Abstract

Topology optimization for photonic device design, has been mostly used to optimize binary structures based on refractive index as the free parameter for each design cell. Typically, a constraint on the optimization variable to be z-invariant and a smoothing operation on small features are applied to make the structure fabricable by conventional lithography. To enable topology optimization to design fabricable 3D structures using emerging methods like grayscale lithography and focused ion beam milling, we propose here a framework that uses the refractive index step position as the free parameter for each 3D voxel. This choice of framework enables us to reuse the same mesh in each iteration and thereby reduce the time for optimization. We apply the framework to the fabricable design of both free-space and integrated photonic devices, at different wavelengths, demonstrating high-efficiency ultra-compact designs with wide wavelength tunability.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
    [Crossref]
  2. J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
    [Crossref]
  3. 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(23), 28210–28222 (2017).
    [Crossref]
  4. W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter,” Opt. Express 26(18), 24135–24144 (2018).
    [Crossref] [PubMed]
  5. 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]
  6. C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21(18), 21693–21701 (2013).
    [Crossref] [PubMed]
  7. L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24(15), 16866–16873 (2016).
    [Crossref] [PubMed]
  8. L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
    [Crossref]
  9. Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
    [Crossref]
  10. W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
    [Crossref]
  11. B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
    [Crossref]
  12. J. C. C. Mak, C. Sideris, J. Jeong, A. Hajimiri, and J. K. S. Poon, “Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform,” Opt. Lett. 41(16), 3868–3871 (2016).
    [Crossref] [PubMed]
  13. A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
    [Crossref] [PubMed]
  14. Z. Yu, H. Cui, and X. Sun, “Genetic-algorithm-optimized wideband on-chip polarization rotator with an ultrasmall footprint,” Opt. Lett. 42(16), 3093–3096 (2017).
    [Crossref] [PubMed]
  15. S. Zhou, W. Li, G. Sun, and Q. Li, “A level-set procedure for the design of electromagnetic metamaterials,” Opt. Express 18(7), 6693–6702 (2010).
    [Crossref] [PubMed]
  16. A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, “Topology optimization of heat conduction problems using the finite volume method,” Struct. Multidiscipl. Optim. 31(4), 251–259 (2006).
    [Crossref]
  17. O. Sigmund, “A 99 line topology optimization code written in Matlab,” Struct. Multidiscipl. Optim. 21(2), 120–127 (2001).
    [Crossref]
  18. O. Sigmund, “On the Design of Compliant Mechanisms Using Topology Optimization,” Mech. Struct. Mach. 25(4), 493–524 (1997).
    [Crossref]
  19. K. S. Friis and O. Sigmund, “Robust topology design of periodic grating surfaces,” J. Opt. Soc. Am. B 29(10), 2935–2943 (2012).
    [Crossref]
  20. P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
    [Crossref] [PubMed]
  21. A. R. Diaz and O. Sigmund, “A topology optimization method for design of negative permeability metamaterials,” Struct. Multidiscipl. Optim. 41(2), 163–177 (2010).
    [Crossref]
  22. E. W. Wang, D. Sell, T. Phan, and J. A. Fan, “Robust design of topology-optimized metasurfaces,” Opt. Mater. Express 9(2), 469–482 (2019).
    [Crossref]
  23. J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidiscipl. Optim. 43(6), 731–743 (2011).
    [Crossref]
  24. T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
    [Crossref]
  25. L. A. Giannuzzi and F. A. Stevie, “A review of focused ion beam milling techniques for TEM specimen preparation,” Micron 30(3), 197–204 (1999).
    [Crossref]
  26. C. Edwards, K. Wang, R. Zhou, B. Bhaduri, G. Popescu, and L. L. Goddard, “Digital projection photochemical etching defines gray-scale features,” Opt. Express 21(11), 13547–13554 (2013).
    [Crossref] [PubMed]
  27. C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
    [Crossref]
  28. L. J. Guo, “Nanoimprint Lithography: Methods and Material Requirements,” Adv. Mater. 19(4), 495–513 (2007).
    [Crossref]
  29. T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
    [Crossref]
  30. V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells,” IEEE J. Photovolt. 4(1), 175–182 (2014).
    [Crossref]
  31. J. L. Pita, I. Aldaya, P. Dainese, H. E. Hernandez-Figueroa, and L. H. Gabrielli, “Design of a compact CMOS-compatible photonic antenna by topological optimization,” Opt. Express 26(3), 2435–2442 (2018).
    [Crossref] [PubMed]
  32. N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
    [Crossref] [PubMed]
  33. K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
    [Crossref]
  34. C. McDonnell, E. Coyne, and G. M. O’Connor, “Grey-scale silicon diffractive optics for selective laser ablation of thin conductive films,” Appl. Opt. 57(24), 6966–6970 (2018).
    [Crossref] [PubMed]
  35. T. Dillon, J. Murakowski, S. Shi, and D. Prather, “Fiber-to-waveguide coupler based on the parabolic reflector,” Opt. Lett. 33(9), 896–898 (2008).
    [Crossref] [PubMed]
  36. D. L. Voronov, E. M. Gullikson, F. Salmassi, T. Warwick, and H. A. Padmore, “Enhancement of diffraction efficiency via higher-order operation of a multilayer blazed grating,” Opt. Lett. 39(11), 3157–3160 (2014).
    [Crossref] [PubMed]
  37. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
    [Crossref] [PubMed]
  38. A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
    [Crossref] [PubMed]
  39. M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
    [Crossref]
  40. L. Li and K. Khandelwal, “Volume preserving projection filters and continuation methods in topology optimization,” Eng. Struct. 85, 144–161 (2015).
    [Crossref]
  41. F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscipl. Optim. 43(6), 767–784 (2011).
    [Crossref]

