Abstract

We design an extremely compact photonic crystal waveguide spatial mode converter which converts the fundamental even mode to the higher order odd mode with nearly 100% efficiency. We adapt a previously developed design and optimization process that allows these types of devices to be designed in a matter of minutes. We also present an extremely compact optical diode device and clarify its general properties and its relation to spatial mode converters. Finally, we connect the results here to a general theory on the complexity of optical designs.

© 2012 OSA

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  1. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
    [CrossRef]
  2. L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun.3, 1217 (2012).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. V. Liu, Y. Jiao, D. A. B. Miller, and S. Fan, “Design methodology for compact photonic-crystal-based wavelength division multiplexers,” Opt. Lett.36, 591–593 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett.81, 1163–1165 (2002).
    [CrossRef]
  20. Y. Li and J.-M. Jin, “A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems,” IEEE Trans. Antennas Propag.54, 3000–3009 (2006).
    [CrossRef]
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    [CrossRef]
  23. V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE (Accepted).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  28. A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80, 155117 (2009).
    [CrossRef]
  29. C. Wang, C.-Z. Zhou, and Z.-Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express19, 26948–26955 (2011).
    [CrossRef]
  30. C. Lu, X. Hu, H. Yang, and Q. Gong, “Ultrahigh-contrast and wideband nanoscale photonic crystal all-optical diode,” Opt. Lett.36, 4668–4670 (2011).
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  31. 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,” Science335, 38 (2012).
    [CrossRef] [PubMed]

2012 (4)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun.3, 1217 (2012).
[CrossRef] [PubMed]

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

D. A. B. Miller, “All linear optical devices are mode converters,” Opt. Express20, 23985–23993 (2012).
[CrossRef] [PubMed]

2011 (4)

2010 (1)

S. Y. Tseng and M. C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” IEEE Photon. Technol. Lett.22, 1211–1213 (2010).
[CrossRef]

2009 (1)

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80, 155117 (2009).
[CrossRef]

2008 (1)

2006 (3)

Y. Huang and Y. Y. Lu, “Scattering from periodic arrays of cylinders by dirichlet-to-neumann maps,” J. Lightwave Technol.24, 3448–3453 (2006).
[CrossRef]

Y. Li and J.-M. Jin, “A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems,” IEEE Trans. Antennas Propag.54, 3000–3009 (2006).
[CrossRef]

Y. Jiao, S. Fan, and D. A. B. Miller, “Systematic photonic crystal device design: global and local optimization and sensitivity analysis,” IEEE J. Quantum Elect.42, 266–279 (2006).
[CrossRef]

2005 (3)

2004 (4)

M. Greenberg and M. Orenstein, “Irreversible coupling by use of dissipative optics,” Opt. Lett.29, 451–453 (2004).
[CrossRef] [PubMed]

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

I. L. Gheorma, S. Haas, and A. F. J. Levi, “Aperiodic nanophotonic design,” J. Appl. Phys.95, 1420–1426 (2004).
[CrossRef]

G. G. Denisov, G. I. Kalynova, and D. I. Sobolev, “Method for synthesis of waveguide mode converters,” Radiophys. Quantum El.47, 615–620 (2004).
[CrossRef]

2003 (1)

2002 (5)

2001 (1)

1996 (1)

V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun.127, 7–13 (1996).
[CrossRef]

Agio, M.

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Assefa, S.

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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Baets, R.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Bienstman, P.

Blasco, J.

P. Sanchis, J. Marti, A. Garcia, A. Martinez, and J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett.38, 961–962 (2002).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express10, 1391–1397 (2002).
[CrossRef] [PubMed]

Brinkmeyer, E.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Castro, J.

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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Denisov, G. G.

G. G. Denisov, G. I. Kalynova, and D. I. Sobolev, “Method for synthesis of waveguide mode converters,” Radiophys. Quantum El.47, 615–620 (2004).
[CrossRef]

Doerr, C. R.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Dutton, R. W.

Eich, M.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Fan, S.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

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

Y. Jiao, S. Fan, and D. A. B. Miller, “Systematic photonic crystal device design: global and local optimization and sensitivity analysis,” IEEE J. Quantum Elect.42, 266–279 (2006).
[CrossRef]

Y. Jiao, S. Fan, and D. A. B. Miller, “Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator,” Opt. Lett.30, 141–143 (2005).
[CrossRef] [PubMed]

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

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE (Accepted).

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
[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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Fontaine, M.

V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun.127, 7–13 (1996).
[CrossRef]

Forchel, A.

Freude, W.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun.3, 1217 (2012).
[CrossRef] [PubMed]

Garcia, A.

P. Sanchis, J. Marti, A. Garcia, A. Martinez, and J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett.38, 961–962 (2002).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express10, 1391–1397 (2002).
[CrossRef] [PubMed]

Geraghty, D. F.

Gheorma, I. L.

I. L. Gheorma, S. Haas, and A. F. J. Levi, “Aperiodic nanophotonic design,” J. Appl. Phys.95, 1420–1426 (2004).
[CrossRef]

Gong, Q.

Greenberg, M.

Greiner, C. M.

Haas, S.

I. L. Gheorma, S. Haas, and A. F. J. Levi, “Aperiodic nanophotonic design,” J. Appl. Phys.95, 1420–1426 (2004).
[CrossRef]

Happ, T. D.

