Abstract

We applied nonlinear optimization to design integrated digital metamaterials in silicon for unidirectional energy flow. Two devices, one for each polarization state, were designed, fabricated, and characterized. Both devices offer comparable or higher transmission efficiencies and extinction ratios, are easier to fabricate, exhibit larger bandwidths and are more tolerant to fabrication errors, when compared to alternatives. Furthermore, each device footprint is only 3μm × 3μm, which is the smallest optical diode ever reported. To illustrate the versatility of digital metamaterials, we also designed a polarization-independent optical diode.

© 2015 Optical Society of America

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References

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2014 (7)

2013 (4)

J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21(11), 13351–13367 (2013).
[Crossref] [PubMed]

G. Kim, J.-A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

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]

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

2012 (4)

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci Rep 2, 674 (2012).
[PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012).
[Crossref] [PubMed]

2011 (4)

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

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

L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011).
[Crossref] [PubMed]

C. Wang, C. Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express 19(27), 26948–26955 (2011).
[Crossref] [PubMed]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

2009 (1)

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

2007 (1)

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90(2), 023514 (2007).
[Crossref]

2005 (2)

2004 (2)

Akosman, A. E.

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Baets, R.

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]

Bahlmann, N.

Bi, L.

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

Bremel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Chen, H.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Chen, Y.-F.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Ding, Y.

Dionne, G. F.

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

Doerr, C. R.

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]

Dominguez-Caballero, J.-A.

G. Kim, J.-A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Dötsch, H.

Eich, M.

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]

Espinola, R. L.

Fainman, Y.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Fan, S.

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]

V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012).
[Crossref] [PubMed]

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

Feng, L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Freude, W.

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]

Friedman, D. J.

G. Kim, J.-A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Gerhardt, R.

Gu, C.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Guo, X.

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90(2), 023514 (2007).
[Crossref]

Hammer, M.

Hertel, P.

Hou, B.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Hu, J.

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

Huang, J.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Hvam, J. M.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Izuhara, T.

Jalas, D.

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]

Jiang, P.

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

Joannopoulos, J. D.

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]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[Crossref] [PubMed]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Kan, Q.

Kim, D. H.

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

Kim, G.

G. Kim and R. Menon, “An ultra-small three dimensional computational microscope,” Appl. Phys. Lett. 105(6), 061114 (2014).
[Crossref]

G. Kim, J.-A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Kimerling, L. C.

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

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).
[Crossref] [PubMed]

Lai, Y.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Lee, H.

G. Kim, J.-A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Levy, M. A.

Li, J.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Li, Z. Y.

Liu, L.

Liu, V.

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).
[Crossref] [PubMed]

J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21(11), 13351–13367 (2013).
[Crossref] [PubMed]

Lu, M.-H.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Melloni, A.

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]

Menon, R.

Miller, D. A. B.

Mutlu, M.

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Osgood, R. M.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Ozbay, E.

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

Petrov, A.

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]

Petykiewicz, 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).
[Crossref] [PubMed]

Piggott, A. Y.

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).
[Crossref] [PubMed]

Polson, R.

Popkov, A. F.

Popovic, M.

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]

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Ram, R. J.

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90(2), 023514 (2007).
[Crossref]

Renner, H.

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]

Ross, C. A.

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

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Scherer, A.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Serebryannikov, A. E.

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

Shen, B.

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Soljacic, M.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[Crossref] [PubMed]

Tsai, M.-C.

Vanwolleghem, M.

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]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Vuckovic, 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).
[Crossref] [PubMed]

J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21(11), 13351–13367 (2013).
[Crossref] [PubMed]

Wang, C.

Wang, G. P.

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Wang, P.

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Wilkens, L.

Xu, Y.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Xu, Y.-L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Yu, Z.

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]

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

Yvind, K.

Zaman, T. R.

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90(2), 023514 (2007).
[Crossref]

Zhang, Y.

Zhong, X. L.

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci Rep 2, 674 (2012).
[PubMed]

Zhou, C. Z.

Zhuromskyy, O.

Appl. Phys. Lett. (2)

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” Appl. Phys. Lett. 90(2), 023514 (2007).
[Crossref]

G. Kim and R. Menon, “An ultra-small three dimensional computational microscope,” Appl. Phys. Lett. 105(6), 061114 (2014).
[Crossref]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref] [PubMed]

Nat. Mater. (1)

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[Crossref] [PubMed]

Nat. Photonics (3)

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

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

Opt. Express (6)

Opt. Lett. (3)

Optica (1)

Phys. Rev. Lett. (2)

G. Kim, J.-A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref] [PubMed]

Sci Rep (2)

C. Wang, X. L. Zhong, and Z. Y. Li, “Linear and passive silicon optical isolator,” Sci Rep 2, 674 (2012).
[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).
[Crossref] [PubMed]

Science (2)

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333(6043), 729–733 (2011).
[Crossref] [PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Supplementary Material (3)

» Media 1: MOV (7762 KB)     
» Media 2: MOV (6592 KB)     
» Media 3: MOV (7428 KB)     

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Figures (6)

Fig. 1
Fig. 1

Ultra-compact integrated optical diodes. (a) Geometry of the device for TE. Steady-state light intensity distribution in the (b) forward and (c) backward directions for TE (Media 1). (d) Geometry of the device for TM. Steady-state light intensity distributions in the (e) forward and (f) backward directions for TM (Media 2). Green arrows indicate the incident light propagation directions.

Fig. 2
Fig. 2

Scanning-electron micrograph of fabricated devices designed for (a) TE and (b) TM polarizations. (c) Schematic of the measurement system. Measured and simulated forward and backward transmission efficiencies as a function of wavelength for the optical diode designed for (d) TE and (e) TM polarizations. In (d) and (e), forward and backward efficiencies are denoted by red and blue lines, respectively. The experimental and simulation data are represented using solid and dashed lines, respectively.

Fig. 3
Fig. 3

On-chip polarizer. (a) Permittivity distribution of the design of on-chip polarizer. (b) Scanning-electron micrograph of fabricated on-chip polarizer. (c)-(d) Steady-state electric field patterns for TM and TE at 1550nm, respectively.

Fig. 4
Fig. 4

(a) Simulated extinction ratio as a function of mode order. (b) The profile of input mode of second order and its corresponding intensity pattern in the (c) forward and (d) backward directions. (e) The profile of input mode of third order and its corresponding intensity pattern in the (f) forward and (g) backward directions. Green arrows indicate the incident light propagation direction. Simulated transmission efficiency as a function of the silicon thickness for the diodes designed for (h) TE and (i) TM polarizations.

Fig. 5
Fig. 5

Fourier transforms of a metamaterials with pixels arranged in (a) random pattern and (b) pattern optimized for optical diode in Ez. (a) The wave-vectors of the random pattern are very diffuse compared to (b) those of the optimized pattern. The size of each device is 3μmX3μm.

Fig. 6
Fig. 6

Polarization-independent optical diode. (a) Geometry of the optimized device. (b) Simulated transmission efficiencies for both polarization states in the forward and backward directions. (c) - (f) Steady-state light-intensity distributions for both polarization states in forward and backward directions (Media 3). Green arrows indicate the incident light propagation directions.

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