2019 (2)

E. W. Wang, D. Sell, T. Phan, and J. A. Fan, “Robust design of topology-optimized metasurfaces,” Opt. Mater. Express 9(2), 469–482 (2019).
[Crossref]

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

2018 (6)

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
[Crossref]

J. L. Pita, I. Aldaya, P. Dainese, H. E. Hernandez-Figueroa, and L. H. Gabrielli, “Design of a compact CMOS-compatible photonic antenna by topological optimization,” Opt. Express 26(3), 2435–2442 (2018).
[Crossref] [PubMed]

C. McDonnell, E. Coyne, and G. M. O’Connor, “Grey-scale silicon diffractive optics for selective laser ablation of thin conductive films,” Appl. Opt. 57(24), 6966–6970 (2018).
[Crossref] [PubMed]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref] [PubMed]

2017 (4)

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref] [PubMed]

Z. Yu, H. Cui, and X. Sun, “Genetic-algorithm-optimized wideband on-chip polarization rotator with an ultrasmall footprint,” Opt. Lett. 42(16), 3093–3096 (2017).
[Crossref] [PubMed]

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(23), 28210–28222 (2017).
[Crossref]

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
[Crossref] [PubMed]

2016 (3)

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

J. C. C. Mak, C. Sideris, J. Jeong, A. Hajimiri, and J. K. S. Poon, “Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform,” Opt. Lett. 41(16), 3868–3871 (2016).
[Crossref] [PubMed]

L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24(15), 16866–16873 (2016).
[Crossref] [PubMed]

2015 (3)

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]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

L. Li and K. Khandelwal, “Volume preserving projection filters and continuation methods in topology optimization,” Eng. Struct. 85, 144–161 (2015).
[Crossref]

2014 (2)

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells,” IEEE J. Photovolt. 4(1), 175–182 (2014).
[Crossref]

D. L. Voronov, E. M. Gullikson, F. Salmassi, T. Warwick, and H. A. Padmore, “Enhancement of diffraction efficiency via higher-order operation of a multilayer blazed grating,” Opt. Lett. 39(11), 3157–3160 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[Crossref]

K. S. Friis and O. Sigmund, “Robust topology design of periodic grating surfaces,” J. Opt. Soc. Am. B 29(10), 2935–2943 (2012).
[Crossref]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

2011 (3)

J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidiscipl. Optim. 43(6), 731–743 (2011).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscipl. Optim. 43(6), 767–784 (2011).
[Crossref]

2010 (2)

