Abstract

We combine a statistical learning-based global optimization strategy with a high order 3D Discontinuous Galerkin Time-Domain (DGTD) solver to design a compact and highly efficient graded index photonic metalens. The metalens is composed of silicon (Si) strips of varying widths (in the transverse direction) and lengths (in the propagation direction) and operates at the telecommunication wavelength. In our work, we tackle the challenging Transverse Electric case (TE) where the incident electric field is polarized perpendicular to strips direction. We reveal that the focusing efficiency approaches 80% for the traditional design with fixed strip lengths and varying widths. Nevertheless, we demonstrate numerically that the efficiency is as high as 87% for a design with varying strip lengths along the propagation direction.

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Hunsperger, ed., Integrated optics: theory and technology, Topics in Applied Physics (Springer Netherlands, New-York, 2002).
  2. K. Hassan, C. Durantin, V. Hugues, B. Szelag, and A. Glière, “Robust silicon-on-insulator adiabatic splitter optimized by metamodeling,” Appl. Opt. 56(8), 2047–2052 (2017).
    [Crossref]
  3. V. Kalt, A. K. González-Alcalde, S. Es-Saidi, R. Salas-Montiel, S. Blaize, and D. Macías, “Metamodeling of high-contrast-index gratings for color reproduction,” J. Opt. Soc. Am. A 36(1), 79–88 (2019).
    [Crossref]
  4. P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
    [Crossref]
  5. A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
    [Crossref]
  6. L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023 (2018).
    [Crossref]
  7. N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
    [Crossref]
  8. A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
    [Crossref]
  9. A. Udupa, J. Zhu, and L. L. Goddard, “Voxelized topology optimization for fabrication-compatible inverse design of 3d photonic devices,” Opt. Express 27(15), 21988–21998 (2019).
    [Crossref]
  10. M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.
  11. M. Teng, A. Honardoost, Y. Alahmadi, S. S. Polkoo, K. Kojima, H. Wen, C. K. Renshaw, P. LiKamWa, G. Li, and S. Fathpour, “Miniaturized silicon photonics devices for integrated optical signal processors,” J. Lightwave Technol. 38(1), 6–17 (2020).
    [Crossref]
  12. J. M. Castro, D. F. Geraghty, S. Honkanen, C. M. Greiner, D. Iazikov, and T. W. Mossberg, “Demonstration of mode conversion using anti-symmetric waveguide bragg gratings,” Opt. Express 13(11), 4180–4184 (2005).
    [Crossref]
  13. B.-T. Lee and S.-Y. Shin, “Mode-order converter in a multimode waveguide,” Opt. Lett. 28(18), 1660–1662 (2003).
    [Crossref]
  14. K. Hassan, J.-A. Dallery, P. Brianceau, and S. Boutami, “Integrated photonic guided metalens based on a pseudo-graded index distribution,” Sci. Rep. 10(1), 1123 (2020).
    [Crossref]
  15. U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
    [Crossref]
  16. J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
    [Crossref]
  17. S. Nambiar, P. Sethi, and S. K. Selvaraja, “Grating-assisted fiber to chip coupling for soi photonic circuits,” Appl. Sci. 8(7), 1142 (2018).
    [Crossref]
  18. D. Jones, “Efficient global optimization of expensive black-box functions,” J. Glob. Optim. 13(4), 455–492 (1998).
    [Crossref]
  19. M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
    [Crossref]
  20. R. L. Haupt and D. H. Werner, Genetic algorithms in electromagnetics (John Wiley & Sons, 2007).
  21. J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
    [Crossref]
  22. F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
    [Crossref]
  23. L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on phc-like metamaterial structure,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2016), pp. 1–3.
  24. V. Egorov, M. Eitan, and J. Scheuer, “Genetically optimized all-dielectric metasurfaces,” Opt. Express 25(3), 2583–2593 (2017).
    [Crossref]
  25. P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
    [Crossref]
  26. DIOGENeS: A Discontinuous-Galerkin based software suite for nano-optics. Https://diogenes.inria.fr/.
  27. J. Viquerat, “Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain method,” Ph.D. thesis, University of Nice-Sophia Antipolis (2015).
  28. L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
    [Crossref]

2020 (2)

2019 (6)

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

V. Kalt, A. K. González-Alcalde, S. Es-Saidi, R. Salas-Montiel, S. Blaize, and D. Macías, “Metamodeling of high-contrast-index gratings for color reproduction,” J. Opt. Soc. Am. A 36(1), 79–88 (2019).
[Crossref]