Honkanen, S.

Hu, X.

Hu, Z.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
[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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Huang, Y.

Iazikov, D.

Jalas, D.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Jiao, Y.

Jin, J.-M.

Y. Li and J.-M. Jin, “A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems,” IEEE Trans. Antennas Propag.54, 3000–3009 (2006).
[CrossRef]

Joannopoulos, J. D.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B20, 1817–1821 (2003).
[CrossRef]

Johnson, S. G.

Kalynova, G. I.

G. G. Denisov, G. I. Kalynova, and D. I. Sobolev, “Method for synthesis of waveguide mode converters,” Radiophys. Quantum El.47, 615–620 (2004).
[CrossRef]

Kamp, M.

Khoo, E.

Kolodziejski, L. A.

Krause, M.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Lalanne, P.

Levi, A. F. J.

I. L. Gheorma, S. Haas, and A. F. J. Levi, “Aperiodic nanophotonic design,” J. Appl. Phys.95, 1420–1426 (2004).
[CrossRef]

Li, Y.

Y. Li and J.-M. Jin, “A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems,” IEEE Trans. Antennas Propag.54, 3000–3009 (2006).
[CrossRef]

Li, Z.-Y.

Lipson, M.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun.3, 1217 (2012).
[CrossRef] [PubMed]

Liu, A.

Liu, D.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun.3, 1217 (2012).
[CrossRef] [PubMed]

Liu, V.

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

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE (Accepted).

Lu, C.

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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Lu, Y. Y.

Marti, J.

P. Sanchis, J. Marti, A. Garcia, A. Martinez, and J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett.38, 961–962 (2002).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express10, 1391–1397 (2002).
[CrossRef] [PubMed]

Martinez, A.

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express10, 1391–1397 (2002).
[CrossRef] [PubMed]

P. Sanchis, J. Marti, A. Garcia, A. Martinez, and J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett.38, 961–962 (2002).
[CrossRef]

Melloni, A.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Miller, D. A. B.

Mossberg, T. W.

Orenstein, M.

Petrich, G. S.

Petrov, A.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Popovic, M.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Qiu, M.

M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett.81, 1163–1165 (2002).
[CrossRef]

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photon.6, 488–496 (2012).
[CrossRef]

Renner, H.

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

Sanchis, P.

P. Sanchis, J. Marti, A. Garcia, A. Martinez, and J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett.38, 961–962 (2002).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express10, 1391–1397 (2002).
[CrossRef] [PubMed]

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,” Science333, 729–733 (2011).
[CrossRef] [PubMed]

Serebryannikov, A. E.

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80, 155117 (2009).
[CrossRef]

Sobolev, D. I.

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Science (2)

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,” Science335, 38 (2012).
[CrossRef] [PubMed]

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,” Science333, 729–733 (2011).
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Other (2)

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE (Accepted).

D. A. B. Miller, “How complicated must an optical component be?,” Submitted to J. Opt. Soc. Am. A. http://arxiv.org/abs/1209.5499 .

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Figures (8)

Fig. 1
Fig. 1

Schematic of template structure. Background dielectric rods are indicated with solid circles. Black open circles are the 20 rods that can be added or removed, while the black dashed circles are determined automatically by inversion symmetry. The blue highlighted regions show the waveguides, and the orange highlighted region shows the coupler region where search and optimization are performed.

Fig. 2
Fig. 2

(a) Ideal mode converter specification. The letters denote different modes. The red and blue arrows represent input and output in each mode, respectively. The gray region represents the converter device. (b) The scattering matrix of the device.

Fig. 3
Fig. 3

(a) Spectral conversion efficiency of the mode converter shown in the right side of Fig. 1. (b) Representative field patterns for both input modes from the left at normalized frequency 0.4025 × 2πc/a.

Fig. 4
Fig. 4

(a) Ideal optical diode specification. Similar to the ideal mode converter, an input even mode from the left is converted to an odd mode on the right, and vice versa. However, an odd mode from the left or an even mode from the right are completely reflected. (b) The scattering matrix of the device.

Fig. 5
Fig. 5

Schematic of optimized structures. (a) Candidate structure resulting from the combinatorial search. The blue highlighted regions show the waveguides, and the orange highlighted region shows the coupler region where search and optimization are performed. (b) Final rod radius optimized structure of the corresponding structure on the left.

Fig. 6
Fig. 6

Spectral conversion efficiency of optical diode device. (a) The transmission spectrum from mode A to mode D (black line) and the reflection spectrum for mode C to mode C (red line) for the unoptimized structure shown in Fig. 5(a). (b) The same spectra for the optimized structure in Fig. 5(b).

Fig. 7
Fig. 7

Field patterns of the radius-optimized optical diode device shown in Fig. 5(b). The top row shows excitation from the left, while the bottom row shows excitation from the right.

Fig. 8
Fig. 8

Final candidate spectra obtained from the combinatorial search over 220 possibilities at frequencies near 0.4 × 2πc/a. The vertical axis shows the conversion efficiency from mode A to mode D, and only spectra for structures with peak efficiency greater than 95% are shown.

Equations (3)

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J = ω ( 1 p ω ) 2
( 2 M 1 ) + ( 2 M 5 ) + + [ 2 M 4 ( M 2 1 ) 1 ] = M 2 ( M + 1 )
N D = M 2 / 2

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