Abstract

Dielectric metasurfaces are ultra-thin devices that can shape optical wavefronts with extreme control. While an assortment of materials possessing a wide range of dielectric constants have been proposed and implemented, the minimum dielectric contrast required for metasurfaces to achieve high-efficiency performance, for a given device function and feature size constraint, is unclear. In this Article, we examine the impact of dielectric material selection on metasurface efficiency at optical frequencies. As a model system, we design transmissive, single-layer periodic metasurfaces (i.e., metagratings) using topology optimization, and we sweep device thickness and light deflection angle for differing material types. We find that for modest deflection angles below 40 degrees, materials with relatively low dielectric constants near 4 can be used to produce metagratings with efficiencies over 80%. However, ultra-high-efficiency devices designed for large deflection angles and multiple functions require materials with high dielectric constants comparable to silicon. We also identify, for all materials, a minimum device thickness required for optimal metagrating performance that scales inversely with dielectric constant. Our work presents materials selection guidelines for high-performance metasurfaces operating at visible and infrared wavelengths.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (4)

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large angle, multi-functional metagratings based on freeform multimode geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

D. G. Baranov, D. A. Zuev, S. I. Lepeshov, O. V. Kotov, A. E. Krasnok, A. B. Evlyukhin, and B. N. Chichkov, “All-dielectric nanophotonics: the quest for better materials and fabrication techniques,” Optica 4(7), 814–825 (2017).
[Crossref]

J. Yang and J. Fan, “Investigating the impact of initial geometric layout on topology-optimized metagrating performance,” Opt. Lett. 42, 3161–3164 (2017).
[Crossref] [PubMed]

2016 (8)

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Z. Wang, S. He, Q. Liu, and W. Wang, “Visible light metasurfaces based on gallium nitride high contrast gratings,” Opt. Commun. 367, 144–148 (2016).
[Crossref]

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

S. Liu, G. A. Keeler, J. L. Reno, M. B. Sinclair, and I. Brener, “III–V semiconductor nanoresonators—a new strategy for passive, active, and nonlinear all-dielectric metamaterials,” Adv. Opt. Mater. 4(10), 1457–1462 (2016).
[Crossref]

P. P. Iyer, M. Pendharkar, and J. A. Schuller, “Electrically reconfigurable metasurfaces using heterojunction resonators,” Adv. Opt. Mater. 4(10), 1582–1588 (2016).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2(5), e1501258 (2016).
[Crossref] [PubMed]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref]

2015 (3)

P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015).
[Crossref] [PubMed]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

M. Khorasaninejad, W. Zhu, and K. B. Crozier, “Efficient polarization beam splitter pixels based on a dielectric metasurface,” Optica 2(4), 376–382 (2015).
[Crossref]

2014 (3)

M. S. Seghilani, M. Sellahi, M. Devautour, P. Lalanne, I. Sagnes, G. Beaudoin, M. Myara, X. Lafosse, L. Legratiet, J. Yang, and A. Garnache, “Photonic crystal-based flat lens integrated on a Bragg mirror for High-Q external cavity low noise laser,” Opt. Express 22(5), 5962–5976 (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]

2013 (1)

2010 (1)

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
[Crossref]

2006 (1)

1999 (1)

1998 (1)

Aieta, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Ambrosio, A.

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2(5), e1501258 (2016).
[Crossref] [PubMed]

Astilean, S.

Baranov, D. G.

Beaudoin, G.

Brener, I.

S. Liu, G. A. Keeler, J. L. Reno, M. B. Sinclair, and I. Brener, “III–V semiconductor nanoresonators—a new strategy for passive, active, and nonlinear all-dielectric metamaterials,” Adv. Opt. Mater. 4(10), 1457–1462 (2016).
[Crossref]

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]

Cambril, E.

Capasso, F.

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2(5), e1501258 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015).
[Crossref] [PubMed]

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

Chavel, P.

Chen, W. T.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Chichkov, B. N.

Colburn, S.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

Crozier, K. B.

Devautour, M.

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Dodson, C. M.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

Doshay, S.

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large angle, multi-functional metagratings based on freeform multimode geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Evlyukhin, A. B.

Fan, J.

Fan, J. A.

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large angle, multi-functional metagratings based on freeform multimode geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

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]

Fang, H.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

Fryett, T. K.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

Garnache, A.

Genevet, P.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015).
[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]

He, S.

Z. Wang, S. He, Q. Liu, and W. Wang, “Visible light metasurfaces based on gallium nitride high contrast gratings,” Opt. Commun. 367, 144–148 (2016).
[Crossref]

Hugonin, J. P.

