Abstract

Three-dimensional elements, with refractive index distribution structured at subwavelength scale, provide an expansive optical design space that can be harnessed for demonstrating multifunctional free-space optical devices. Here we present 3D dielectric elements, designed to be placed on top of the pixels of image sensors, that sort and focus light based on its color and polarization with efficiency significantly surpassing 2D absorptive and diffractive filters. The devices are designed via iterative gradient-based optimization to account for multiple target functions while ensuring compatibility with existing nanofabrication processes, and they are experimentally validated using a scaled device that operates at microwave frequencies. This approach combines arbitrary functions into a single compact element, even where there is no known equivalent in bulk optics, enabling novel integrated photonic applications.

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

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References

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L. Zheng, K. Kurselis, A. El-Tamer, U. Hinze, C. Reinhardt, L. Overmeyer, and B. Chichkov, Nanoscale Res. Lett. 14, 134 (2019).
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T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, Light Sci. Appl. 8, 48 (2019).
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2018 (5)

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, ACS Photon. 5, 3132 (2018).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Nat. Photonics 12, 659 (2018).
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F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, Sci. Rep. 8, 1358 (2018).
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2017 (4)

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
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A. Arbabi and A. Faraon, Sci. Rep. 7, 43722 (2017).
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2016 (4)

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Q. Chen, X. Hu, L. Wen, Y. Yu, and D. R. S. Cumming, Small 12, 4922 (2016).
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2015 (3)

X. Zhou, Y. Hou, and J. Lin, AIP Adv. 5, 030701 (2015).
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A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, Nat. Photonics 9, 374 (2015).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
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2014 (1)

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2013 (3)

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, Opt. Express 21, 21693 (2013).
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2011 (3)

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2010 (1)

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2007 (1)

2005 (1)

1988 (1)

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A. Arbabi and A. Faraon, Sci. Rep. 7, 43722 (2017).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
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E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, ACS Photon. 5, 3132 (2018).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
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Bhargava, S.

Bissett, W. P.

Bowles, J. H.

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E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
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B. Buchegger, J. Kreutzer, B. Plochberger, R. Wollhofen, D. Sivun, J. Jacak, G. J. Schütz, U. Schubert, and T. A. Klar, ACS Nano 10, 1954 (2016).
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F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, Sci. Rep. 8, 1358 (2018).
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Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, Phys. Rev. Appl. 9, 1 (2018).
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N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
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Q. Chen, X. Hu, L. Wen, Y. Yu, and D. R. S. Cumming, Small 12, 4922 (2016).
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Cumming, D. R. S.

Q. Chen, X. Hu, L. Wen, Y. Yu, and D. R. S. Cumming, Small 12, 4922 (2016).
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Davis, C. O.

Doshay, S.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, Light Sci. Appl. 8, 48 (2019).
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D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, Nano Lett. 17, 3752 (2017).
[Crossref]

Downes, T. V.

Edee, K.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, Light Sci. Appl. 8, 48 (2019).
[Crossref]

El-Tamer, A.

L. Zheng, K. Kurselis, A. El-Tamer, U. Hinze, C. Reinhardt, L. Overmeyer, and B. Chichkov, Nanoscale Res. Lett. 14, 134 (2019).
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Fan, J. A.

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, Light Sci. Appl. 8, 48 (2019).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, Nano Lett. 17, 3752 (2017).
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Faraon, A.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, ACS Photon. 5, 3132 (2018).
[Crossref]

A. Arbabi and A. Faraon, Sci. Rep. 7, 43722 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, Sci. Rep. 6, 32803 (2016).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Fujii, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. A. Suzuki, Nat. Photonics 7, 240 (2013).
[Crossref]

Gerke, T. D.

T. D. Gerke and R. Piestun, Nat. Photonics 4, 188 (2010).
[Crossref]

Gibson, R.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Gleason, A.

Groever, B.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, Phys. Rev. Appl. 9, 1 (2018).
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Hasman, E.

