Abstract

We present a gradient-based algorithm to design general 1D grating couplers without any human input from start to finish, including a choice of initial condition. We show that we can reliably design efficient couplers to have multiple functionalities in different geometries, including conventional couplers for single-polarization and single-wavelength operation, polarization-insensitive couplers, and wavelength-demultiplexing couplers. In particular, we design a fiber-to-chip blazed grating with under 0.2 dB insertion loss that requires a single etch to fabricate and no back-reflector.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Binary particle swarm optimized 2  ×  2 power splitters in a standard foundry silicon photonic platform

Jason C. C. Mak, Constantine Sideris, Junho Jeong, Ali Hajimiri, and Joyce K. S. Poon
Opt. Lett. 41(16) 3868-3871 (2016)

A compact and low loss Y-junction for submicron silicon waveguide

Yi Zhang, Shuyu Yang, Andy Eu-Jin Lim, Guo-Qiang Lo, Christophe Galland, Tom Baehr-Jones, and Michael Hochberg
Opt. Express 21(1) 1310-1316 (2013)

Inverse design of near unity efficiency perfectly vertical grating couplers

Andrew Michaels and Eli Yablonovitch
Opt. Express 26(4) 4766-4779 (2018)

References

  • View by:
  • |
  • |
  • |

  1. L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University Press, 2015).
    [Crossref]
  2. R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, and S. Laval, “High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide,” Appl. Opt. 39, 5773–5777 (2000).
    [Crossref]
  3. A. Bozzola, L. Carroll, D. Gerace, I. Cristiani, and L. C. Andreani, “Optimising apodized grating couplers in a pure SOI platform to −0.5 db coupling efficiency,” Opt. Express 23, 16289–16304 (2015).
    [Crossref] [PubMed]
  4. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29, 2749–2751 (2004).
    [Crossref] [PubMed]
  5. X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
    [Crossref]
  6. F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
    [Crossref]
  7. W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective cmos-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20, B238–B243 (2012).
    [Crossref] [PubMed]
  8. B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
    [Crossref] [PubMed]
  9. W. D. Sacher, Y. Huang, L. Ding, B. J. Taylor, H. Jayatilleka, G.-Q. Lo, and J. K. Poon, “Wide bandwidth and high coupling efficiency si3n4-on-SOI dual-level grating coupler,” Opt. Express 22, 10938–10947 (2014).
    [Crossref] [PubMed]
  10. A. Michaels and E. Yablonovtich, “Inverse design of near unity efficiency perfectly vertical grating couplers,” arXiv preprint arXiv:1705.07186 (2017).
  11. C. Li, H. Zhang, M. Yu, and G. Lo, “Cmos-compatible high efficiency double-etched apodized waveguide grating coupler,” Opt. Express 21, 7868–7874 (2013).
    [Crossref] [PubMed]
  12. X. Chen, D. J. Thomson, L. Crudginton, A. Z. Khokhar, and G. T. Reed, “Dual-etch apodised grating couplers for efficient fibre-chip coupling near 1310 nm wavelength,” Opt. Express 25, 17864–17871 (2017).
    [Crossref] [PubMed]
  13. G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency silicon-on-insulator grating coupler based on a poly-silicon overlay,” Opt. Express 14, 11622–11630 (2006).
    [Crossref] [PubMed]
  14. D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced cmos-compatible silicon-on-insulator platform,” Opt. Express 18, 18278–18283 (2010).
    [Crossref] [PubMed]
  15. M. Matsumoto, “Analysis of the blazing effect in second-order gratings,” IEEE J. of Quantum Electron. 28, 2016–2023 (1992).
    [Crossref]
  16. B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884–1886 (2005).
    [Crossref]
  17. J. Yang, Z. Zhou, H. Jia, X. Zhang, and S. Qin, “High-performance and compact binary blazed grating coupler based on an asymmetric subgrating structure and vertical coupling,” Opt. Lett. 36, 2614–2617 (2011).
    [Crossref] [PubMed]
  18. N. Na, H. Frish, I.-W. Hsieh, O. Harel, R. George, A. Barkai, and H. Rong, “Efficient broadband silicon-on-insulator grating coupler with low backreflection,” Opt. Lett. 36, 2101–2103 (2011).
    [Crossref] [PubMed]
  19. A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 db efficiency,” Opt. Lett. 41, 3013–3016 (2016).
    [Crossref]
  20. J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
    [Crossref]
  21. J. Covey and R. T. Chen, “Efficient surface normal multi-stage grating couplers in silicon based waveguides,” in “Optical Interconnects Conference, 2013 IEEE,” (IEEE, 2013), pp. 130–131.
  22. W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus, and J. Burghartz, “Bridging the gap between optical fibers and silicon photonic integrated circuits,” Opt. Express 22, 1277–1286 (2014).
    [Crossref] [PubMed]
  23. Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant, “Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces,” Opt. Express 22, 18224–18231 (2014).
    [Crossref] [PubMed]
  24. B. Wohlfeil, L. Zimmermann, and K. Petermann, “Optimization of fiber grating couplers on SOI using advanced search algorithms,” Opt. Lett. 39, 3201–3203 (2014).
    [Crossref] [PubMed]
  25. R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
    [Crossref]
  26. C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design,” Opt. Express 21, 21693–21701 (2013).
    [Crossref] [PubMed]
  27. Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117, 107402 (2016).
    [Crossref] [PubMed]
  28. 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, 16866–16873 (2016).
    [Crossref] [PubMed]
  29. D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-angle, multifunctional metagratings based on freeform multimode geometries,” Nano Lett. 17, 3752–3757 (2017).
    [Crossref] [PubMed]
  30. L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
    [Crossref]
  31. A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7, 1786 (2017).
    [Crossref] [PubMed]
  32. R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
    [Crossref]
  33. D. Kraft, “A software package for sequential quadratic programming,” Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt (1988).
  34. W. Shin and S. Fan, “Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell’s equations solvers,” J. Comput. Phys. 231, 3406–3431 (2012).
    [Crossref]
  35. W. Shin and S. Fan, “Accelerated solution of the frequency-domain Maxwell’s equations by engineering the eigenvalue distribution,” Opt. Express 21, 22578–22595 (2013).
    [Crossref] [PubMed]
  36. K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
    [Crossref]
  37. Z. Cheng and H. K. Tsang, “Experimental demonstration of polarization-insensitive air-cladding grating couplers for silicon-on-insulator waveguides,” Opt. Lett. 39, 2206–2209 (2014).
    [Crossref] [PubMed]
  38. G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon-on-insulator ultra-compact duplexer based on a diffractive grating structure,” Opt. Express 15, 10091–10096 (2007).
    [Crossref] [PubMed]
  39. M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
    [Crossref]
  40. 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, 7210 (2014).
    [PubMed]