Iyer, P. P.

P. P. Iyer, M. Pendharkar, and J. A. Schuller, “Electrically reconfigurable metasurfaces using heterojunction resonators,” Adv. Opt. Mater. 4(10), 1582–1588 (2016).
[Crossref]

Kanhaiya, P.

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2(5), e1501258 (2016).
[Crossref] [PubMed]

Kats, M. A.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Keeler, G. A.

S. Liu, G. A. Keeler, J. L. Reno, M. B. Sinclair, and I. Brener, “III–V semiconductor nanoresonators—a new strategy for passive, active, and nonlinear all-dielectric metamaterials,” Adv. Opt. Mater. 4(10), 1457–1462 (2016).
[Crossref]

Khorasaninejad, M.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2(5), e1501258 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. Zhu, and K. B. Crozier, “Efficient polarization beam splitter pixels based on a dielectric metasurface,” Optica 2(4), 376–382 (2015).
[Crossref]

Kivshar, Y. S.

Kotov, O. V.

Krasnok, A. E.

Krauss, T. F.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

Kravchenko, I.

Kruk, S.

Lafosse, X.

Lalanne, P.

Launois, H.

Lederer, F.

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
[Crossref]

Legratiet, L.

Lepeshov, S. I.

Li, J.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

Li, K.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

Li, T.

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]

Liu, J.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

Liu, Q.

Z. Wang, S. He, Q. Liu, and W. Wang, “Visible light metasurfaces based on gallium nitride high contrast gratings,” Opt. Commun. 367, 144–148 (2016).
[Crossref]

Liu, S.

S. Liu, G. A. Keeler, J. L. Reno, M. B. Sinclair, and I. Brener, “III–V semiconductor nanoresonators—a new strategy for passive, active, and nonlinear all-dielectric metamaterials,” Adv. Opt. Mater. 4(10), 1457–1462 (2016).
[Crossref]

Lu, J.

Majumdar, A.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

Myara, M.

Neshev, D. N.

Oh, J.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Paul, T.

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
[Crossref]

Pendharkar, M.

P. P. Iyer, M. Pendharkar, and J. A. Schuller, “Electrically reconfigurable metasurfaces using heterojunction resonators,” Adv. Opt. Mater. 4(10), 1582–1588 (2016).
[Crossref]

Reardon, C. P.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
[Crossref]

Reno, J. L.

S. Liu, G. A. Keeler, J. L. Reno, M. B. Sinclair, and I. Brener, “III–V semiconductor nanoresonators—a new strategy for passive, active, and nonlinear all-dielectric metamaterials,” Adv. Opt. Mater. 4(10), 1457–1462 (2016).
[Crossref]

Rockstuhl, C.

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
[Crossref]

Sagnes, I.

Sauvan, C.

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
[Crossref]

Schuller, J. A.

P. P. Iyer, M. Pendharkar, and J. A. Schuller, “Electrically reconfigurable metasurfaces using heterojunction resonators,” Adv. Opt. Mater. 4(10), 1582–1588 (2016).
[Crossref]

Seghilani, M. S.

Sell, D.

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large angle, multi-functional metagratings based on freeform multimode geometries,” Nano Lett. 17(6), 3752–3757 (2017).
[Crossref] [PubMed]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photonics 3(10), 1919–1925 (2016).
[Crossref]

Sellahi, M.

Sinclair, M. B.

S. Liu, G. A. Keeler, J. L. Reno, M. B. Sinclair, and I. Brener, “III–V semiconductor nanoresonators—a new strategy for passive, active, and nonlinear all-dielectric metamaterials,” Adv. Opt. Mater. 4(10), 1457–1462 (2016).
[Crossref]

Stellinga, D.

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Trivedi, R.

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Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017).
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Opt. Lett. (2)

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Figures (8)

Fig. 1
Fig. 1

Schematics of topology-optimized metagratings. (a) 2D (periodic along x axis) and (b) 3D designs (periodic along x and y axes). For the 3D designs, the y-period is subwavelength-scale, so that diffraction only occurs in x-z plane. In this report, all the metagratings are illuminated by a plane wave at normal incidence. The metagratings are binary structures made of air and the dielectric material, and they are on a SiO2 substrate.

Fig. 2
Fig. 2

Absolute deflection efficiency of 2D topology-optimized metagrating deflectors based on different optical materials. (a) Efficiency data from metagratings based on Ge, Si, TiO2, SiN, Al2O3, and SiO2. (b) Histograms of deflection efficiencies for 1000 topology-optimized metagrating deflectors based on Si (left) and TiO2 (right). Si (TiO2) deflectors have thickness t = 1µm (t = 0.8µm) and angle of deflection θ = 50 (θ = 45) degrees. All devices are designed to operate at λ0 = 1800nm. We define absolute efficiency as the deflected power, normalized to the incident power.