S. Zhou, W. Li, G. Sun, and Q. Li, “A level-set procedure for the design of electromagnetic metamaterials,” Opt. Express 18(7), 6693–6702 (2010).
[Crossref] [PubMed]

A. R. Diaz and O. Sigmund, “A topology optimization method for design of negative permeability metamaterials,” Struct. Multidiscipl. Optim. 41(2), 163–177 (2010).
[Crossref]

2009 (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

2008 (2)

T. Dillon, J. Murakowski, S. Shi, and D. Prather, “Fiber-to-waveguide coupler based on the parabolic reflector,” Opt. Lett. 33(9), 896–898 (2008).
[Crossref] [PubMed]

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

2007 (1)

L. J. Guo, “Nanoimprint Lithography: Methods and Material Requirements,” Adv. Mater. 19(4), 495–513 (2007).
[Crossref]

2006 (1)

A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, “Topology optimization of heat conduction problems using the finite volume method,” Struct. Multidiscipl. Optim. 31(4), 251–259 (2006).
[Crossref]

2004 (2)

P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
[Crossref] [PubMed]

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[Crossref]

2001 (1)

O. Sigmund, “A 99 line topology optimization code written in Matlab,” Struct. Multidiscipl. Optim. 21(2), 120–127 (2001).
[Crossref]

1999 (1)

L. A. Giannuzzi and F. A. Stevie, “A review of focused ion beam milling techniques for TEM specimen preparation,” Micron 30(3), 197–204 (1999).
[Crossref]

1997 (1)

O. Sigmund, “On the Design of Compliant Mechanisms Using Topology Optimization,” Mech. Struct. Mach. 25(4), 493–524 (1997).
[Crossref]

1987 (1)

K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
[Crossref]

Albooyeh, M.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Aldaya, I.

Ao, Y.

Arbabi, A.

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Babinec, T. M.

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]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Bendsøe, M. P.

A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, “Topology optimization of heat conduction problems using the finite volume method,” Struct. Multidiscipl. Optim. 31(4), 251–259 (2006).
[Crossref]

Bhaduri, B.

Bhargava, S.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21(18), 21693–21701 (2013).
[Crossref] [PubMed]

Borel, P.

Braun, P. V.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Bravo-Abad, J.

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[Crossref]

Capasso, F.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Capolino, F.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Chang, W.

Chen, H.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Chen, W. T.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Cheng, M.

Choquette, K. D.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

Cifci, O. S.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Coyne, E.

Cui, H.

Dainese, P.

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Deng, L.

Diaz, A. R.

A. R. Diaz and O. Sigmund, “A topology optimization method for design of negative permeability metamaterials,” Struct. Multidiscipl. Optim. 41(2), 163–177 (2010).
[Crossref]

Dillon, T.

Ding, Y.

Edwards, C.

C. Edwards, K. Wang, R. Zhou, B. Bhaduri, G. Popescu, and L. L. Goddard, “Digital projection photochemical etching defines gray-scale features,” Opt. Express 21(11), 13547–13554 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Elesin, Y.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[Crossref]

Erdmann, A.

T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
[Crossref]

Fan, J. A.

Frandsen, L.

Frandsen, L. H.

Frei, W. R.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

Frellsen, L. F.

Friis, K. S.

Gabrielli, L. H.

Ganapati, V.

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells,” IEEE J. Photovolt. 4(1), 175–182 (2014).
[Crossref]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Gersborg-Hansen, A.

A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, “Topology optimization of heat conduction problems using the finite volume method,” Struct. Multidiscipl. Optim. 31(4), 251–259 (2006).
[Crossref]

Giannuzzi, L. A.

L. A. Giannuzzi and F. A. Stevie, “A review of focused ion beam milling techniques for TEM specimen preparation,” Micron 30(3), 197–204 (1999).
[Crossref]

Giessen, H.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Gissibl, T.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Goddard, L. L.

C. Edwards, K. Wang, R. Zhou, B. Bhaduri, G. Popescu, and L. L. Goddard, “Digital projection photochemical etching defines gray-scale features,” Opt. Express 21(11), 13547–13554 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Gullikson, E. M.

Guo, L. J.

L. J. Guo, “Nanoimprint Lithography: Methods and Material Requirements,” Adv. Mater. 19(4), 495–513 (2007).
[Crossref]

Hajimiri, A.

