Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

R. Duggan, J. del Pino, E. Verhagen, and A. Alù, “Optomechanically induced birefringence and optomechanically induced Faraday effect,” Phys. Rev. Lett. 123(2), 023602 (2019).
[Crossref]

R. Duggan, D. Sounas, and A. Alù, “Optically driven effective Faraday effect in instantaneous nonlinear media,” Optica 6(9), 1152–1157 (2019).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

A. Honardoost, F. A. Juneghani, R. Safian, and S. Fathpour, “Towards subterahertz bandwidth ultracompact lithium niobate electrooptic modulators,” Opt. Express 27(5), 6495–6501 (2019).
[Crossref]

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Magnetic-free nonreciprocal photonic platform based on time-modulated graphene capacitors,” Phys. Rev. B 98(16), 165428 (2018).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

R. Yamaguchi, Y. Shoji, and T. Mizumoto, “Low-loss waveguide optical isolator with tapered mode converter and magneto-optical phase shifter for TE mode input,” Opt. Express 26(16), 21271–21278 (2018).
[Crossref]

E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

D. A. B. Miller, “Attojoule optoelectronics for low-energy information processing and communications,” J. Lightwave Technol. 35(3), 346–396 (2017).
[Crossref]

C. Zhang, P. Dulal, B. J. Stadler, and D. C. Hutchings, “Monolithically-integrated TE-mode 1D silicon-on-insulator isolators using seedlayer-free garnet,” Sci. Rep. 7(1), 5820 (2017).
[Crossref]

D. L. Sounas and A. Alù, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11(12), 774–783 (2017).
[Crossref]

C. Klitis, G. Cantarella, M. J. Strain, and M. Sorel, “High-extinction-ratio TE/TM selective bragg grating filters on silicon-on-insulator,” Opt. Lett. 42(15), 3040–3043 (2017).
[Crossref]

Y. Shi, W. Shin, and S. Fan, “Multi-frequency finite-difference frequency-domain algorithm for active nanophotonic device simulations,” Optica 3(11), 1256–1259 (2016).
[Crossref]

D. L. Sounas and A. Alù, “Angular-momentum-biased nanorings to realize magnetic-free integrated optical isolation,” ACS Photonics 1(3), 198–204 (2014).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: A review,” IEEE Photonics J. 6(1), 1–15 (2014).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

X. Xiao, H. Xu, X. Li, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed, low-loss silicon Mach-Zehnder modulators with doping optimization,” Opt. Express 21(4), 4116–4125 (2013).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

C. R. Doerr, N. Dupuis, and L. Zhang, “Optical isolator using two tandem phase modulators,” Opt. Lett. 36(21), 4293–4295 (2011).
[Crossref]

Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron. 16(2), 459–466 (2010).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006).
[Crossref]

L. Aplet and J. Carson, “A Faraday effect optical isolator,” Appl. Opt. 3(4), 544–545 (1964).
[Crossref]

R. Duggan, J. del Pino, E. Verhagen, and A. Alù, “Optomechanically induced birefringence and optomechanically induced Faraday effect,” Phys. Rev. Lett. 123(2), 023602 (2019).
[Crossref]

R. Duggan, D. Sounas, and A. Alù, “Optically driven effective Faraday effect in instantaneous nonlinear media,” Optica 6(9), 1152–1157 (2019).
[Crossref]

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Magnetic-free nonreciprocal photonic platform based on time-modulated graphene capacitors,” Phys. Rev. B 98(16), 165428 (2018).
[Crossref]

D. L. Sounas and A. Alù, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11(12), 774–783 (2017).
[Crossref]

D. L. Sounas and A. Alù, “Angular-momentum-biased nanorings to realize magnetic-free integrated optical isolation,” ACS Photonics 1(3), 198–204 (2014).
[Crossref]

