Abstract

Optical metasurfaces are two-dimensional arrays of meta-atoms that modify different characteristics of light such as phase, amplitude, and polarization. One intriguing feature that distinguishes them from conventional optical components is their multifunctional capability. However, multifunctional metasurfaces with efficiencies approaching those of their single-functional counterparts require more degrees of freedom. Here we show that 2.5D metastructures, which are stacked layers of interacting metasurface layers, provide sufficient degrees of freedom to implement efficient multifunctional devices. The large number of design parameters and their intricate intercoupling make the design of multifunctional 2.5D metastructures a complex task, and unit-cell approaches to metasurface design produce suboptimal devices. We address this issue by designing 2.5D metastructures using the adjoint optimization technique. Instead of designing unit cells individually, our technique considers the structure as a whole, accurately accounting for inter-post and inter-layer coupling. As proof of concept, we experimentally demonstrate a double-wavelength metastructure, designed using adjoint optimization, that has significantly higher efficiencies than a similar device designed with a simplified approach conventionally used in metasurface design. The 2.5D metastructure architecture empowered by the optimization-based design technique is a general platform for realizing high-performance multifunctional components and systems.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

M. Mansouree and A. Arbabi, “Multi-layer multifunctional metasurface design using the adjoint sensitivity technique,” Proc. SPIE 10928, 109281N (2019).
[Crossref]

2018 (7)

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7, 1041–1068 (2018).
[Crossref]

X. Cheng, T. He, Z. Zhou, J. Zhang, H. Jiao, and Z. Wang, “Multilayer enhanced metasurfaces with high efficiency and additional functionalities,” Proc. SPIE 10691, 1069103 (2018).
[Crossref]

M. S. Faraji-Dana, E. Arbabi, A. Arbabi, S. M. Kamali, H. Kwon, and A. Faraon, “Compact folded metasurface spectrometer,” Nat. Commun. 9, 4196 (2018).
[Crossref]

Y. Zhou, I. I. Kravchenko, H. Wang, J. R. Nolen, G. Gu, and J. Valentine, “Multilayer noninteracting dielectric metasurfaces for multiwavelength metaoptics,” Nano Lett. 18, 7529–7537 (2018).
[Crossref]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).
[Crossref]

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, “Topology-optimized multilayered metaoptics,” Phys. Rev. Appl. 9, 044030 (2018).
[Crossref]

A. Zhan, T. K. Fryett, S. Colburn, and A. Majumdar, “Inverse design of optical elements based on arrays of dielectric spheres,” Appl. Opt. 57, 1437–1446 (2018).
[Crossref]

2017 (8)

J. Yang and J. A. Fan, “Topology-optimized metasurfaces: impact of initial geometric layout,” Opt. Lett. 42, 3161–3164 (2017).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, M. S. Faraji-Dana, and A. Faraon, “Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under different illumination angles,” Phys. Rev. X 7, 041056 (2017).
[Crossref]

S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

J. Ding, S. An, B. Zheng, and H. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta-atoms: toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1–8 (2017).
[Crossref]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11, 415–420 (2017).
[Crossref]

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

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

A. Iguchi, Y. Tsuji, T. Yasui, and K. Hirayama, “Efficient topology optimization of optical waveguide devices utilizing semi-vectorial finite-difference beam propagation method,” Opt. Express 25, 28210–28222 (2017).

2016 (5)

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79, 1–59 (2016).
[Crossref]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref]

W. Zhao, B. Liu, H. Jiang, J. Song, Y. Pei, and Y. Jiang, “Full-color hologram using spatial multiplexing of dielectric metasurface,” Opt. Lett. 41, 147–150 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3, 628–633 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6, 32803 (2016).
[Crossref]

2015 (5)

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]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vukovi, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref]

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

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

2014 (3)

2013 (3)

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21, 21693–21701 (2013).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
[Crossref]

2012 (2)

V. Liu and S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183, 2233–2244 (2012).
[Crossref]

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mater. 24, 6300–6304 (2012).
[Crossref]

2011 (3)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

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

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

2010 (2)

R. Matzen, J. S. Jensen, and O. Sigmund, “Topology optimization for transient response of photonic crystal structures,” J. Opt. Soc. Am. B 27, 2040–2050 (2010).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2004 (1)

1998 (1)

Aieta, F.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

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

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

Alù, A.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

An, S.

J. Ding, S. An, B. Zheng, and H. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta-atoms: toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1–8 (2017).
[Crossref]

Arbabi, A.