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

A. Udupa, J. Zhu, and L. L. Goddard, “Voxelized topology optimization for fabrication-compatible inverse design of 3d photonic devices,” Opt. Express 27(15), 21988–21998 (2019).
[Crossref]

2018 (4)

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023 (2018).
[Crossref]

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

S. Nambiar, P. Sethi, and S. K. Selvaraja, “Grating-assisted fiber to chip coupling for soi photonic circuits,” Appl. Sci. 8(7), 1142 (2018).
[Crossref]

2017 (2)

2015 (2)

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

2007 (1)

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

2005 (2)

J. M. Castro, D. F. Geraghty, S. Honkanen, C. M. Greiner, D. Iazikov, and T. W. Mossberg, “Demonstration of mode conversion using anti-symmetric waveguide bragg gratings,” Opt. Express 13(11), 4180–4184 (2005).
[Crossref]

L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
[Crossref]

2003 (1)

1998 (1)

D. Jones, “Efficient global optimization of expensive black-box functions,” J. Glob. Optim. 13(4), 455–492 (1998).
[Crossref]

1989 (1)

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
[Crossref]

Abashin, M.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Alahmadi, Y.

Atwater, H.

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Aydin, K.

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

Babinec, T. M.

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Blaize, S.

Boutami, S.

K. Hassan, J.-A. Dallery, P. Brianceau, and S. Boutami, “Integrated photonic guided metalens based on a pseudo-graded index distribution,” Sci. Rep. 10(1), 1123 (2020).
[Crossref]

Brianceau, P.

K. Hassan, J.-A. Dallery, P. Brianceau, and S. Boutami, “Integrated photonic guided metalens based on a pseudo-graded index distribution,” Sci. Rep. 10(1), 1123 (2020).
[Crossref]

Brière, G.

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

Burger, S.

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Callewaert, F.

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

Castro, J. M.

Cheben, P.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Cunningham, J.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Dallery, J.-A.

K. Hassan, J.-A. Dallery, P. Brianceau, and S. Boutami, “Integrated photonic guided metalens based on a pseudo-graded index distribution,” Sci. Rep. 10(1), 1123 (2020).
[Crossref]

Dapogny, C.

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

de Oliva-Rubio, J.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Durantin, C.

Duvigneau, R.

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

Egorov, V.

Eitan, M.

Elsawy, M. M. R.

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

Es-Saidi, S.

Fainman, Y.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Fathpour, S.

Fezoui, L.

L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
[Crossref]

Garcia Santiago, X.

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Genevet, P.

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

Geraghty, D. F.

Gliere, A.

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

Glière, A.

Goddard, L. L.

González-Alcalde, A. K.

Greiner, C. M.

Halir, R.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Hammerschmidt, M.

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Hassan, K.

K. Hassan, J.-A. Dallery, P. Brianceau, and S. Boutami, “Integrated photonic guided metalens based on a pseudo-graded index distribution,” Sci. Rep. 10(1), 1123 (2020).
[Crossref]

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

K. Hassan, C. Durantin, V. Hugues, B. Szelag, and A. Glière, “Robust silicon-on-insulator adiabatic splitter optimized by metamodeling,” Appl. Opt. 56(8), 2047–2052 (2017).
[Crossref]

Haupt, R. L.

R. L. Haupt and D. H. Werner, Genetic algorithms in electromagnetics (John Wiley & Sons, 2007).

Honardoost, A.

Honkanen, S.

Hugues, V.

Iazikov, D.

Ikeda, K.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Jones, D.

D. Jones, “Efficient global optimization of expensive black-box functions,” J. Glob. Optim. 13(4), 455–492 (1998).
[Crossref]

Kalt, V.

Koike-Akino, T.

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

Kojima, K.

M. Teng, A. Honardoost, Y. Alahmadi, S. S. Polkoo, K. Kojima, H. Wen, C. K. Renshaw, P. LiKamWa, G. Li, and S. Fathpour, “Miniaturized silicon photonics devices for integrated optical signal processors,” J. Lightwave Technol. 38(1), 6–17 (2020).
[Crossref]

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

Krishnamoorthy, A.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Kumar, P.

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

Lagoudakis, K. G.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

Lanteri, S.

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
[Crossref]

Lebbe, N.

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

Lee, B.-T.

Levy, U.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Li, G.

LiKamWa, P.

Lin, C.

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

Liu, D.

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on phc-like metamaterial structure,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2016), pp. 1–3.

