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

[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, 378–382 (2015).

[Crossref]

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

[Crossref]

X. Guo, W. Zhang, and W. Zhong, “Explicit feature control in structural topology optimization via level set method,” Comput. Methods Appl. Mech. Engrg. 272, 354–378 (2014).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, “Feasible adjoint sensitivity technique for EM design optimization,” IEEE Trans. Microwave Theory Tech. 50, 2751–2758 (2002).

[Crossref]

O. J. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909 (1998).

[Crossref]

G. F. Oster, N. Shubin, J. D. Murray, and P. Alberch, “Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny,” Evolution 42, 862–884 (1988).

[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).

[Crossref]

S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations,” J. Comput. Phys. 79, 12–49 (1988).

[Crossref]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705 (1973).

[Crossref]

G. F. Oster, N. Shubin, J. D. Murray, and P. Alberch, “Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny,” Evolution 42, 862–884 (1988).

[Crossref]

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

[Crossref]

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, “Feasible adjoint sensitivity technique for EM design optimization,” IEEE Trans. Microwave Theory Tech. 50, 2751–2758 (2002).

[Crossref]

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, “Feasible adjoint sensitivity technique for EM design optimization,” IEEE Trans. Microwave Theory Tech. 50, 2751–2758 (2002).

[Crossref]

M. P. Bendsøe and O. Sigmund, Topology Optimization Theory, Methods and Applications (Springer, 2003).

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).

[Crossref]

P. D. Dunning and H. A. Kim, “A new hole insertion method for level set based structural topology optimization,” Int. J. Numer. Methods Eng. 93(1), 118–134 (2013).

[Crossref]

E. N. Economou, Green’s Functions in Quantum Physics, 2nd ed. (Springer-Verlag, 1990).

S. Boutami and S. Fan, “Efficient pixel-by-pixel optimization of photonic devices utilizing the Dyson’s equation in a Green function formalism: Part II. implementation using standard electromagnetic solvers,” J. Opt. Soc. Am. B 36, 2387–2394 (2019).

[Crossref]

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]

V. Liu, Y. Jiao, D. A. Miller, and S. Fan, “Design methodology for compact photonic-crystal-based wavelength division multiplexers,” Opt. Lett. 36, 591–593 (2011).

[Crossref]

G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29, 2288–2290 (2004).

[Crossref]

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B 12, 1267–1272 (1995).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, “Feasible adjoint sensitivity technique for EM design optimization,” IEEE Trans. Microwave Theory Tech. 50, 2751–2758 (2002).

[Crossref]

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, “Feasible adjoint sensitivity technique for EM design optimization,” IEEE Trans. Microwave Theory Tech. 50, 2751–2758 (2002).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

X. Guo, W. Zhang, and W. Zhong, “Explicit feature control in structural topology optimization via level set method,” Comput. Methods Appl. Mech. Engrg. 272, 354–378 (2014).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

P. D. Dunning and H. A. Kim, “A new hole insertion method for level set based structural topology optimization,” Int. J. Numer. Methods Eng. 93(1), 118–134 (2013).

[Crossref]

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

[Crossref]

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

[Crossref]

J. Lu and J. Vučković, “Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes,” Opt. Express 20, 7221–7236 (2012).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[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, 378–382 (2015).

[Crossref]

G. F. Oster, N. Shubin, J. D. Murray, and P. Alberch, “Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny,” Evolution 42, 862–884 (1988).

[Crossref]

S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations,” J. Comput. Phys. 79, 12–49 (1988).

[Crossref]

G. F. Oster, N. Shubin, J. D. Murray, and P. Alberch, “Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny,” Evolution 42, 862–884 (1988).

[Crossref]

D. Pavesi, Silicon Fundamentals for Photonics Applications. Silicon photonics (2004).

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705 (1973).

[Crossref]

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

[Crossref]

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

[Crossref]

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

[Crossref]

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

[Crossref]

O. J. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909 (1998).

[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, 378–382 (2015).

[Crossref]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705 (1973).

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations,” J. Comput. Phys. 79, 12–49 (1988).

[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, 378–382 (2015).

[Crossref]

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]

G. F. Oster, N. Shubin, J. D. Murray, and P. Alberch, “Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny,” Evolution 42, 862–884 (1988).

[Crossref]

M. P. Bendsøe and O. Sigmund, Topology Optimization Theory, Methods and Applications (Springer, 2003).

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

[Crossref]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

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

[Crossref]

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

[Crossref]

J. Lu and J. Vučković, “Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes,” Opt. Express 20, 7221–7236 (2012).

[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, 378–382 (2015).

[Crossref]

X. Guo, W. Zhang, and W. Zhong, “Explicit feature control in structural topology optimization via level set method,” Comput. Methods Appl. Mech. Engrg. 272, 354–378 (2014).

[Crossref]

X. Guo, W. Zhang, and W. Zhong, “Explicit feature control in structural topology optimization via level set method,” Comput. Methods Appl. Mech. Engrg. 272, 354–378 (2014).

[Crossref]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705 (1973).

[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).

[Crossref]

X. Guo, W. Zhang, and W. Zhong, “Explicit feature control in structural topology optimization via level set method,” Comput. Methods Appl. Mech. Engrg. 272, 354–378 (2014).

[Crossref]

G. F. Oster, N. Shubin, J. D. Murray, and P. Alberch, “Evolution and morphogenetic rules: the shape of the vertebrate limb in ontogeny and phylogeny,” Evolution 42, 862–884 (1988).

[Crossref]

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, “Feasible adjoint sensitivity technique for EM design optimization,” IEEE Trans. Microwave Theory Tech. 50, 2751–2758 (2002).

[Crossref]

P. D. Dunning and H. A. Kim, “A new hole insertion method for level set based structural topology optimization,” Int. J. Numer. Methods Eng. 93(1), 118–134 (2013).

[Crossref]

S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations,” J. Comput. Phys. 79, 12–49 (1988).

[Crossref]

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]

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B 12, 1267–1272 (1995).

[Crossref]

S. Boutami and S. Fan, “Efficient pixel-by-pixel optimization of photonic devices utilizing the Dyson’s equation in a Green function formalism: Part II. implementation using standard electromagnetic solvers,” J. Opt. Soc. Am. B 36, 2387–2394 (2019).

[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, 378–382 (2015).

[Crossref]

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

[Crossref]

M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15, 4694–4704 (2007).

[Crossref]

J. Lu and J. Vučković, “Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes,” Opt. Express 20, 7221–7236 (2012).

[Crossref]

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]

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).

[Crossref]

V. Liu, Y. Jiao, D. A. Miller, and S. Fan, “Design methodology for compact photonic-crystal-based wavelength division multiplexers,” Opt. Lett. 36, 591–593 (2011).

[Crossref]

G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29, 2288–2290 (2004).

[Crossref]

O. J. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909 (1998).

[Crossref]

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

[Crossref]

O. D. Miller, “Photonic design: from fundamental solar cell physics to computational inverse design,” arXiv:1308.0212 (2013).

D. Pavesi, Silicon Fundamentals for Photonics Applications. Silicon photonics (2004).

M. P. Bendsøe and O. Sigmund, Topology Optimization Theory, Methods and Applications (Springer, 2003).

E. N. Economou, Green’s Functions in Quantum Physics, 2nd ed. (Springer-Verlag, 1990).