Abstract

We present a general approach for coupling a specific mode in a planar photonic crystal (PC) waveguide to a desired free-space mode. We apply this approach to a W1 PC waveguide by introducing small index perturbations to selectively couple a particular transverse mode to an approximately Gaussian, slowly diverging free space mode. This “perturbative photonic crystal waveguide coupler” (PPCWC) enables efficient interconversion between selectable propagating photonic crystal and free space modes with minimal design perturbations.

© 2011 OSA

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed., (Princeton University Press, 2008).
  2. T. Baba, “Slow light in photonic crystals,” Nature Photonics 2, 465–473 (2008).
    [CrossRef]
  3. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef] [PubMed]
  4. J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
    [CrossRef] [PubMed]
  5. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
    [CrossRef]
  6. H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
    [CrossRef] [PubMed]
  7. E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005).
    [CrossRef] [PubMed]
  8. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
    [CrossRef]
  9. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators, and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
    [CrossRef] [PubMed]
  10. 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. B 20, 1817–1821 (2003).
    [CrossRef]
  11. P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
    [CrossRef]
  12. B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
    [CrossRef] [PubMed]
  13. A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).
  14. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Dipole induced transparency in waveguide coupled photonic crystal cavities,” Opt. Express 16, 12154–12162 (2008).
    [CrossRef] [PubMed]
  15. M. Toishi, D. Englund, A. Faraon, and J. Vuckovic, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
    [CrossRef] [PubMed]
  16. N. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
    [CrossRef]
  17. Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
    [CrossRef]
  18. A. Yariv, Optical Electronics in Modern Communications, 5th ed., (Oxford University Press, New York, 1997).
  19. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
    [CrossRef]
  20. X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
    [CrossRef]

2010 (2)

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef] [PubMed]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

2009 (2)

M. Toishi, D. Englund, A. Faraon, and J. Vuckovic, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef] [PubMed]

N. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[CrossRef]

2008 (2)

2006 (2)

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[CrossRef] [PubMed]

Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
[CrossRef]

2005 (2)

E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (2)

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. B 20, 1817–1821 (2003).
[CrossRef]

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[CrossRef]

2002 (1)

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

2000 (1)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

Asakawa, K.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Asano, T.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[CrossRef] [PubMed]

Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
[CrossRef]

Assefa, S.

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. B 20, 1817–1821 (2003).
[CrossRef]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nature Photonics 2, 465–473 (2008).
[CrossRef]

Baets, R.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Barclay, P. E.

Bienstman, P.

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. B 20, 1817–1821 (2003).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Chen, X.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

Combrie, S.

N. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[CrossRef]

De Rossi, A.

N. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[CrossRef]

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Englund, D.

Fan, S.

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

Faraon, A.

Fung, C. K. Y.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

Fushman, I.

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Ibanescu, M.

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

Ikeda, Naoki

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

Ippen, E.

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

Jiang, J.

Joannopoulos, J. D.

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. B 20, 1817–1821 (2003).
[CrossRef]

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed., (Princeton University Press, 2008).

Johnson, S. G.

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. B 20, 1817–1821 (2003).
[CrossRef]

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed., (Princeton University Press, 2008).

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kitagawa, Y.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Kolodziejski, L. A.

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. B 20, 1817–1821 (2003).
[CrossRef]

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kuramochi, E.

Kwong, D. L.

Laere, F.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Li, C.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

Lo, S. M. G.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

McMillan, J. F.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed., (Princeton University Press, 2008).

Mitsugi, S.

Mizutani, A.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Noda, S.

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[CrossRef] [PubMed]

Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

Nordin, G. P.

Notomi, M.

Ozaki, N.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Painter, O.

Petrich, G. S.

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. B 20, 1817–1821 (2003).
[CrossRef]

Petroff, P.

Ryu, H.

Shinya, A.

Soljacic, M.

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

Song, B. S.

Srinivasan, K.

Stoltz, N.

Sugimoto, Y.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Takano, H.

Takata, Y.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Tanaka, Y.

Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
[CrossRef]

Toishi, M.

Tran, N.

N. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[CrossRef]

Tsang, H. K.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

Tymczenko, M.

Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
[CrossRef]

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Vuckovic, J.

Waks, E.

E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005).
[CrossRef] [PubMed]

Wang, B.

Watanabe, Y.

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed., (Princeton University Press, 2008).

Wong, C. W.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

A. Yariv, Optical Electronics in Modern Communications, 5th ed., (Oxford University Press, New York, 1997).

Yu, M.