Lohrengel, S.

L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
[Crossref]

Lu, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

Lu, L.

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on phc-like metamaterial structure,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2016), pp. 1–3.

Luque-González, J. M.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Macías, D.

Mitchell, T.

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
[Crossref]

Mohamed, M. S.

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

Molina-Fernández, Í.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Mossberg, T. W.

Nambiar, S.

S. Nambiar, P. Sethi, and S. K. Selvaraja, “Grating-assisted fiber to chip coupling for soi photonic circuits,” Appl. Sci. 8(7), 1142 (2018).
[Crossref]

Ortega-Moñux, A.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Oudet, E.

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

Parsons, K.

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

Petykiewicz, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

Piggott, A. Y.

L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023 (2018).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

Piperno, S.

L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
[Crossref]

Polkoo, S. S.

Renshaw, C. K.

Rockstuhl, C.

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Sacks, J.

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
[Crossref]

Sahakian, A. V.

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

Salas-Montiel, R.

Sapra, N. V.

Scheuer, J.

Schmid, J.

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Schmid, J. H.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Schneider, P.-I.

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Selvaraja, S. K.

S. Nambiar, P. Sethi, and S. K. Selvaraja, “Grating-assisted fiber to chip coupling for soi photonic circuits,” Appl. Sci. 8(7), 1142 (2018).
[Crossref]

Sethi, P.

S. Nambiar, P. Sethi, and S. K. Selvaraja, “Grating-assisted fiber to chip coupling for soi photonic circuits,” Appl. Sci. 8(7), 1142 (2018).
[Crossref]

Shin, S.-Y.

Smith, D.

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Soltwisch, V.

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Su, L.

Szelag, B.

Teng, M.

M. Teng, A. Honardoost, Y. Alahmadi, S. S. Polkoo, K. Kojima, H. Wen, C. K. Renshaw, P. LiKamWa, G. Li, and S. Fathpour, “Miniaturized silicon photonics devices for integrated optical signal processors,” J. Lightwave Technol. 38(1), 6–17 (2020).
[Crossref]

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

Trivedi, R.

Udupa, A.

Velev, V.

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

Vercruysse, D.

Viquerat, J.

J. Viquerat, “Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain method,” Ph.D. thesis, University of Nice-Sophia Antipolis (2015).

Vuckovic, J.

L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023 (2018).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Wang, B.

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

Wangüemert-Pérez, J. G.

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Welch, W.

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
[Crossref]

Wen, H.

Werner, D. H.

R. L. Haupt and D. H. Werner, Genetic algorithms in electromagnetics (John Wiley & Sons, 2007).

Wynn, H.

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
[Crossref]

Zhang, M.

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on phc-like metamaterial structure,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2016), pp. 1–3.

Zhou, F.

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on phc-like metamaterial structure,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2016), pp. 1–3.

Zhu, J.

ACS Photonics (1)

P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019).
[Crossref]

Appl. Opt. (1)

Appl. Sci. (1)

S. Nambiar, P. Sethi, and S. K. Selvaraja, “Grating-assisted fiber to chip coupling for soi photonic circuits,” Appl. Sci. 8(7), 1142 (2018).
[Crossref]

ESAIM: Math. Modell. Numer. Anal. (1)

L. Fezoui, S. Lanteri, S. Lohrengel, and S. Piperno, “Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes,” ESAIM: Math. Modell. Numer. Anal. 39(6), 1149–1176 (2005).
[Crossref]

J. Comput. Phys. (1)

N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, and A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method,” J. Comput. Phys. 395, 710–746 (2019).
[Crossref]

J. Glob. Optim. (1)

D. Jones, “Efficient global optimization of expensive black-box functions,” J. Glob. Optim. 13(4), 455–492 (1998).
[Crossref]

J. Lightwave Technol. (1)

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

Laser Photonics Rev. (1)

J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact grin-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019).
[Crossref]

Nat. Photonics (1)

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015).
[Crossref]

Nature (1)

P. Cheben, R. Halir, J. Schmid, H. Atwater, and D. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref]

Sci. Rep. (4)

K. Hassan, J.-A. Dallery, P. Brianceau, and S. Boutami, “Integrated photonic guided metalens based on a pseudo-graded index distribution,” Sci. Rep. 10(1), 1123 (2020).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vučković, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4(1), 7210 (2015).
[Crossref]

M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Sci. Rep. 9(1), 17918 (2019).
[Crossref]

F. Callewaert, V. Velev, P. Kumar, A. V. Sahakian, and K. Aydin, “Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices,” Sci. Rep. 8(1), 1358 (2018).
[Crossref]

Stat. Sci. (1)

J. Sacks, W. Welch, T. Mitchell, and H. Wynn, “Design and analysis of computer experiments,” Stat. Sci. 4(4), 409–423 (1989).
[Crossref]

Other (6)

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on phc-like metamaterial structure,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2016), pp. 1–3.

