Abstract

We demonstrate an extremely compact bend for a photonic crystal waveguide supporting three spatial modes. The bend exhibits nearly 100% transmission over a relative bandwidth of 1% with less than 1% crosstalk. We show that our design is robust with respect to fabrication errors. Our design method is applied to create a structure consisting of dielectric rods, as well as a structure consisting of air holes in a dielectric background.

© 2013 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. Photonics6, 488–496 (2012).
    [CrossRef]
  2. X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E70, 055601 (2004).
    [CrossRef]
  3. P. B. Catrysse and S. Fan, “Routing of deep-subwavelength optical beams and images without reflection and diffraction using infinitely anisotropic metamaterials,” Adv. Mater.25, 194–198 (2012).
    [CrossRef] [PubMed]
  4. 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]
  5. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  6. J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett.84, 2022–2024 (2004).
    [CrossRef]
  7. A. Miroshnichenko and Y. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear fano resonators,” Opt. Express13, 3969–3976 (2005).
    [CrossRef] [PubMed]
  8. F. Monifi, M. Djavid, A. Ghaffari, and M. S. Abrishamian, “Design of efficient photonic crystal bend and power splitter using super defects,” J. Opt. Soc. Am. B25, 1805–1810 (2008).
    [CrossRef]
  9. Z. Hu and Y. Y. Lu, “Improved bends for two-dimensional photonic crystal waveguides,” Opt. Commun.284, 2812–2816 (2011).
    [CrossRef]
  10. S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
    [CrossRef] [PubMed]
  11. M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
    [CrossRef]
  12. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ = 1.55 μm wavelengths,” Opt. Lett.26, 286–288 (2001).
    [CrossRef]
  13. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
    [CrossRef]
  14. L. Frandsen, A. Harpøth, P. Borel, M. Kristensen, J. Jensen, and O. Sigmund, “Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization,” Opt. Express12, 5916–5921 (2004).
    [CrossRef] [PubMed]
  15. P. Strasser, G. Stark, F. Robin, D. Erni, K. Rauscher, R. Wüest, and H. Jäckel, “Optimization of a 60 ° waveguide bend in inp-based 2d planar photonic crystals,” J. Opt. Soc. Am. B25, 67–73 (2008).
    [CrossRef]
  16. M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett.81, 1163–1165 (2002).
    [CrossRef]
  17. 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]
  18. 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]
  19. V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE101, 484–493 (2013).
    [CrossRef]
  20. G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett.29, 2288–2290 (2004).
    [CrossRef] [PubMed]
  21. Y. Jiao, S. Fan, and D. Miller, “Systematic photonic crystal device design: global and local optimization and sensitivity analysis,” IEEE J. Quantum Electron.42, 266–279 (2006).
    [CrossRef]
  22. 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]

2013 (1)

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE101, 484–493 (2013).
[CrossRef]

2012 (3)

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. Photonics6, 488–496 (2012).
[CrossRef]

P. B. Catrysse and S. Fan, “Routing of deep-subwavelength optical beams and images without reflection and diffraction using infinitely anisotropic metamaterials,” Adv. Mater.25, 194–198 (2012).
[CrossRef] [PubMed]

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]

2011 (2)

2008 (2)

2006 (2)

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

2005 (2)

2004 (4)

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

L. Frandsen, A. Harpøth, P. Borel, M. Kristensen, J. Jensen, and O. Sigmund, “Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization,” Opt. Express12, 5916–5921 (2004).
[CrossRef] [PubMed]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett.84, 2022–2024 (2004).
[CrossRef]

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E70, 055601 (2004).
[CrossRef]

2002 (2)

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

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

2001 (1)

2000 (1)

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
[CrossRef]

1998 (1)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Abrishamian, M. S.

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. Photonics6, 488–496 (2012).
[CrossRef]

Benisty, H.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Borel, P.

Catrysse, P. B.

P. B. Catrysse and S. Fan, “Routing of deep-subwavelength optical beams and images without reflection and diffraction using infinitely anisotropic metamaterials,” Adv. Mater.25, 194–198 (2012).
[CrossRef] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chow, E.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ = 1.55 μm wavelengths,” Opt. Lett.26, 286–288 (2001).
[CrossRef]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

Djavid, M.

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. Photonics6, 488–496 (2012).
[CrossRef]

Dutton, R. W.

Erni, D.

Fan, S.

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE101, 484–493 (2013).
[CrossRef]

P. B. Catrysse and S. Fan, “Routing of deep-subwavelength optical beams and images without reflection and diffraction using infinitely anisotropic metamaterials,” Adv. Mater.25, 194–198 (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. Miller, “Systematic photonic crystal device design: global and local optimization and sensitivity analysis,” IEEE J. Quantum Electron.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]

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E70, 055601 (2004).
[CrossRef]

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

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

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. Photonics6, 488–496 (2012).
[CrossRef]

Frandsen, L.

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]

Ghaffari, A.

Harpøth, A.

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

Houdré, R.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Hu, Z.

