Abstract

Frequency conversion efficiency via four-wave mixing in coupled 1-D photonic crystal defect structures is studied numerically. In structures where all interacting frequencies coincide with intraband defect resonances, energy conversion efficiencies greater than 5% are predicted. Because the frequency spacings are determined by the free-spectral range, thereby requiring long defects for small spacings using intraband resonances, four-wave mixing using coupled-defect miniband resonances in more compact structures is also studied. Conversion efficiencies of greater than 1% are obtained in this case.

© 2005 Optical Society of America

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  1. E. Yablonovitch “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. S. John “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  3. T. F. Krauss “Planar photonic crystal waveguide devices for integrated optics,” Physica Status Solidi A 197, 688–702 (2003).
    [CrossRef]
  4. M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan “Nonlinear photonic crystal microcavities for optical integration,” Opt. Lett. 28, 637–639 (2003).
    [CrossRef] [PubMed]
  5. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  6. D. M. Pustai, A. Sharkawy, S. Shouyuan, and D. W. Prather “Tunable photonic crystal microcavities,” Appl. Optics 41, 5574–5579 (2002).
    [CrossRef]
  7. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
    [CrossRef]
  8. A. S. Jugessur, P. Pottier, and R. M. D. L. Rue “Engineering the filter response of photonic crystal microcavity filters,” Opt. Express 12, 1304–1312 (2004).
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    [CrossRef]
  11. R. Houdre and U. Oesterle “Miniband transmission in a photonic crystal coupled-resonator optical waveguide,” Opt. Lett. 26, 1019–1021 (2001).
    [CrossRef]
  12. S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E65, (2002).
    [CrossRef]
  13. S. Blair “Nonlinear sensitivity enhancement with one-dimensional photonic bandgap microcavity arrays,” Opt. Lett. 27, 613–615 (2002).
    [CrossRef]
  14. 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, 2052–2059 (2002).
    [CrossRef]
  15. S. Blair “Self-focusing of narrow one-dimensional beams in photonic microcavity arrays,” J. Opt. Soc. Am. B 20, 1520–1526 (2003).
    [CrossRef]
  16. G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
    [CrossRef]
  17. G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
    [CrossRef]
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    [CrossRef]
  19. M. J. Steel and C. M. de Sterke “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
    [CrossRef]
  20. T. Hattori, N. Tsurumachi, and H. Nakatsuka “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
    [CrossRef]
  21. N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
    [CrossRef]
  22. G. J. Schneider and G. H. Watson “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 83, 5350–5352 (2003).
    [CrossRef]
  23. A. Melloni, F. Morichetti, and M. Martinelli “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
    [CrossRef]
  24. Y. Chen and S. Blair “Nonlinearity enhancement in finite coupled-resonator slow-light waveguides,” Opt. Express 12, 3353–3366 (2004).
    [CrossRef] [PubMed]
  25. Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair “Engineering the nonlinear phase shift using multi-stage auto-regressive moving-average optical filters,” Appl. Opt. 13, 2564–2574 (2005).
    [CrossRef]

2005 (2)

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair “Engineering the nonlinear phase shift using multi-stage auto-regressive moving-average optical filters,” Appl. Opt. 13, 2564–2574 (2005).
[CrossRef]

2004 (3)

2003 (5)

T. F. Krauss “Planar photonic crystal waveguide devices for integrated optics,” Physica Status Solidi A 197, 688–702 (2003).
[CrossRef]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan “Nonlinear photonic crystal microcavities for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef] [PubMed]

S. Blair “Self-focusing of narrow one-dimensional beams in photonic microcavity arrays,” J. Opt. Soc. Am. B 20, 1520–1526 (2003).
[CrossRef]

G. J. Schneider and G. H. Watson “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 83, 5350–5352 (2003).
[CrossRef]

A. Melloni, F. Morichetti, and M. Martinelli “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
[CrossRef]

2002 (3)

2001 (1)

2000 (1)

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

1999 (3)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer “Coupled-resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

1998 (1)

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

1997 (2)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

1996 (1)

M. J. Steel and C. M. de Sterke “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

1987 (2)

E. Yablonovitch “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Baets, R.

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

Bienstman, P.

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

Blair, S.

Chen, Y.