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
[Crossref]

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, Science 352, 1202 (2016).
[Crossref]

Hendrickson, J. R.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Hinze, U.

L. Zheng, K. Kurselis, A. El-Tamer, U. Hinze, C. Reinhardt, L. Overmeyer, and B. Chichkov, Nanoscale Res. Lett. 14, 134 (2019).
[Crossref]

Hiramoto, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. A. Suzuki, Nat. Photonics 7, 240 (2013).
[Crossref]

Horie, Y.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, Sci. Rep. 6, 32803 (2016).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Hou, Y.

X. Zhou, Y. Hou, and J. Lin, AIP Adv. 5, 030701 (2015).
[Crossref]

Hu, X.

Q. Chen, X. Hu, L. Wen, Y. Yu, and D. R. S. Cumming, Small 12, 4922 (2016).
[Crossref]

Ichael, M.

Iessen, H. A. G.

Issibl, T. I. M. O. G.

Jacak, J.

B. Buchegger, J. Kreutzer, B. Plochberger, R. Wollhofen, D. Sivun, J. Jacak, G. J. Schütz, U. Schubert, and T. A. Klar, ACS Nano 10, 1954 (2016).
[Crossref]

Jarrahi, M.

Y. Luo, D. Mengu, N. T. Yardimci, Y. Rivenson, M. Veli, M. Jarrahi, and A. Ozcan, Light Sci. Appl. 8, 112 (2019).
[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, Science 361, 1004 (2018).
[Crossref]

Jensen, J. S.

J. S. Jensen and O. Sigmund, Laser Photon. Rev. 5, 308 (2011).
[Crossref]

Jin, W.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Nat. Photonics 12, 659 (2018).
[Crossref]

Kamali, S. M.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, ACS Photon. 5, 3132 (2018).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, Sci. Rep. 6, 32803 (2016).
[Crossref]

Klar, T. A.

B. Buchegger, J. Kreutzer, B. Plochberger, R. Wollhofen, D. Sivun, J. Jacak, G. J. Schütz, U. Schubert, and T. A. Klar, ACS Nano 10, 1954 (2016).
[Crossref]

Kleiner, V.

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
[Crossref]

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, Science 352, 1202 (2016).
[Crossref]

Kohler, D. D. R.

Kosten, E. D.

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light Sci. Appl. 2, e45 (2013).
[Crossref]

Kreutzer, J.

B. Buchegger, J. Kreutzer, B. Plochberger, R. Wollhofen, D. Sivun, J. Jacak, G. J. Schütz, U. Schubert, and T. A. Klar, ACS Nano 10, 1954 (2016).
[Crossref]

Kumar, P.

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, Sci. Rep. 8, 1358 (2018).
[Crossref]

Kurselis, K.

L. Zheng, K. Kurselis, A. El-Tamer, U. Hinze, C. Reinhardt, L. Overmeyer, and B. Chichkov, Nanoscale Res. Lett. 14, 134 (2019).
[Crossref]

Lagoudakis, K. G.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, Nat. Photonics 9, 374 (2015).
[Crossref]

Lalau-Keraly, C. M.

Lazarov, B. S.

F. Wang, B. S. Lazarov, and O. Sigmund, Struct. Multidiscip. Optim. 43, 767 (2011).
[Crossref]

Leathers, R. A.

Lin, J.

X. Zhou, Y. Hou, and J. Lin, AIP Adv. 5, 030701 (2015).
[Crossref]

Lin, X.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, Science 361, 1004 (2018).
[Crossref]

Lin, Z.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Nat. Photonics 12, 659 (2018).
[Crossref]

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, Phys. Rev. Appl. 9, 1 (2018).
[Crossref]

Lipson, M.

Loncar, M.

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, Phys. Rev. Appl. 9, 1 (2018).
[Crossref]

Louchard, E. M.

Lu, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, Nat. Photonics 9, 374 (2015).
[Crossref]

Luo, Y.