Håkansson, A.

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[Crossref]

Hanifeh, M.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Harpøth, A.

Hernandez-Figueroa, H. E.

Hirayama, K.

Huang, Y.-W.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Iguchi, A.

Jensen, J.

Jensen, J. S.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidiscipl. Optim. 43(6), 731–743 (2011).
[Crossref]

Jeong, J.

Jin, W.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

Johnson, H. T.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

Kamandi, M.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Kaspar, C.

T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
[Crossref]

Khandelwal, K.

L. Li and K. Khandelwal, “Volume preserving projection filters and continuation methods in topology optimization,” Eng. Struct. 85, 144–161 (2015).
[Crossref]

Khorasaninejad, M.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Kristensen, M.

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]

Lalau-Keraly, C. M.

Lazarov, B. S.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[Crossref]

F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscipl. Optim. 43(6), 767–784 (2011).
[Crossref]

Li, L.

L. Li and K. Khandelwal, “Volume preserving projection filters and continuation methods in topology optimization,” Eng. Struct. 85, 144–161 (2015).
[Crossref]

Li, Q.

Li, W.

Lin, Z.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Liu, D.

López-Zanón, D.

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[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]

Lu, L.

Mak, J. C. C.

McDonnell, C.

Meem, M.

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
[Crossref] [PubMed]

Menon, R.

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
[Crossref] [PubMed]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Miller, O. D.

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells,” IEEE J. Photovolt. 4(1), 175–182 (2014).
[Crossref]

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21(18), 21693–21701 (2013).
[Crossref] [PubMed]

Mohammad, N.

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
[Crossref] [PubMed]

Molesky, S.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

Murakowski, J.

O’Connor, G. M.

Onanuga, T.

T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
[Crossref]

Padmore, H. A.

Petykiewicz, J.

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref] [PubMed]

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]

Phan, T.

Piggott, A. Y.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref] [PubMed]

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]

Pita, J. L.

Polson, R.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Poon, J. K. S.

Popescu, G.

C. Edwards, K. Wang, R. Zhou, B. Bhaduri, G. Popescu, and L. L. Goddard, “Digital projection photochemical etching defines gray-scale features,” Opt. Express 21(11), 13547–13554 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Prather, D.

Qiu, C.-W.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Rajaei, M.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Ren, X.

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Rodriguez, A. W.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Sailer, H.

T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
[Crossref]

Salmassi, F.

Sánchez-Dehesa, J.

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[Crossref]

Sanchis, L.

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[Crossref]

Sanjeev, V.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Sell, D.

Shen, B.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Shi, P.

Shi, S.

Sideris, C.

Sigmund, O.

L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24(15), 16866–16873 (2016).
[Crossref] [PubMed]

K. S. Friis and O. Sigmund, “Robust topology design of periodic grating surfaces,” J. Opt. Soc. Am. B 29(10), 2935–2943 (2012).
[Crossref]

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscipl. Optim. 43(6), 767–784 (2011).
[Crossref]

A. R. Diaz and O. Sigmund, “A topology optimization method for design of negative permeability metamaterials,” Struct. Multidiscipl. Optim. 41(2), 163–177 (2010).
[Crossref]

A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, “Topology optimization of heat conduction problems using the finite volume method,” Struct. Multidiscipl. Optim. 31(4), 251–259 (2006).
[Crossref]

P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
[Crossref] [PubMed]

O. Sigmund, “A 99 line topology optimization code written in Matlab,” Struct. Multidiscipl. Optim. 21(2), 120–127 (2001).
[Crossref]

O. Sigmund, “On the Design of Compliant Mechanisms Using Topology Optimization,” Mech. Struct. Mach. 25(4), 493–524 (1997).
[Crossref]

Stevie, F. A.

L. A. Giannuzzi and F. A. Stevie, “A review of focused ion beam milling techniques for TEM specimen preparation,” Micron 30(3), 197–204 (1999).
[Crossref]

Su, L.

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref] [PubMed]

Sun, G.

Sun, X.

Svanberg, K.

K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
[Crossref]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Toussaint, K. C.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Tsuji, Y.

