrashort taper of 22.5-μm to connect a 10-μm-wide input waveguide and a 0.5-μm-wide output waveguide, achieving a transmission up to nearly 95.4% numerically in the communication band. The length of which is one-twentieth of that for the traditional taper. To our best knowledge, this work is the first demonstration of an ultrashort taper based on flat lens, which significantly improves the integration of the photonics integrated circuits, and indicates an effective solution for potential applications in compactly integrated micro/nano optical devices.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

22 August 2017: A typographical correction was made to Ref. 11.


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References

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2017 (3)

2016 (5)

Y. Chen, R. Halir, Í. Molina-Fernández, P. Cheben, and J. J. He, “High-efficiency apodized-imaging chip-fiber grating coupler for silicon nitride waveguides,” Opt. Lett. 41(21), 5059–5062 (2016).
[Crossref] [PubMed]

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

Z. L. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016).
[Crossref] [PubMed]

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

2015 (3)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

M. R. Uphuy, O. M. Siddiqui, and O. M. Ramahi, “Electrically thin flat lenses and reflectors,” J. Opt. Soc. Am. A 32(4), 1700–1706 (2015).
[Crossref]

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

2014 (2)

2013 (2)

2012 (1)

J. Yang and Z. Zhou, “Double-structure, bidirectional and polarization-independent subwavelength grating beam splitter,” Opt. Commun. 285(6), 1494–1500 (2012).
[Crossref]

2010 (1)

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]

2009 (2)

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]

A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
[Crossref]

2007 (2)

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam manipulating by metallic nano-optic lens containing nonlinear media,” Opt. Express 15(15), 9541–9546 (2007).
[Crossref] [PubMed]

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

2004 (2)

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]

Z. J. 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]

1995 (1)

Acoleyen, K. V.

K. V. Acoleyen and R. Baets, “Compact lens-assisted focusing tapers fabricated on Silicon-On-Insulator,” in IEE International Conference on Group IV Photonics (2011), pp. 157–159.
[Crossref]

Aieta, F.

Arbabi, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Baets, R.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

K. V. Acoleyen and R. Baets, “Compact lens-assisted focusing tapers fabricated on Silicon-On-Insulator,” in IEE International Conference on Group IV Photonics (2011), pp. 157–159.
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[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]

Beausoleil, R. G.

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]

Beigang, R.

Bogaerts, W.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Bojko, R.

Brongersma, M. L.

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]

Capasso, F.

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, S.

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

Cheben, P.

Chen, C.

Chen, F. T.

Chen, J.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Chen, Y.

Cheng, Z.

Chrostowski, L.

Chu, T.

Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photonics Res. 2(3), A41–A44 (2014).
[Crossref]

Chu, W.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Claes, T.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Craighead, H. G.

Davis, A.

A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
[Crossref]

Deng, Y.

Deng, Z. L.

Ding, J.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Dong, F.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[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]

Faraon, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Fattal, D.

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.

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]

Fu, Y.

Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photonics Res. 2(3), A41–A44 (2014).
[Crossref]

Genevet, P.

Ghosh, S.

Goda, K.

Gong, Q.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Gopalakrisna, K. L.

Haldar, A.

Halir, R.

He, J. J.

Horie, Y.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Huang, J.

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

Jiao, X.

Kang, J.

Kats, M.

Kim, H. K.

Z. J. 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]

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]

Kumar, S.

Laere, F. V.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Lai, J.

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, Q. T.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Li, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

Li, Y.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Lin, Y.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Lu, H.

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

Luo, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

Ma, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

Min, C.

Ming, H.

Molina-Fernández, Í.

Neu, J.

O’Faolain, L.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Patel, D.

Peng, Z.

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]

Plant, D. V.

Pu, M.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

Rahm, M.

Ramahi, O. M.

Reinhard, B.

Ren, H.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Samani, A.

Scheerlinck, S.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Schrauwen, J.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Sethi, P.

Shi, W.

Siddiqui, O. M.

Song, Z.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Sun, C.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Sun, J.

Sun, Z.

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]

Sun, Z. J.

Z. J. 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]

Taillaert, D.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Takenaka, M.

Tang, W.

Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photonics Res. 2(3), A41–A44 (2014).
[Crossref]

Thourhout, D. V.

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Tsang, H. K.

Uphuy, M. R.

Veerasubramanian, V.

Verslegers, L.

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]

Volk, M. F.

Wang, B.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Wang, G. P.

Wang, P.

Wang, S.

Wang, Y.

White, J. 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]

Wu, T.

Wu, W.

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

Xiao, T. H.