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair “Engineering the nonlinear phase shift using multi-stage auto-regressive moving-average optical filters,” Appl. Opt. 13, 2564–2574 (2005).
[CrossRef]

Y. Chen and S. Blair “Nonlinearity enhancement in finite coupled-resonator slow-light waveguides,” Opt. Express 12, 3353–3366 (2004).
[CrossRef] [PubMed]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

de Sterke, C. M.

M. J. Steel and C. M. de Sterke “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

Fan, S.

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan “Nonlinear photonic crystal microcavities for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef] [PubMed]

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, 2052–2059 (2002).
[CrossRef]

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Farhang-Boroujeny, B.

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair “Engineering the nonlinear phase shift using multi-stage auto-regressive moving-average optical filters,” Appl. Opt. 13, 2564–2574 (2005).
[CrossRef]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Fuji, T.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

Hattori, T.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

Houdre, R.

Ibanescu, M.

Ippen, E.

Ippen, E. P.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Joannopoulos, J. D.

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan “Nonlinear photonic crystal microcavities for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef] [PubMed]

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, 2052–2059 (2002).
[CrossRef]

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

John, S.

S. John “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

Jugessur, A. S.

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Kolodziejski, L. A.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

Krauss, T. F.

T. F. Krauss “Planar photonic crystal waveguide devices for integrated optics,” Physica Status Solidi A 197, 688–702 (2003).
[CrossRef]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer “Coupled-resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

Lim, K.-Y.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

Luo, C.

Maes, B.

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
[CrossRef]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
[CrossRef]

Modinos, A.

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Mookherjea, S.

S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E65, (2002).
[CrossRef]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
[CrossRef]

Morthier, G.

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

Muroi, N.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

Nakatsuka, H.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

Notebaert, I.

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Oesterle, U.

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Pasrija, G.

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair “Engineering the nonlinear phase shift using multi-stage auto-regressive moving-average optical filters,” Appl. Opt. 13, 2564–2574 (2005).
[CrossRef]

Petrich, G. S.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

Pottier, P.

Prather, D. W.

D. M. Pustai, A. Sharkawy, S. Shouyuan, and D. W. Prather “Tunable photonic crystal microcavities,” Appl. Optics 41, 5574–5579 (2002).
[CrossRef]

Priem, G.

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

Pustai, D. M.

D. M. Pustai, A. Sharkawy, S. Shouyuan, and D. W. Prather “Tunable photonic crystal microcavities,” Appl. Optics 41, 5574–5579 (2002).
[CrossRef]

Ripin, D. J.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

Rue, R. M. D. L.

Scherer, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer “Coupled-resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Schneider, G. J.

G. J. Schneider and G. H. Watson “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 83, 5350–5352 (2003).
[CrossRef]

Sharkawy, A.

D. M. Pustai, A. Sharkawy, S. Shouyuan, and D. W. Prather “Tunable photonic crystal microcavities,” Appl. Optics 41, 5574–5579 (2002).
[CrossRef]

Shouyuan, S.

D. M. Pustai, A. Sharkawy, S. Shouyuan, and D. W. Prather “Tunable photonic crystal microcavities,” Appl. Optics 41, 5574–5579 (2002).
[CrossRef]

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Soljacic, M.

Steel, M. J.

M. J. Steel and C. M. de Sterke “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

Stefanou, N.

N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Thoen, E. R.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Tsurumachi, N.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

Villeneuve, P. R.

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Watson, G. H.

G. J. Schneider and G. H. Watson “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 83, 5350–5352 (2003).
[CrossRef]

Xu, Y.

Yablonovitch, E.

E. Yablonovitch “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yamashita, S.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
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A. Yariv, Y. Xu, R. K. Lee, and A. Scherer “Coupled-resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
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S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E65, (2002).
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Appl. Opt. (1)

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair “Engineering the nonlinear phase shift using multi-stage auto-regressive moving-average optical filters,” Appl. Opt. 13, 2564–2574 (2005).
[CrossRef]

Appl. Optics (1)

D. M. Pustai, A. Sharkawy, S. Shouyuan, and D. W. Prather “Tunable photonic crystal microcavities,” Appl. Optics 41, 5574–5579 (2002).
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Appl. Phys. Lett. (1)