L. Aplet and J. Carson, “A Faraday effect optical isolator,” Appl. Opt. 3(4), 544–545 (1964).
[Crossref]

E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

C. Klitis, G. Cantarella, M. J. Strain, and M. Sorel, “High-extinction-ratio TE/TM selective bragg grating filters on silicon-on-insulator,” Opt. Lett. 42(15), 3040–3043 (2017).
[Crossref]

L. Aplet and J. Carson, “A Faraday effect optical isolator,” Appl. Opt. 3(4), 544–545 (1964).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

X. Xiao, H. Xu, X. Li, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed, low-loss silicon Mach-Zehnder modulators with doping optimization,” Opt. Express 21(4), 4116–4125 (2013).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Magnetic-free nonreciprocal photonic platform based on time-modulated graphene capacitors,” Phys. Rev. B 98(16), 165428 (2018).
[Crossref]

R. Duggan, J. del Pino, E. Verhagen, and A. Alù, “Optomechanically induced birefringence and optomechanically induced Faraday effect,” Phys. Rev. Lett. 123(2), 023602 (2019).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

C. R. Doerr, N. Dupuis, and L. Zhang, “Optical isolator using two tandem phase modulators,” Opt. Lett. 36(21), 4293–4295 (2011).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

R. Duggan, D. Sounas, and A. Alù, “Optically driven effective Faraday effect in instantaneous nonlinear media,” Optica 6(9), 1152–1157 (2019).
[Crossref]

R. Duggan, J. del Pino, E. Verhagen, and A. Alù, “Optomechanically induced birefringence and optomechanically induced Faraday effect,” Phys. Rev. Lett. 123(2), 023602 (2019).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

C. Zhang, P. Dulal, B. J. Stadler, and D. C. Hutchings, “Monolithically-integrated TE-mode 1D silicon-on-insulator isolators using seedlayer-free garnet,” Sci. Rep. 7(1), 5820 (2017).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

C. R. Doerr, N. Dupuis, and L. Zhang, “Optical isolator using two tandem phase modulators,” Opt. Lett. 36(21), 4293–4295 (2011).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

Y. Shi, W. Shin, and S. Fan, “Multi-frequency finite-difference frequency-domain algorithm for active nanophotonic device simulations,” Optica 3(11), 1256–1259 (2016).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref]

Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron. 16(2), 459–466 (2010).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108(15), 153901 (2012).
[Crossref]

A. Honardoost, F. A. Juneghani, R. Safian, and S. Fathpour, “Towards subterahertz bandwidth ultracompact lithium niobate electrooptic modulators,” Opt. Express 27(5), 6495–6501 (2019).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Magnetic-free nonreciprocal photonic platform based on time-modulated graphene capacitors,” Phys. Rev. B 98(16), 165428 (2018).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

A. Honardoost, F. A. Juneghani, R. Safian, and S. Fathpour, “Towards subterahertz bandwidth ultracompact lithium niobate electrooptic modulators,” Opt. Express 27(5), 6495–6501 (2019).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
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Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

C. Zhang, P. Dulal, B. J. Stadler, and D. C. Hutchings, “Monolithically-integrated TE-mode 1D silicon-on-insulator isolators using seedlayer-free garnet,” Sci. Rep. 7(1), 5820 (2017).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

A. Honardoost, F. A. Juneghani, R. Safian, and S. Fathpour, “Towards subterahertz bandwidth ultracompact lithium niobate electrooptic modulators,” Opt. Express 27(5), 6495–6501 (2019).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

C. Klitis, G. Cantarella, M. J. Strain, and M. Sorel, “High-extinction-ratio TE/TM selective bragg grating filters on silicon-on-insulator,” Opt. Lett. 42(15), 3040–3043 (2017).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
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L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
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E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

R. Yamaguchi, Y. Shoji, and T. Mizumoto, “Low-loss waveguide optical isolator with tapered mode converter and magneto-optical phase shifter for TE mode input,” Opt. Express 26(16), 21271–21278 (2018).
[Crossref]