2017 (3)

X. Chen, D. J. Thomson, L. Crudginton, A. Z. Khokhar, and G. T. Reed, “Dual-etch apodised grating couplers for efficient fibre-chip coupling near 1310 nm wavelength,” Opt. Express 25, 17864–17871 (2017).
[Crossref] [PubMed]

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

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

2016 (3)

2015 (1)

2014 (7)

W. D. Sacher, Y. Huang, L. Ding, B. J. Taylor, H. Jayatilleka, G.-Q. Lo, and J. K. Poon, “Wide bandwidth and high coupling efficiency si3n4-on-SOI dual-level grating coupler,” Opt. Express 22, 10938–10947 (2014).
[Crossref] [PubMed]

W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus, and J. Burghartz, “Bridging the gap between optical fibers and silicon photonic integrated circuits,” Opt. Express 22, 1277–1286 (2014).
[Crossref] [PubMed]

Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant, “Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces,” Opt. Express 22, 18224–18231 (2014).
[Crossref] [PubMed]

B. Wohlfeil, L. Zimmermann, and K. Petermann, “Optimization of fiber grating couplers on SOI using advanced search algorithms,” Opt. Lett. 39, 3201–3203 (2014).
[Crossref] [PubMed]

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

Z. Cheng and H. K. Tsang, “Experimental demonstration of polarization-insensitive air-cladding grating couplers for silicon-on-insulator waveguides,” Opt. Lett. 39, 2206–2209 (2014).
[Crossref] [PubMed]

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, 7210 (2014).
[PubMed]

2013 (4)

2012 (2)

W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective cmos-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20, B238–B243 (2012).
[Crossref] [PubMed]

W. Shin and S. Fan, “Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell’s equations solvers,” J. Comput. Phys. 231, 3406–3431 (2012).
[Crossref]

2011 (2)

2010 (3)

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced cmos-compatible silicon-on-insulator platform,” Opt. Express 18, 18278–18283 (2010).
[Crossref] [PubMed]

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
[Crossref]

2007 (2)

G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon-on-insulator ultra-compact duplexer based on a diffractive grating structure,” Opt. Express 15, 10091–10096 (2007).
[Crossref] [PubMed]

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[Crossref]

2006 (1)

2005 (1)

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884–1886 (2005).
[Crossref]

2004 (2)

2000 (1)

1995 (1)

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[Crossref]

1993 (1)

K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
[Crossref]

1992 (1)

M. Matsumoto, “Analysis of the blazing effect in second-order gratings,” IEEE J. of Quantum Electron. 28, 2016–2023 (1992).
[Crossref]

Absil, P.