IEEE Photon. Technol. Lett. (1)

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 20, 1156–1158 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

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

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2058 (2002).
[CrossRef]

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. B 20, 1817–1821 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Japanese J. Appl. Phys. (1)

Y. Tanaka, M. Tymczenko, T. Asano, and S. Noda, “Fabrication of two-dimensional photonic crystal slab point-defect cavity employing local three-dimensional structures,” Japanese J. Appl. Phys. 45, 6096–6102 (2006).
[CrossRef]

Nature (London) (1)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

Nature Photonics (1)

T. Baba, “Slow light in photonic crystals,” Nature Photonics 2, 465–473 (2008).
[CrossRef]

Opt. Express (1)

E. Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt. Express 13, 5064–5073 (2005).
[CrossRef] [PubMed]

Opt. Express (6)

Phys. Rev. Lett. (1)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Phys. Rev. B (1)

N. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[CrossRef]

Other (3)

A. Yariv, Optical Electronics in Modern Communications, 5th ed., (Oxford University Press, New York, 1997).

A. Mizutani, Naoki Ikeda, Y. Watanabe, N. Ozaki, Y. Takata, Y. Kitagawa, F. Laere, R. Baets, Y. Sugimoto, and K. Asakawa, “Planar focusing lens grating for vertical coupling on 2D photonic crystal slab waveguide,” in Lasers and Electro-Optics Society, 2006. LEOS 2006. 19th Annual Meeting of the IEEE, pp. 843–844 (2006).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed., (Princeton University Press, 2008).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic showing the coupling system. (b) The dispersion relation of a W1 PC waveguide. The fundamental mode (the blue line) and a higher mode (the green line), having frequencies ω = 0.2436 and 0.3151(2πc/a), respectively, at wave-vector kx = π/a, are labeled in the figure.

Fig. 2
Fig. 2

FDTD Simulation of PC waveguide and calculated coupling strength of index perturbed vertical coupler. (a) (b) and ŷ components of electric field of the waveguide mode ω = 0.2436. (c) A Gaussian beam profile which we expect as the scattered light. (d) Dot product of the ŷ component of the waveguide mode and the target Gaussian mode. (e) Calculated coupling strength κba (Eq. (4)) for target Gaussian modes with different divergences. (f) The resulting perturbed PC structure (the left panel) and the index perturbation distribution (the right panel) of the case with the perturbation size of 0.3244, in units of the fractional area of unit cell, in (e).

Fig. 3
Fig. 3

Structures and simulation results of a line defect PC waveguides with and index perturbation introduced. Figures shows the distributions of the ŷ component of the electric field of the waveguide modes at (a) ω = 0.2436 and (b) ω = 0.3078, respectively.

Fig. 4
Fig. 4

(a) The intensity distributions of the ŷ component of the electric field, Ey, of the scattering from a 5-period long coupler, of which the perturbation pattern is as shown in 2(f), viewed in a vertical plane passing through the middle of the waveguide, where z = 0 is the center of the PC slab. The waveguide is excited at ω = 0.2436. (b) The three dimensional view of the density isosurface of the ŷ component of the electric field, Ey. The structure of the PC waveguide with a coupler is shown at the bottom.

Fig. 5
Fig. 5

The control of the scattering direction. (a) Intensities of the scattered fields at different feeding frequencies. (b) The structure of the a 5-period long coupler with increasing perturbation size. The brown shade area in the right panel labels the perturbation introduced. (c) The intensity distribution of the scattering field radiated from the coupler as shown in (b). The bottom panel is a x – z cross-section through the center of the first row of holes.

Fig. 6
Fig. 6

(a) Dispersion relations of waveguides without (left) and with index perturbation (right). The insets show the unit cells of the periodic structure for each case. The perturbed structure is the same as shown in Fig. 2(f). (b) Comparison of the changes in the relative decay rate of the fundamental mode (the blue line) and a higher mode (the green line). (c) Comparison of the changes in mode frequency of the fundamental mode (the blue line) and a higher mode (the green line).

Fig. 7
Fig. 7

The calculated relative strength of transmission (black solid line), scattering (red solid line), reflection (gray solid line), and planar leakage (gray dotted line) of the 5-period long couplers with different index perturbation distributions introduced. The horizontal axis denotes the perturbation size. r0 is the radius of holes at the center of the waveguide, and the perturbation size introduced on the side is in units of the fractional area of unit cell.

Fig. 8
Fig. 8

(a) The structure of a coupler with additional index perturbation introduction to the 6th row from the waveguide. (b), (d) The intensity distribution viewed in a transverse plane through the center of the coupler shown in Fig. 3. (c), (e) The intensity distribution of the scattering from a coupler as shown in (a). Δ is the beam width (FWHM) measured at different heights above the center of waveguide, in units of lattice constant, a.

Equations (8)

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× × E = ɛ ( r ) c 2 2 E t 2 ,
E w = B w ( r ) e i ( ω ( k ) t k x ) .
E = a ( t ) A ( r ) e i ω G t + k B k ( r ) e i ω ( k ) t [ b ( k , t ) e i k x + c ( k , t ) e i k x ] .
κ ba ( k ) = dr Δ ɛ w ( r ) c 2 e i k x A * B k 2 dr ɛ t ( r ) c 2 | A | 2
E ( r ) = i = 1 N E i ( r ) e i k w ( r i r 1 ) α | r i r 1 | ,
E i ( r ) = u ( r r i ) | r r i | e i k 0 ( r r i )
T c = S × | E scatt E G | 2 E scatt 2 E G 2 ,
D = P U P U + P D ,

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