G. J. Schneider and G. H. Watson “Nonlinear optical spectroscopy in one-dimensional photonic crystals,” Appl. Phys. Lett. 83, 5350–5352 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

G. Priem, I. Notebaert, B. Maes, P. Bienstman, G. Morthier, and R. Baets “Design of all-optical nonlinear functionalities based on resonators,” IEEE J. Sel. Top. Quantum Electron. 10, 1070–1078 (2004).
[CrossRef]

J. Appl. Phys. (2)

G. Priem, I. Notebaert, P. Bienstman, G. Morthier, and R. Baets “Resonator-based all-optical Kerr-nonlinear phase shifting: design and limitations,” J. Appl. Phys. 97, 023104 (2005).
[CrossRef]

D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–1580 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys. 38, 6302–6308 (1999).
[CrossRef]

Nature (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–154 (1997).
[CrossRef]

Opt. Express (2)

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A. Melloni, F. Morichetti, and M. Martinelli “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
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N. Stefanou and A. Modinos “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
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M. J. Steel and C. M. de Sterke “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

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E. Yablonovitch “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
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S. John “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
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Physica Status Solidi A (1)

T. F. Krauss “Planar photonic crystal waveguide devices for integrated optics,” Physica Status Solidi A 197, 688–702 (2003).
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Science (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Other (1)

S. Mookherjea and A. Yariv “Second harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E65, (2002).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

One-dimensional photonic crystal coupled-defect structure. The layer sequence for this structure is given by (LH)3[(H)7 (LH)6]2(H)7 (LH)2L, and consists of three coupled defects of 8 H-layers each.

Fig. 2.
Fig. 2.

Linear transmission spectra of the coupled-defect structure of equation 1 showing the mangitude transmission (solid linestyle) and phase (dashed linestyle) of the intraband resonances.

Fig. 3.
Fig. 3.

Frequency conversion efficiency for a structure with layer sequence given by equation 1 (data points indicated by ‘*’), a bulk layer of equal thickness 440 H (data points indicated by ‘+’), and single defect structure of the form (LH)6H127(LH)5L (data points indicated by diamonds). The initial pump to signal intensity ratio is 10.

Fig. 4.
Fig. 4.

Frequency conversion efficiency for a structure with three coupled defects and defect cavity length of 256 H (data points indicated by ‘*’) and a bulk layer of equal thickness 828 H (data points indicated by ‘+’). The initial pump to signal intensity ratio is 10.

Fig. 5.
Fig. 5.

Linear transmission spectra of the coupled-defect structure of equation 2 (with M=5 and N=8) showing the transmission magnitude (solid linestyle) and phase (dashed linestyle) of the central miniband resonances.

Fig. 6.
Fig. 6.

Frequency conversion efficiency for a structure with layer sequence given by equation 2 with M=5 and N=8 (data points indicated by ‘*’, pump to signal intensity ratio of 10 connected by dashed lines, ratio of 1 connected by dotted lines) and a bulk layer of equal thickness 116 H (data points indicated by ‘+’).

Fig. 7.
Fig. 7.

Frequency conversion efficiency for a structure with layer sequence given by equation 2 with M=5 and N=8 (data points indicated by ‘*’) versus initial pump to signal intensity ratio. The normalized pump intensity n 2 Ip =5×10-5.

Fig. 8.
Fig. 8.

Frequency conversion efficiency for a structure with layer sequence given by equation 2 with N=8 versus the number of mirror pairs M. The efficiency is plotted at three different pump intensity levels. The initial pump to signal intensity ratio is 10.

Fig. 9.
Fig. 9.

Frequency conversion efficiency for a structure with layer sequence given by equation 2 with M=5 as a function of the number of defects. The efficiency is plotted at three different pump intensity levels. The initial pump to signal intensity ratio is 10.

Tables (2)

Tables Icon

Table 1. Linear parameters for coupled-defect structures of equation 2 with N=8.

Tables Icon

Table 2. Linear parameters for coupled-defect structure of equation 2 with M=5.

Equations (2)

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( L H ) 4 [ ( H ) 127 ( L H ) 8 ] 2 ( H ) 127 ( L H ) 3 L ,
( L H ) M [ H ( L H ) M ] N 1 H ( L H ) M 1 L ,

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