E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: A review,” IEEE Photonics J. 6(1), 1–15 (2014).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

A. Honardoost, F. A. Juneghani, R. Safian, and S. Fathpour, “Towards subterahertz bandwidth ultracompact lithium niobate electrooptic modulators,” Opt. Express 27(5), 6495–6501 (2019).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
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Y. Shi, W. Shin, and S. Fan, “Multi-frequency finite-difference frequency-domain algorithm for active nanophotonic device simulations,” Optica 3(11), 1256–1259 (2016).
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Y. Shi, W. Shin, and S. Fan, “Multi-frequency finite-difference frequency-domain algorithm for active nanophotonic device simulations,” Optica 3(11), 1256–1259 (2016).
[Crossref]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006).
[Crossref]

R. Yamaguchi, Y. Shoji, and T. Mizumoto, “Low-loss waveguide optical isolator with tapered mode converter and magneto-optical phase shifter for TE mode input,” Opt. Express 26(16), 21271–21278 (2018).
[Crossref]

E. Ishida, K. Miura, Y. Shoji, H. Yokoi, T. Mizumoto, N. Nishiyama, and S. Arai, “Amorphous-Si waveguide on a garnet magneto-optical isolator with a TE mode nonreciprocal phase shift,” Opt. Express 25(1), 452–462 (2017).
[Crossref]

C. Klitis, G. Cantarella, M. J. Strain, and M. Sorel, “High-extinction-ratio TE/TM selective bragg grating filters on silicon-on-insulator,” Opt. Lett. 42(15), 3040–3043 (2017).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

R. Duggan, D. Sounas, and A. Alù, “Optically driven effective Faraday effect in instantaneous nonlinear media,” Optica 6(9), 1152–1157 (2019).
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D. L. Sounas and A. Alù, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11(12), 774–783 (2017).
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D. L. Sounas and A. Alù, “Angular-momentum-biased nanorings to realize magnetic-free integrated optical isolation,” ACS Photonics 1(3), 198–204 (2014).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

K. Srinivasan, C. Zhang, P. Dulal, C. Radu, T. E. Gage, D. C. Hutchings, and B. J. Stadler, “High-gyrotropy seedlayer-free Ce: TbIG for monolithic laser-matched SOI optical isolators,” ACS Photonics 6(10), 2455–2461 (2019).
[Crossref]

C. Zhang, P. Dulal, B. J. Stadler, and D. C. Hutchings, “Monolithically-integrated TE-mode 1D silicon-on-insulator isolators using seedlayer-free garnet,” Sci. Rep. 7(1), 5820 (2017).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: A review,” IEEE Photonics J. 6(1), 1–15 (2014).
[Crossref]

C. Klitis, G. Cantarella, M. J. Strain, and M. Sorel, “High-extinction-ratio TE/TM selective bragg grating filters on silicon-on-insulator,” Opt. Lett. 42(15), 3040–3043 (2017).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
[Crossref]

D. C. Hutchings, B. M. Holmes, C. Zhang, P. Dulal, A. D. Block, S.-Y. Sung, N. C. Seaton, and B. J. Stadler, “Quasi-phase-matched Faraday rotation in semiconductor waveguides with a magnetooptic cladding for monolithically integrated optical isolators,” IEEE Photonics J. 5(6), 6602512 (2013).
[Crossref]

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. Hu, D. J. Thomson, K. Li, P. R. Wilson, S.-W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is–and what is not–an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on “ Nonreciprocal light propagation in a silicon photonic circuit”,” Science 335(6064), 38 (2012).
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Y. Zhang, Q. Du, C. Wang, T. Fakhrul, S. Liu, L. Deng, D. Huang, P. Pintus, J. Bowers, C. A. Ross, J. Hu, and L. Bi, “Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics,” Optica 6(4), 473–478 (2019).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006).
[Crossref]

M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019).
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