DIOGENeS: A Discontinuous-Galerkin based software suite for nano-optics. Https://diogenes.inria.fr/.

J. Viquerat, “Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain method,” Ph.D. thesis, University of Nice-Sophia Antipolis (2015).

R. L. Haupt and D. H. Werner, Genetic algorithms in electromagnetics (John Wiley & Sons, 2007).

M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband soi mode order converter based on topology optimization,” in 2018 Optical Fiber Communications Conference and Exposition (OFC), (IEEE, 2018), pp. 1–3.

R. Hunsperger, ed., Integrated optics: theory and technology, Topics in Applied Physics (Springer Netherlands, New-York, 2002).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. Schematic view of the 3D photonic metalens. The structure consists of Si region (green part) on top of subtrate made of SiO$_{2}$ (red part). The Si region is divided into three parts; the input port with width $W=3000~$nm, the output port with width $w=300~$nm, and in-between, several Si strips with lenght L and height $h=310~$nm. The input mode is injected from the surface $S_{in}$ and the FOM (see Eq. (1)) is computed at the output surface $S_{out}$. The widths of the strips are denoted by $e_{i}$, $i \in \{0,6\}$.
Fig. 2.
Fig. 2. Optimization results: (a): represents the 1 - FOM (to maximize the FOM given by Eq. (1)) as a function of the solver calls. The blue points represent the DOE (50 points), the black ones represent the optimization iterations, and the green curve indicates the best results obtained along the optimization process. (b): the merit function versus the number of solver calls (for the optimization iterations, i.e, after 50 iterations as indicated by the green curve in (a)).
Fig. 3.
Fig. 3. (a): Field map of $\Re e(H_{y})$ for the optimized design in the $x-z$ plane obtained from our DGTD solver using $\mathbb {P}_{4}$ interpolation and a mesh with $334~000$ cells. The parameters are given in the first row in Table 1. (b): numerical convergence assessment for the TE case using the values provided in Table 3 as a function of the length of the strips L using different polynomial orders, and different mesh sizes. As it can be seen from the shaded region, there are three global points similar to what we have found in Table 1 and the best FOM is obtained at $L=3700$ nm.
Fig. 4.
Fig. 4. FDTD convergence study (a): TE case where the parameters are identical to the ones used in Fig. 3(b) for the DGTD solver. (b): TM case considered in Ref. [14], where all the opto-geometrical parameters are identical to the ones used in Ref. [14].
Fig. 5.
Fig. 5. (a): 3D mesh for the optimized design with different lengths for the strips. (b): Field map of $\Re e(H_{y})$ for the optimized design with changing length in the $x-z$ plane obtained from our DGTD solver using $\mathbb {P}_{4}$ interpolation and mesh with $334~000$ cells. The strips width parameters are given in the first row in Table 1.

Tables (4)

Tables Icon

Table 1. Optimized deigns obtained from the EGO (L and e i in nm). The results show that there are two global points in our design with nearly the same FOM 80 % ., however, the parameters are slightly different. Here, we considered PML thickness of 500 nm, which is proved to be enough.

Tables Icon

Table 2. The convergence of the optimized design using EGO (first row in Table 1) as a function of the mesh size and the polynomial order in the DGTD solver for the total transmission T (third column) and for the FOM (last column).

Tables Icon

Table 3. Values of the strip widths to obtain a gradient index lens profile for TE polarization ( e i in nm). These widths are determined by computing the effective mode index for each strip [14], see the text for more details.

Tables Icon

Table 4. Optimized values of the strip lengths obtained from the EGO method (L i in nm) with1 FOM = 87 % . The values of the strip widths are similar to the ones in the first row in Table 1. Here we fix the the three length of the center strips (value shown in first row in Table 1) and change the lengths of the five outer strips (symmetry is applied).

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

FOM = | S o u t ( E × H o u t ) .   n   d S + S o u t ( E o u t × H ) .   n   d S | 2 4 [ S i n e ( E i n × H i n ) .   n   d S ] [ S o u t e ( E o u t × H o u t ) .   n   d S ] .