Alonso-Ramos, C. A.

Andkjær, J.

J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
[Crossref]

Andreani, L. C.

Ayre, M.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[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, 7210 (2014).
[PubMed]

Baehr-Jones, T.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
[Crossref]

Baets, R.

Barkai, A.

Bates, K. A.

K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
[Crossref]

Berroth, M.

Bhargava, S.

Bienstman, P.

Bogaerts, W.

Bojko, R.

Bozzola, A.

Burghartz, J.

Burke, J. J.

K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
[Crossref]

Butschke, J.

Byrd, R. H.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[Crossref]

Carroll, L.

Cheben, P.

Chen, R. T.

J. Covey and R. T. Chen, “Efficient surface normal multi-stage grating couplers in silicon based waveguides,” in “Optical Interconnects Conference, 2013 IEEE,” (IEEE, 2013), pp. 130–131.

Chen, X.

X. Chen, D. J. Thomson, L. Crudginton, A. Z. Khokhar, and G. T. Reed, “Dual-etch apodised grating couplers for efficient fibre-chip coupling near 1310 nm wavelength,” Opt. Express 25, 17864–17871 (2017).
[Crossref] [PubMed]

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

Cheng, Z.

Cher, R. T. P.

Chrostowski, L.

Covey, J.

J. Covey and R. T. Chen, “Efficient surface normal multi-stage grating couplers in silicon based waveguides,” in “Optical Interconnects Conference, 2013 IEEE,” (IEEE, 2013), pp. 130–131.

Cristiani, I.

Crudginton, L.

Ding, L.

Ding, Y.

Doshay, S.

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

Fan, J. A.

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

Fan, S.

W. Shin and S. Fan, “Accelerated solution of the frequency-domain Maxwell’s equations by engineering the eigenvalue distribution,” Opt. Express 21, 22578–22595 (2013).
[Crossref] [PubMed]

W. Shin and S. Fan, “Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell’s equations solvers,” J. Comput. Phys. 231, 3406–3431 (2012).
[Crossref]

Frandsen, L. H.

Frellsen, L. F.

Frish, H.

Fung, C. K.

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

George, R.

Gerace, D.

Ghosh, S.

Gualous, H.

Guan, H.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

Halir, R.

Harel, O.

Hochberg, M.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
[Crossref]

L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University Press, 2015).
[Crossref]

Hsieh, I.-W.

Huang, Y.

Jayatilleka, H.

Jia, H.

Jiang, J.

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884–1886 (2005).
[Crossref]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
[Crossref] [PubMed]

Khokhar, A. Z.

Koster, A.

Kraft, D.

D. Kraft, “A software package for sequential quadratic programming,” Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt (1988).

Krauss, T. F.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[Crossref]

Kunze, A.

Lagoudakis, K. G.

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, 7210 (2014).
[PubMed]

Lalau-Keraly, C. M.

Laval, S.

Layadi, A.

Lepage, G.

Letzkus, F.

Li, C.

C. Li, H. Zhang, M. Yu, and G. Lo, “Cmos-compatible high efficiency double-etched apodized waveguide grating coupler,” Opt. Express 21, 7868–7874 (2013).
[Crossref] [PubMed]

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

Li, L.

K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
[Crossref]

Lim, A. E.-J.

Lim, E.-J.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

Lin, Z.

Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117, 107402 (2016).
[Crossref] [PubMed]

Lo, G.

Lo, G.-Q.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

W. D. Sacher, Y. Huang, L. Ding, B. J. Taylor, H. Jayatilleka, G.-Q. Lo, and J. K. Poon, “Wide bandwidth and high coupling efficiency si3n4-on-SOI dual-level grating coupler,” Opt. Express 22, 10938–10947 (2014).
[Crossref] [PubMed]

Lo, P. G.-Q.

Lo, S. M.

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

Loncar, M.

Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117, 107402 (2016).
[Crossref] [PubMed]

Lu, J.