Y. Luo, D. Mengu, N. T. Yardimci, Y. Rivenson, M. Veli, M. Jarrahi, and A. Ozcan, Light Sci. Appl. 8, 112 (2019).
[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, Science 361, 1004 (2018).
[Crossref]

Maguid, E.

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
[Crossref]

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, Science 352, 1202 (2016).
[Crossref]

Majumdar, A.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Mengu, D.

Y. Luo, D. Mengu, N. T. Yardimci, Y. Rivenson, M. Veli, M. Jarrahi, and A. Ozcan, Light Sci. Appl. 8, 112 (2019).
[Crossref]

Miller, D.

Miller, O. D.

Mobley, C. D.

Molesky, S.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Nat. Photonics 12, 659 (2018).
[Crossref]

Montes, M. J.

Nakamura, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. A. Suzuki, Nat. Photonics 7, 240 (2013).
[Crossref]

Nishiwaki, S.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. A. Suzuki, Nat. Photonics 7, 240 (2013).
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J. S. Jensen and O. Sigmund, Laser Photon. Rev. 5, 308 (2011).
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F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, Sci. Rep. 8, 1358 (2018).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Nat. Photonics 12, 659 (2018).
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A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, Nat. Photonics 9, 374 (2015).
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Yu, N.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
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Yu, Y.

Q. Chen, X. Hu, L. Wen, Y. Yu, and D. R. S. Cumming, Small 12, 4922 (2016).
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E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
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A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, Sci. Adv. 5, eaax4769 (2019).
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L. Zheng, K. Kurselis, A. El-Tamer, U. Hinze, C. Reinhardt, L. Overmeyer, and B. Chichkov, Nanoscale Res. Lett. 14, 134 (2019).
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ACS Nano (1)

B. Buchegger, J. Kreutzer, B. Plochberger, R. Wollhofen, D. Sivun, J. Jacak, G. J. Schütz, U. Schubert, and T. A. Klar, ACS Nano 10, 1954 (2016).
[Crossref]

ACS Photon. (1)

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, ACS Photon. 5, 3132 (2018).
[Crossref]

AIP Adv. (1)

X. Zhou, Y. Hou, and J. Lin, AIP Adv. 5, 030701 (2015).
[Crossref]

Appl. Opt. (1)

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

Laser Photon. Rev. (1)

J. S. Jensen and O. Sigmund, Laser Photon. Rev. 5, 308 (2011).
[Crossref]

Light Sci. Appl. (4)

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, Light Sci. Appl. 6, e17027 (2017).
[Crossref]

Y. Luo, D. Mengu, N. T. Yardimci, Y. Rivenson, M. Veli, M. Jarrahi, and A. Ozcan, Light Sci. Appl. 8, 112 (2019).
[Crossref]

T. Phan, D. Sell, E. W. Wang, S. Doshay, K. Edee, J. Yang, and J. A. Fan, Light Sci. Appl. 8, 48 (2019).
[Crossref]

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light Sci. Appl. 2, e45 (2013).
[Crossref]

Nano Lett. (1)

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, Nano Lett. 17, 3752 (2017).
[Crossref]

Nanoscale Res. Lett. (1)

L. Zheng, K. Kurselis, A. El-Tamer, U. Hinze, C. Reinhardt, L. Overmeyer, and B. Chichkov, Nanoscale Res. Lett. 14, 134 (2019).
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Nat. Mater. (1)

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
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Nat. Nanotechnol. (1)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
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Nat. Photonics (4)

T. D. Gerke and R. Piestun, Nat. Photonics 4, 188 (2010).
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S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Nat. Photonics 12, 659 (2018).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, Nat. Photonics 9, 374 (2015).
[Crossref]

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. A. Suzuki, Nat. Photonics 7, 240 (2013).
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Opt. Express (2)

Opt. Mater. Express (1)

Phys. Rev. Appl. (1)

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, Phys. Rev. Appl. 9, 1 (2018).
[Crossref]

Phys. Rev. Lett. (1)