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Voronov, D. L.

Vuckovic, J.

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref] [PubMed]

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]

Wan, X.

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
[Crossref] [PubMed]

Wang, E. W.

Wang, F.

F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscipl. Optim. 43(6), 767–784 (2011).
[Crossref]

Wang, K.

Wang, P.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Warwick, T.

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Wickramasinghe, H. K.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Xiao, T. P.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Yablonovitch, E.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells,” IEEE J. Photovolt. 4(1), 175–182 (2014).
[Crossref]

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21(18), 21693–21701 (2013).
[Crossref] [PubMed]

Yasui, T.

Yu, Z.

Zaidi, A.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Zeng, J.

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Zhang, M.

Zhou, R.

Zhou, S.

Zhou, W.

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

Zhu, A. Y.

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

ACS Photonics (2)

T. P. Xiao, O. S. Cifci, S. Bhargava, H. Chen, T. Gissibl, W. Zhou, H. Giessen, K. C. Toussaint, E. Yablonovitch, and P. V. Braun, “Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing,” ACS Photonics 3(5), 886–894 (2016).
[Crossref]

M. Rajaei, J. Zeng, M. Albooyeh, M. Kamandi, M. Hanifeh, F. Capolino, and H. K. Wickramasinghe, “Giant Circular Dichroism at Visible Frequencies Enabled by Plasmonic Ramp-Shaped Nanostructures,” ACS Photonics 6(4), 924–931 (2019).
[Crossref]

Adv. Mater. (1)

L. J. Guo, “Nanoimprint Lithography: Methods and Material Requirements,” Adv. Mater. 19(4), 495–513 (2007).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, and J. Sánchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84(22), 4460–4462 (2004).
[Crossref]

Eng. Struct. (1)

L. Li and K. Khandelwal, “Volume preserving projection filters and continuation methods in topology optimization,” Eng. Struct. 85, 144–161 (2015).
[Crossref]

IEEE J. Photovolt. (1)

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells,” IEEE J. Photovolt. 4(1), 175–182 (2014).
[Crossref]

Int. J. Numer. Methods Eng. (1)

K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” Int. J. Numer. Methods Eng. 24(2), 359–373 (1987).
[Crossref]

J. Appl. Phys. (1)

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[Crossref]

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

Laser Photonics Rev. (1)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5(2), 308–321 (2011).
[Crossref]

Light Sci. Appl. (2)

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018).
[Crossref] [PubMed]

Mech. Struct. Mach. (1)

O. Sigmund, “On the Design of Compliant Mechanisms Using Topology Optimization,” Mech. Struct. Mach. 25(4), 493–524 (1997).
[Crossref]

Micron (1)

L. A. Giannuzzi and F. A. Stevie, “A review of focused ion beam milling techniques for TEM specimen preparation,” Micron 30(3), 197–204 (1999).
[Crossref]

Nat. Photonics (3)

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]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12(11), 659–670 (2018).
[Crossref]

Opt. Express (8)

P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
[Crossref] [PubMed]

S. Zhou, W. Li, G. Sun, and Q. Li, “A level-set procedure for the design of electromagnetic metamaterials,” Opt. Express 18(7), 6693–6702 (2010).
[Crossref] [PubMed]

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21(18), 21693–21701 (2013).
[Crossref] [PubMed]

L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24(15), 16866–16873 (2016).
[Crossref] [PubMed]

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(23), 28210–28222 (2017).
[Crossref]

W. Chang, X. Ren, Y. Ao, L. Lu, M. Cheng, L. Deng, D. Liu, and M. Zhang, “Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter,” Opt. Express 26(18), 24135–24144 (2018).
[Crossref] [PubMed]

C. Edwards, K. Wang, R. Zhou, B. Bhaduri, G. Popescu, and L. L. Goddard, “Digital projection photochemical etching defines gray-scale features,” Opt. Express 21(11), 13547–13554 (2013).
[Crossref] [PubMed]

J. L. Pita, I. Aldaya, P. Dainese, H. E. Hernandez-Figueroa, and L. H. Gabrielli, “Design of a compact CMOS-compatible photonic antenna by topological optimization,” Opt. Express 26(3), 2435–2442 (2018).
[Crossref] [PubMed]