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, 7210 (2014).
[PubMed]

Lu, P.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[Crossref]

Luque-González, J. M.

Matsumoto, M.

M. Matsumoto, “Analysis of the blazing effect in second-order gratings,” IEEE J. of Quantum Electron. 28, 2016–2023 (1992).
[Crossref]

Michaels, A.

A. Michaels and E. Yablonovtich, “Inverse design of near unity efficiency perfectly vertical grating couplers,” arXiv preprint arXiv:1705.07186 (2017).

Miller, O. D.

Molina-Fernández, Í.

Na, N.

Nishiwaki, S.

J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
[Crossref]

Nocedal, J.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[Crossref]

Nomura, T.

J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
[Crossref]

Nordin, G. P.

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884–1886 (2005).
[Crossref]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
[Crossref] [PubMed]

Novack, A.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
[Crossref]

Orobtchouk, R.

Ortega-Moñux, A.

Pascal, D.

Patel, D.

Petermann, K.

Petykiewicz, J.

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

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, 7210 (2014).
[PubMed]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
[Crossref]

Pick, A.

Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117, 107402 (2016).
[Crossref] [PubMed]

Piggott, A. Y.

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

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, 7210 (2014).
[PubMed]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
[Crossref]

Plant, D. V.

Poon, J. K.

Qin, S.

Reed, G. T.

Rodriguez, A. W.

Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117, 107402 (2016).
[Crossref] [PubMed]

Roelkens, G.

Roncone, R. L.

K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
[Crossref]

Rong, H.

Rosa, M. F.

Sacher, W. D.

Samani, A.

Sánchez-Postigo, A.

Sapra, N. V.

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
[Crossref]

Schmid, J. H.

Schrauwen, J.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[Crossref]

Sell, D.

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

Selvaraja, S.

Shi, R.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
[Crossref]

Shi, W.

Shin, W.

W. Shin and S. Fan, “Accelerated solution of the frequency-domain Maxwell’s equations by engineering the eigenvalue distribution,” Opt. Express 21, 22578–22595 (2013).
[Crossref] [PubMed]

W. Shin and S. Fan, “Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell’s equations solvers,” J. Comput. Phys. 231, 3406–3431 (2012).
[Crossref]

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, 16866–16873 (2016).
[Crossref] [PubMed]

J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
[Crossref]

Streshinsky, M.

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
[Crossref]

Su, L.

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

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
[Crossref]

Taillaert, D.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[Crossref]

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29, 2749–2751 (2004).
[Crossref] [PubMed]

Taylor, B. J.

Thomson, D. J.

Tsang, H. K.

Z. Cheng and H. K. Tsang, “Experimental demonstration of polarization-insensitive air-cladding grating couplers for silicon-on-insulator waveguides,” Opt. Lett. 39, 2206–2209 (2014).
[Crossref] [PubMed]

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

Van Laere, F.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[Crossref]

Van Thourhout, D.

Veerasubramanian, V.

Verheyen, P.

Vermeulen, D.

Vogel, W.

Vuckovic, J.

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

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, 7210 (2014).
[PubMed]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
[Crossref]

Wang, B.

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884–1886 (2005).
[Crossref]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
[Crossref] [PubMed]

Wang, Y.

Wangüemert-Pérez, J. G.

Wohlfeil, B.

Yablonovitch, E.

Yablonovtich, E.

A. Michaels and E. Yablonovtich, “Inverse design of near unity efficiency perfectly vertical grating couplers,” arXiv preprint arXiv:1705.07186 (2017).

Yang, J.

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

J. Yang, Z. Zhou, H. Jia, X. Zhang, and S. Qin, “High-performance and compact binary blazed grating coupler based on an asymmetric subgrating structure and vertical coupling,” Opt. Lett. 36, 2614–2617 (2011).
[Crossref] [PubMed]

Yang, R.

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

Yu, M.

Zaoui, W. S.

Zhang, H.

Zhang, X.

Zhong, Q.

Zhou, Z.

Zhu, C.

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[Crossref]

Zimmermann, L.