Z. Hu and Y. Y. Lu, “Improved bends for two-dimensional photonic crystal waveguides,” Opt. Commun.284, 2812–2816 (2011).
[CrossRef]

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. Photonics6, 488–496 (2012).
[CrossRef]

Huang, Y.

Jäckel, H.

Jensen, J.

Jensen, J. S.

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett.84, 2022–2024 (2004).
[CrossRef]

Jiao, Y.

Joannopoulos, J. D.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ = 1.55 μm wavelengths,” Opt. Lett.26, 286–288 (2001).
[CrossRef]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Johnson, S. G.

Kivshar, Y.

Kosaka, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
[CrossRef]

Krauss, T. F.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Kristensen, M.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Lin, S. Y.

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

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]

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]

Liu, V.

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE101, 484–493 (2013).
[CrossRef]

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]

Lu, Y. Y.

Z. Hu and Y. Y. Lu, “Improved bends for two-dimensional photonic crystal waveguides,” Opt. Commun.284, 2812–2816 (2011).
[CrossRef]

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]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Miller, D.

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

Miller, D. A. B.

Miroshnichenko, A.

Monifi, F.

Oesterle, U.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Olivier, S.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Qiu, M.

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

Rauscher, K.

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. Photonics6, 488–496 (2012).
[CrossRef]

Robin, F.

Sigmund, O.

L. Frandsen, A. Harpøth, P. Borel, M. Kristensen, J. Jensen, and O. Sigmund, “Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization,” Opt. Express12, 5916–5921 (2004).
[CrossRef] [PubMed]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett.84, 2022–2024 (2004).
[CrossRef]

Smith, C. J. M.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Stark, G.

Strasser, P.

Tokushima, M.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
[CrossRef]

Tomita, A.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
[CrossRef]

Tur, 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. Photonics6, 488–496 (2012).
[CrossRef]

Veronis, G.

Villeneuve, P. R.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Wang, J.

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. Photonics6, 488–496 (2012).
[CrossRef]

Weisbuch, C.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

Wendt, J. R.

Willner, A. E.

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. Photonics6, 488–496 (2012).
[CrossRef]

Wüest, R.

Yamada, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
[CrossRef]

Yan, 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. Photonics6, 488–496 (2012).
[CrossRef]

Yang, J.-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. Photonics6, 488–496 (2012).
[CrossRef]

Yu, X.

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E70, 055601 (2004).
[CrossRef]

Yue, 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. Photonics6, 488–496 (2012).
[CrossRef]

Adv. Mater. (1)

P. B. Catrysse and S. Fan, “Routing of deep-subwavelength optical beams and images without reflection and diffraction using infinitely anisotropic metamaterials,” Adv. Mater.25, 194–198 (2012).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett.84, 2022–2024 (2004).
[CrossRef]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett.76, 952–954 (2000).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

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

J. Light-wave Technol. (1)

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Improved 60 degree bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Light-wave Technol.20, 1198 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

Nat. Commun. (1)

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]

Nat. Photonics (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. Photonics6, 488–496 (2012).
[CrossRef]

Opt. Commun. (1)

Z. Hu and Y. Y. Lu, “Improved bends for two-dimensional photonic crystal waveguides,” Opt. Commun.284, 2812–2816 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. E (1)

X. Yu and S. Fan, “Anomalous reflections at photonic crystal surfaces,” Phys. Rev. E70, 055601 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Proc. IEEE (1)

V. Liu, D. A. B. Miller, and S. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE101, 484–493 (2013).
[CrossRef]

Science (1)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science282, 274–276 (1998).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the optimized bend structure. The blue highlighted regions show the waveguides, and the orange highlighted region shows the bend region where search and optimization were performed. Solid gray circles indicate dielectric rods (refractive index 3.4) surrounded by air. Unlabeled rods have radius 0.2a where a is the lattice constant. The table on the right lists the radii of the labeled rods. The dashed green diagonal line shows the plane of mirror symmetry.

Fig. 2
Fig. 2

Band structure of the waveguide modes within the bandgap of the background photonic crystal. The out-of-plane electric field profiles of the three modes at the operating frequency are shown on the right. The profiles are taken along the edge of the waveguide unit cell and are on the same horizontal scale as the cell shown at the bottom right.

Fig. 3
Fig. 3

Transmission spectra for each of the three waveguide modes shown in Fig. 2 for the structure shown in Fig. 1. The inset shows details of the transmission peaks.

Fig. 4
Fig. 4

Representative field patterns (out-of-plane electric field) for each waveguide mode of the optimized structure shown in Fig. 1 at the operating frequency of ω = 0.4 × 2πc/a.

Fig. 5
Fig. 5

Transmission spectra as in Fig. 3, except for the structure in Fig. 1 with rod radii rounded to three (dashed lines) and two (solid lines) significant digits.

Fig. 6
Fig. 6

(a) Schematic of an alternate optimized bend structure. Solid white circles indicate air holes (refractive index 1) surrounded by dielectric (refractive index (3.481). Unlabeled rods have radius 0.4a where a is the lattice constant. The table on the right lists the radii of the labeled rods. (b) Transmission spectra of the bend for each of the three modes.

Equations (1)

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J = m = 1 3 ( 1 p m ) 2

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