Opt. Lett. (4)

Opt. Mater. Express (1)

Photon. Nanostruct. Fund. Appl. (1)

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[Crossref]

Proc. SPIE (1)

T. Onanuga, C. Kaspar, H. Sailer, and A. Erdmann, “Accurate determination of 3D PSF and resist effects in grayscale laser lithography,” Proc. SPIE 10775, 22 (2018).
[Crossref]

Sci. Rep. (2)

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7(1), 5789 (2017).
[Crossref] [PubMed]

A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017).
[Crossref] [PubMed]

Science (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Struct. Multidiscipl. Optim. (5)

J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidiscipl. Optim. 43(6), 731–743 (2011).
[Crossref]

A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, “Topology optimization of heat conduction problems using the finite volume method,” Struct. Multidiscipl. Optim. 31(4), 251–259 (2006).
[Crossref]

O. Sigmund, “A 99 line topology optimization code written in Matlab,” Struct. Multidiscipl. Optim. 21(2), 120–127 (2001).
[Crossref]

A. R. Diaz and O. Sigmund, “A topology optimization method for design of negative permeability metamaterials,” Struct. Multidiscipl. Optim. 41(2), 163–177 (2010).
[Crossref]

F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscipl. Optim. 43(6), 767–784 (2011).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1       It is a animation showing the evolution of the topology during the optimization, showing also the objective function as a function of iteration number. The voxels are shown to change in height, but actually the mesh does not change; only the refracti

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Figures (6)

Fig. 1
Fig. 1 Comparison of the refractive index assignment in conventional TO with the assignment in the proposed framework. A different value of ρi corresponds to a different refractive index of the mesh element in the conventional case (top row), and to a different refractive index step profile in the grayscale case (bottom row). The step is smoothed over a distance of 10 nm in the grayscale case, which temporarily leads to a region of intermediate refractive indices.
Fig. 2
Fig. 2 Illustration of the problem setup for the design of the chiral nanostructure, with a zoomed-in view of the highlighted unit cell. The parameters are h: 340 nm, w: 100 nm, t: 300 nm, p: 500 nm.
Fig. 3
Fig. 3 Optimization results for the 520-nm case and 800-nm case showing their respective (a, g) optimized topologies of a unit cell, (b, h) transmission into the zeroth diffraction order for LCP and RCP light, (c, i) CD, (d, j) near-field intensity pattern along a cross-section of the unit cell at LCP and RCP illumination, (e, k) diffraction order transmission, (f, l) diffraction order reflection.
Fig. 4
Fig. 4 Progression of the proposed TO with insets showing the field intensity. The power transmission into one output port is 12%, 36%, and 44% after 2, 7, and 15 iterations, respectively. An animation of the optimization during the iteration is available in Visualization 1.
Fig. 5
Fig. 5 (a, c) Final optimized topology of the continuous grayscale and 4-level grayscale designs, and (b, d) their respective intensity profiles, (e) transmission spectrum (into one port) of the optimized 3-dB power splitter for the continuous grayscale and the 4-level grayscale designs.
Fig. 6
Fig. 6 Discretized projection using approximated Heaviside function showing the increasing discretization with increasing values of β for (a) 3-levels, and (b) 5-levels.

Equations (10)

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

n i = ϵ 1 + ρ i ( ϵ 2 ϵ 1 ) .
n(x,y,z)={ n 1 ,z>ρ(x,y)h n 2 ,zρ(x,y)h .
f 1 =( T LCP 0,0 T RCP 0,0 ).
f 2 = 1 2 S 1 ( E × H ) .d S .
ρ i filt = j N i ρ j v j w ij j N i v j w ij .
w ij =R| r i r j |,
p( ρ i ,β,η)= tanh(βη)+tanh(β( ρ i filt η)) tanh(βη)+tanh(β(1η)) .
ρ ˜ i =p( ρ i filt ,β,η).
ρ ˜ i (N) = k=1 N 1 N p(N ρ i filt (k1),β,η) .
ρ ˜ i (N) ={ 0if ρ ˜ i (N) <0 1if ρ ˜ i (N) >1 ρ ˜ i (N) else .

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