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Sci. Adv. (1)

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Sci. Rep. (3)

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, Sci. Rep. 8, 1358 (2018).
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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, Sci. Rep. 6, 32803 (2016).
[Crossref]

A. Arbabi and A. Faraon, Sci. Rep. 7, 43722 (2017).
[Crossref]

Science (2)

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, Science 352, 1202 (2016).
[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, Science 361, 1004 (2018).
[Crossref]

Small (1)

Q. Chen, X. Hu, L. Wen, Y. Yu, and D. R. S. Cumming, Small 12, 4922 (2016).
[Crossref]

Struct. Multidiscip. Optim. (1)

F. Wang, B. S. Lazarov, and O. Sigmund, Struct. Multidiscip. Optim. 43, 767 (2011).
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Supplementary Material (4)

NameDescription
» Supplement 1       Primary supplemental material for main manuscript
» Visualization 1       Video showing the intensity on the focal plane for an x-polarized input plane wave in simulation for the 5-layer Bayer filter. Each frame corresponds to the response of the device to a different wavelength.
» Visualization 2       Video showing the intensity on the focal plane for an x-polarized input plane wave in the microwave experimental measurement setup. Each frame corresponds to the response of the device to a different wavelength.
» Visualization 3       Video showing the intensity on the focal plane for a y-polarized input plane wave in the microwave experimental measurement setup. Each frame corresponds to the response of the device to a different wavelength.

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Figures (3)

Fig. 1.
Fig. 1. Inverse-designed color and polarization sorter. (a) Spectral filter consisting of a 3D nanostructured polymer cube. Incident light is efficiently focused into four sub-pixels on a focal plane below the device. (b) Red (600–700 nm) and blue (400–500 nm) spectral bands are sorted into opposite quadrants. The color indicates field intensity. The brightness of the output field intensity demonstrates the focusing nature of the devices. (c) Similarly, the green (500–600 nm) band is further split according to linear polarization. Red and blue quadrants are polarization independent.
Fig.
2.
Fig. 2. Spectral filter designed for multilayer lithography. (a) Three-dimensional scattering element constructed by stacking multiple two-dimensional layers. (b) Each layer consists of a series of ${{\rm TiO}_2}$ mesas, which can be fabricated using standard lithography and material deposition. Posts are infiltrated with an ${{\rm SiO}_2}$ matrix, forming a flat substrate for subsequent layers. (c) When combined, the five-layer stack performs the same function as the freeform design shown in Fig. 1. Linearly polarized light is focused into distinct sensor regions depending on frequency and polarization. (d) Sorting efficiency within the visible spectrum, defined as the fraction of incident power reaching the target quadrant as indicated in (c). The yellow curve indicates light present at the cross-polarized quadrant. See Visualization 1 for movie showing focal plane intensity as the input wavelength is swept across the design bandwidth. (e) Spectrum-averaged sorting efficiency, polarization contrast, and color contrast for devices with increasing number of layers, each 400 nm thick.
Fig.
3.
Fig. 3. Microwave measurement and simulation results. (a) and (b) Microwave filter composed of patterned polypropylene sheets, assembled into a cube. The cube is illuminated by a collimated microwave source operating in the ${{\rm K}_{\rm a}}$ band (26–40 GHz). (c) and (d) Field intensity at the focal plane of the microwave filter for linearly polarized illumination, as obtained by full wave simulation. Colors represent the equivalent hue of visible light, scaling the microwave frequency by a factor of $ \times {17}{,}{500}$; (c) and (d) correspond to vertical and horizontal polarization, respectively. (e) and (f) Measured microwave field intensity at the focal plane. See Visualization 2 and Visualization 3 for movies showing focal plane intensity as input wavelength is swept across the measurement bandwidth. (g) and (h) Measured and simulated microwave sorting efficiency for each polarization. Dashed lines represent simulated efficiency, while solid lines represent experimental values. Each color corresponds to a quadrant as indicated by the dots in (c)–(f).

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