Appl. Opt. (1)

Appl. Optics (1)

K. A. Bates, L. Li, R. L. Roncone, and J. J. Burke, “Gaussian beams from variable groove depth grating couplers in planar waveguides,” Appl. Optics 32, 2112–2116 (1993).
[Crossref]

IEEE J. of Quantum Electron. (1)

M. Matsumoto, “Analysis of the blazing effect in second-order gratings,” IEEE J. of Quantum Electron. 28, 2016–2023 (1992).
[Crossref]

IEEE Photon. Technol. Lett. (3)

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884–1886 (2005).
[Crossref]

X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

R. Shi, H. Guan, A. Novack, M. Streshinsky, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “High-efficiency grating couplers near 1310 nm fabricated by 248 nm duv lithography,” IEEE Photon. Technol. Lett. 26, 1569–1572 (2014).
[Crossref]

J. Comput. Phys. (1)

W. Shin and S. Fan, “Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell’s equations solvers,” J. Comput. Phys. 231, 3406–3431 (2012).
[Crossref]

J. Lightw. Technol. (1)

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightw. Technol. 25, 151–156 (2007).
[Crossref]

JOSA B (1)

J. Andkjær, S. Nishiwaki, T. Nomura, and O. Sigmund, “Topology optimization of grating couplers for the efficient excitation of surface plasmons,” JOSA B 27, 1828–1832 (2010).
[Crossref]

Nano Lett. (1)

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

Opt. Express (15)

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, 16866–16873 (2016).
[Crossref] [PubMed]

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

W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus, and J. Burghartz, “Bridging the gap between optical fibers and silicon photonic integrated circuits,” Opt. Express 22, 1277–1286 (2014).
[Crossref] [PubMed]

Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant, “Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces,” Opt. Express 22, 18224–18231 (2014).
[Crossref] [PubMed]

W. Shin and S. Fan, “Accelerated solution of the frequency-domain Maxwell’s equations by engineering the eigenvalue distribution,” Opt. Express 21, 22578–22595 (2013).
[Crossref] [PubMed]

G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon-on-insulator ultra-compact duplexer based on a diffractive grating structure,” Opt. Express 15, 10091–10096 (2007).
[Crossref] [PubMed]

M. Streshinsky, R. Shi, A. Novack, R. T. P. Cher, A. E.-J. Lim, P. G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform,” Opt. Express 21, 31019–31028 (2013).
[Crossref]

A. Bozzola, L. Carroll, D. Gerace, I. Cristiani, and L. C. Andreani, “Optimising apodized grating couplers in a pure SOI platform to −0.5 db coupling efficiency,” Opt. Express 23, 16289–16304 (2015).
[Crossref] [PubMed]

W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective cmos-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20, B238–B243 (2012).
[Crossref] [PubMed]

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
[Crossref] [PubMed]

W. D. Sacher, Y. Huang, L. Ding, B. J. Taylor, H. Jayatilleka, G.-Q. Lo, and J. K. Poon, “Wide bandwidth and high coupling efficiency si3n4-on-SOI dual-level grating coupler,” Opt. Express 22, 10938–10947 (2014).
[Crossref] [PubMed]

C. Li, H. Zhang, M. Yu, and G. Lo, “Cmos-compatible high efficiency double-etched apodized waveguide grating coupler,” Opt. Express 21, 7868–7874 (2013).
[Crossref] [PubMed]

X. Chen, D. J. Thomson, L. Crudginton, A. Z. Khokhar, and G. T. Reed, “Dual-etch apodised grating couplers for efficient fibre-chip coupling near 1310 nm wavelength,” Opt. Express 25, 17864–17871 (2017).
[Crossref] [PubMed]

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency silicon-on-insulator grating coupler based on a poly-silicon overlay,” Opt. Express 14, 11622–11630 (2006).
[Crossref] [PubMed]

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced cmos-compatible silicon-on-insulator platform,” Opt. Express 18, 18278–18283 (2010).
[Crossref] [PubMed]

Opt. Lett. (6)

Phys. Rev. Lett. (1)

Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, “Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals,” Phys. Rev. Lett. 117, 107402 (2016).
[Crossref] [PubMed]

Sci. Rep. (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, 7210 (2014).
[PubMed]

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

SIAM J. Sci. Comput. (1)

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput. 16, 1190–1208 (1995).
[Crossref]

Other (5)

D. Kraft, “A software package for sequential quadratic programming,” Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt (1988).

L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University Press, 2015).
[Crossref]

L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vučković, “Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer,” ACS Photonics (2017).
[Crossref]

J. Covey and R. T. Chen, “Efficient surface normal multi-stage grating couplers in silicon based waveguides,” in “Optical Interconnects Conference, 2013 IEEE,” (IEEE, 2013), pp. 130–131.

A. Michaels and E. Yablonovtich, “Inverse design of near unity efficiency perfectly vertical grating couplers,” arXiv preprint arXiv:1705.07186 (2017).