Xiao, Y. F.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Xu, L.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Xu, N.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Yang, D.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Yang, J.

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

J. Yang and Z. Zhou, “Double-structure, bidirectional and polarization-independent subwavelength grating beam splitter,” Opt. Commun. 285(6), 1494–1500 (2012).
[Crossref]

Ye, T.

Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photonics Res. 2(3), A41–A44 (2014).
[Crossref]

Yu, Z.

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]

Zhang, H.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Zhang, J.

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

Zhang, S.

Zhang, W.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Zhao, Z.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

Zhong, Q.

Zhou, W.

Zhou, Z.

J. Yang and Z. Zhou, “Double-structure, bidirectional and polarization-independent subwavelength grating beam splitter,” Opt. Commun. 285(6), 1494–1500 (2012).
[Crossref]

Appl. Phys. Lett. (2)

Z. J. 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]

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)

F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).
[Crossref]

Infrared Phys. Technol. (1)

J. Zhang, J. Yang, H. Lu, W. Wu, J. Huang, and S. Chang, “Subwavelength TE/TM grating coupler based on silicon-on-insulator,” Infrared Phys. Technol. 71, 542–546 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

Nano Lett. (2)

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]

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multi-wavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Nat. Commun. (1)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

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]

Opt. Commun. (1)

J. Yang and Z. Zhou, “Double-structure, bidirectional and polarization-independent subwavelength grating beam splitter,” Opt. Commun. 285(6), 1494–1500 (2012).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Photonics Res. (1)

Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photonics Res. 2(3), A41–A44 (2014).
[Crossref]

Proc. SPIE (1)

A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
[Crossref]

Sci. Rep. (2)

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6(1), 19885 (2016).
[Crossref] [PubMed]

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6(1), 34020 (2016).
[Crossref] [PubMed]

Other (1)

K. V. Acoleyen and R. Baets, “Compact lens-assisted focusing tapers fabricated on Silicon-On-Insulator,” in IEE International Conference on Group IV Photonics (2011), pp. 157–159.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 The proposed structure consists of grating couplers, thin lens and a taper. The incident light is coupled from the fiber to the slab waveguide by the grating couplers; input light is coupled from multi-mode waveguide to single-mode waveguide by the taper with the lens; the black dotted line represents the detection area, where the micro-nano devices can be placed for testing. Where Pin is the input power, pout is the output power. The transmission efficiency (T) is defined as the ratio of outputs to inputs (T = Pout/Pin) Our structure is based on an SOI wafer with a 220-nm-thickness top silicon layer and a 2-μm-height silica.
Fig. 2
Fig. 2 (a) Schematic of the metasurface lens with one focus; (b) Schematic of the metasurface lens with two focus.
Fig. 3
Fig. 3 (a) The filling factors of each cell; (b) The effective refractive index of each cell; (c) The flat lens induce the phase shift △Φ of each cell with the period T = 0.5μm, the width d = 0.5μm and the etching height H = 220nm.
Fig. 4
Fig. 4 (a) Magnitude of the simulated x directed Poynting vector over the x–y plane; (b) The cross section of the optical field distribution for input; (c) the cross section of the optical field distribution for the output.
Fig. 5
Fig. 5 Magnitude of the simulated x directed Poynting vector over the x–y plane for two focus design.
Fig. 6
Fig. 6 (a) The focus position changed with d; (b) The transmission efficiency of the lens changed with d.
Fig. 7
Fig. 7 (a) The simulation of normalized electric field intensity distribution in taper based on the silicon slit lens for the operated wavelength λ = 1.55μm; (b) without silicon slit lens.
Fig. 8
Fig. 8 The focus position as a function of the wavelength.
Fig. 9
Fig. 9 Transmission efficiency of the tapers as a function of incident wavelength. L = 21.5, T = 0.5μm, the width d = 0.5μm for rectangle, triangle and rhombus; T = 0.5μm, the radius is determined by filling factor of each cell for circular; the etching height H = 220nm.
Fig. 10
Fig. 10 (a) The diameter of the air structures for circular of each layer; (b) The simulation of normalized electric field intensity distribution in taper based on the silicon slit lens with circular air structure for the operated wavelength λ = 1.55μm.
Fig. 11
Fig. 11 Transmission of the tapers as a function of the length (L) for the taper waveguide. T = 0.5μm, and the etching height H = 220nm; the incident wavelength λ = 1550nm.

Equations (3)

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n d + F = n m d + b m
N e f f T E = f n A i r 2 + ( 1 f ) n S i 2
θ < λ 0 2 W n e f f .

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