Fig. 3
Fig. 3

Scattering dynamics of Bloch modes associated with metagratings. Inside the metagrating, energy is carried by multiple propagating Bloch modes (M1-Mn), which are excited by an incident plane wave (thick red arrow) from the substrate. The modes bounce between the top and bottom interfaces. At a metagrating interface, a mode can be back-reflected (solid arrows inside the metagrating), excite other Bloch modes (dashed arrows inside the metagrating), or couple to free space diffraction channels (thin red arrows).

Fig. 4
Fig. 4

Bloch modes of 65-degree metagratings based on different materials. (a) Side-views of a single unit cell of the metagratings based on Si (left), TiO2 (middle), and SiN (right). The spacing (white color) between the dielectric ridges is filled by air. (b) |(E)y| of the three propagating modes (M1-M3) of metagratings based on different materials. The effective mode index neff of each mode is shown. The cyan rectangles represent the nanoridges of the metagratings. All of the devices operate with TE-polarization.

Fig. 5
Fig. 5

Scattering coefficients of Bloch modes in 65-degree metagratings based on different materials. (a)-(d) Values of |(S)B|2, |(S)T|2, |tB|2, and |tT|2, for metagratings based on Si (left), TiO2 (middle), and SiN (right). The coloration scheme is based on the log scale shown at the far right. All these metagratings are designed to operate with TE-polarization.

Fig. 6
Fig. 6

Performance of 3D, 70-degree metagrating deflectors. (a) Deflection efficiencies of metagratings made of different optical materials as a function of device height. The materials include Ge (red), Si (blue), TiO2 (green), SiN (black), Al2O3 (orange), and SiO2 (magenta). The markers represent simulated efficiency values and the solid curves are trend lines. The metagratings are illuminated by normally incident unpolarized light. (b) Layouts (top view) of the individual unit cells of the highest-efficiency metagratings for a given material. The thicknesses of these devices are 0.7µm (Ge), 1µm (Si), 1.6µm (TiO2), 1.8µm (SiN), 1.6µm (Al2O3), and 1.8µm (SiO2). The spacing (white color) between the dielectric structures is filled by air. (c) Plots of highest device efficiency (blue triangles, left axes) and threshold device thickness (red circles, right axes) as a function of the metagrating material refractive index. The red solid line is a fitted curve. (d) Distribution of calculated efficiencies from 200 Si (blue wide bars) and TiO2 (green narrow bars) metagrating deflectors, each designed with different initial random configurations. In (d), the device thickness is h = 1.2µm and the operating wavelength is λ0 = 1800nm. The definition of efficiency can be found in the caption of Fig. 2.

Fig. 7
Fig. 7

Comparison of 70-degree crystalline silicon (c-Si) and TiO2 metagrating deflectors at visible wavelengths. (a) Deflection efficiencies of metagratings based on c-Si (red) and TiO2 (blue) as a function of the device thickness h. The operation wavelengths 650nm and 550nm are shown by triangles and circles, respectively. The definition of efficiency can be found in the caption of Fig. 2. (b) Layouts (top view) of the individual unit cells of the highest-efficiency metagratings for a given material and operating wavelength. The spacing (white color) between the dielectric ridges is filled by air. In the simulation, the refractive indices of materials are nSi = 3.77 (λ0 = 650nm), nSi = 4.02 + 0.001i (λ0 = 550nm), nTiO2 = 2.55 (λ0 = 650nm), and nTiO2 = 2.6 (λ0 = 550nm). Scale bars: 100nm.

Fig. 8
Fig. 8

Comparison of metagrating wavelength-splitters based on crystalline-silicon (c-Si) and TiO2 at visible wavelengths. (a) and (b) show the performance (top panel) and top view layout (bottom panel) of c-Si and TiO2 metagrating wavelength splitters, respectively. The spacing (white color) between the dielectric ridges is filled by air. We define the efficiency as the deflected power, normalized to the incident power. The splitters are designed to direct λ1 = 750nm and λ2 = 633nm into −1 and + 1 diffraction orders, respectively. The metagrating periods along the x- and y-axis are 800nm and 300nm, respectively. Scale bars: 100nm.

Equations (1)

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t= ( t T ) φ t B + ( t T ) j=1 m ( φ S B φ S T ) j t B