M. Mansouree and A. Arbabi, “Multi-layer multifunctional metasurface design using the adjoint sensitivity technique,” Proc. SPIE 10928, 109281N (2019).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7, 1041–1068 (2018).
[Crossref]

M. S. Faraji-Dana, E. Arbabi, A. Arbabi, S. M. Kamali, H. Kwon, and A. Faraon, “Compact folded metasurface spectrometer,” Nat. Commun. 9, 4196 (2018).
[Crossref]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11, 415–420 (2017).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, M. S. Faraji-Dana, and A. Faraon, “Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under different illumination angles,” Phys. Rev. X 7, 041056 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6, 32803 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3, 628–633 (2016).
[Crossref]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref]

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]

M. Mansouree and A. Arbabi, “Large-scale metasurface design using the adjoint sensitivity technique,” in Conference on Lasers and Electro-Optics (CLEO) (2018), paper FF1F.7.

M. Mansouree and A. Arbabi, “Metasurface design using level-set and gradient descent optimization techniques,” in International Applied Computational Electromagnetics Society Symposium (2019).

Arbabi, E.

M. S. Faraji-Dana, E. Arbabi, A. Arbabi, S. M. Kamali, H. Kwon, and A. Faraon, “Compact folded metasurface spectrometer,” Nat. Commun. 9, 4196 (2018).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7, 1041–1068 (2018).
[Crossref]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11, 415–420 (2017).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, M. S. Faraji-Dana, and A. Faraon, “Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under different illumination angles,” Phys. Rev. X 7, 041056 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6, 32803 (2016).
[Crossref]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3, 628–633 (2016).
[Crossref]

Astilean, S.

Babinec, T. M.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vukovi, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[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]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref]

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]

Balthasar Mueller, J. P.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Beausoleil, R. G.

Bermel, P.

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Multifunctional 2.5D metastructure. (a) Schematic of a metastructure with the ability to generate independent wavefronts for different wavelengths. (b) Illustration of one such metastructure which focuses two different wavelengths to two separate focal points. The inset shows a closer picture of a part of the device.
Fig. 2.
Fig. 2. Direct design of metastructures. (a) Illustration of a periodic bilayer metastructure composed of nano-posts with square cross-sections. Transmission coefficients of the metastructure for normally incident light at ${\lambda _1} = {780}$ and ${\lambda _2} = 915\,\, {\rm nm}$ are ${t_1}$ and ${t_2}$, respectively. The inset shows an expanded view of the unit cell and its dimensions. (b) Optimal widths of the bottom and top nano-posts for achieving ${t_1} = {e^{ - j{\phi _1}}}$ and ${t_2} = {e^{ - j{\phi _2}}}$ at ${\lambda _1}$ and ${\lambda _2}$, respectively. (c) Color-coded plots of the nano-post width in the top and bottom layers for the control metalens designed using the graphs shown in (b). Because the structure is symmetric with respect to the $y$ axis, only the nano-post width in the top halves of the layers are plotted.
Fig. 3.
Fig. 3. Multiwavelength metalens design using adjoint technique. (a) Schematic representation of the forward, and (b) the adjoint simulations in the adjoint optimization technique. In the forward simulation, the metalens is excited with the incident wave intended for the device operation, while in the adjoint simulation, it is excited by sources that are equal to the time-reversed (i.e., complex conjugate) of the desired output fields. (c) Color-coded plots of the surface electric current densities that are used as excitation sources in the adjoint simulation at the two wavelengths. The current densities are applied on the dotted plane shown in (b).
Fig. 4.
Fig. 4. Multifunctional metalens designed using adjoint optimization. (a) Evolution of the focusing efficiencies of the device during the optimization process. (b) Color-coded plots of the nano-post widths in the top and bottom layers for the optimized metalens. Because the structure is symmetric with respect to the $y$ axis, only the nano-post widths in the top halves of the layers are plotted. (c) Electric field in the $y {-} z$ plane in the region indicated by a dashed rectangle in the schematic illustration. (d) Electric field distribution on a plane 78 nm above the optimized metalens at 780 and 915 nm. (e) Simulated intensity distributions in the focal plane of the control and optimized metalenses at 780 and 915 nm.
Fig. 5.
Fig. 5. Effects of layer number and interlayer distance. (a) Schematic illustration of a cylindrical multilayer metasurface. The inset shows a cross-section of one layer. (b) Average efficiency (of 780 and 915 nm) for metasurfaces with different numbers of layers, and (c) for bilayer metasurfaces with different spacer thicknesses. Each circle in (a) and (c) shows the final efficiency for different designs.
Fig. 6.
Fig. 6. Experimental results. (a) Scanning electron micrographs of the top and cross-sectional view of the 2.5D metalens. A thin, protective platinum layer (light green) was deposited on the top nano-post layer during cross-sectioning. (b) Schematic of the measurement setup used to characterize the bilayer metalens. (c) Intensity distributions measured in the $y {-} z$ plane at 780 and 915 nm. (d) Intensity distributions measured in the focal plane of the device at 780 and 915 nm. (e) Intensity profile along the dashed lines shown in (c) and (d) at 780 and 915 nm.

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