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 (7)

Fig. 1
Fig. 1 a) Schematic of a typical optimized grating used in the study. b) Close-up schematic of the device. c) Distribution of efficiencies for 100 optimization runs for different discretization procedures for 50 nm and 100 nm feature sizes. Each optimization run ran for a maximum of 400 iterations (100 for continuous stage and 300 for discrete stage). The orange shows the distribution of efficiencies achieved at the end of the continuous stage while the blue shows the distribution at the end of the discrete stage. Notice that forgoing the continuous optimization step leads to worse-performing devices.
Fig. 2
Fig. 2 Grating coupler design for 220 nm SOI platform. The angle of incidence is at 10° from the normal. a) The grating coupler design. The minimum feature size is 100 nm. b) Close-up schematic of the design. c) Simulated coupling efficiency spectrum. The minimum insertion loss is 1.94 dB, and the 1-dB bandwidth is 34 nm.
Fig. 3
Fig. 3 Grating coupler design for 220 nm SOI platform. The device is designed for normal incidence operation. a) The grating coupler design. The minimum feature size is 65 nm. b) Close-up schematic of the design. c) Simulated coupling efficiency spectrum. The minimum insertion loss is 0.25 dB, and the 1-dB bandwidth is 22 nm.
Fig. 4
Fig. 4 Blazed grating coupler with under 0.2 dB loss. a) Fully continuous design that motivates the blazed gratings. By allowing permittivity distribution in the entire coupler to vary continuously between that of air and silicon, the optimized device has over 99% coupling efficiency and suggests that blazed gratings would have improved efficiency compared with vertically-etched gratings. b) The grating coupler design. The device is designed for normal incidence operation. The minimum feature size is 50 nm, and the blazed angle is at 50 degrees from the normal. c) Close-up schematic of the design. d) Simulated coupling efficiency spectrum. The minimum insertion loss is 0.17 dB, and the 1-dB bandwidth is 26 nm.
Fig. 5
Fig. 5 Polarization-insensitive grating coupler design for 220 nm SOI platform. The TE Gaussian mode is coupled to the TE0 mode of the waveguide and the TM Gaussian mode is coupled to the TM0 mode of the waveguide. The device is designed for normal incidence operation. a) The grating coupler design. The minimum feature size is 50 nm. b) Close-up schematic of the design. c) Simulated coupling efficiency spectrum. The minimum insertion loss is 2.9 dB for TE mode and 3.6 dB for TM mode. The 1-dB bandwidth is 28 nm for both modes.
Fig. 6
Fig. 6 Wavelength-demultiplexing grating coupler that sends 1310 nm into the left waveguide and 1490 nm into the right waveguide. The device is designed for normal incidence operation. a) The grating coupler design. The minimum feature size is 50 nm. b) Close-up schematic of the design. c) Simulated coupling efficiency spectrum. The minimum insertion loss is 1.5 dB at 1310 nm and 1.6 dB at 1490 nm with over 21 dB crosstalk suppression. The 1-dB bandwidth is 20 nm at 1310 nm and 24 nm at 1490 nm.
Fig. 7
Fig. 7 Wavelength-demultiplexing grating coupler that splits 1310 nm and 1490 nm in the pass-through configuration. The device is designed for normal incidence operation. a) The pass-through grating coupler geometry used as an optical transceiver. The transmitting laser (blue) couples through an on-chip waveguide to the fiber whereas the receiving wavelength (red) passes through the grating and is detected with a photodetector. b) The grating coupler design. c) Close-up schematic of the design. The minimum feature size is 50 nm. d) Real part of the TE mode electric field at 1310 nm. e) Real part of the TE mode electric field at 1490 nm. f) Simulated coupling efficiency spectrum. The minimum insertion loss is 1.0 dB at 1310 nm and 0.08 dB at 1490 nm. The 1-dB bandwidth is 28 nm at 1310 nm.

Equations (5)

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

minimize p , E 1 , E 2 , , E m i f i ( E i ) subject to × 1 μ 0 × E i ω i 2 ( p ) E i = i ω i J i , i = 1 , 2 , , m
f i M ( E i ) = I + ( | ( E i ) | α i ) + I ( | ( E i ) | β i )
f i P ( E i ) = [ E i × H i * ] d S
minimize p , n R ( p ) q 2 subject to p i + 1 p i + d p 1 0 p n L
minimize q A q q 2 subject to 0 q i 1

Metrics