Abstract

We present a detailed analysis of the influence of the finite length of a photonic crystal (PhC) waveguide on its final response to pulses propagation. The analyzed PhC waveguide is accessed by conventional dielectric waveguides and the lack of a perfect coupling between them produces reflections at the interfaces, leading to the appearance of several output pulses at the end of the PhC waveguide. If the length of the PhC waveguide is short enough these repetitions overlap and the parameters that define the total output pulse (mainly amplitude, temporal width, time delay and group velocity) vary significantly. An oscillatory behavior of these parameters is observed when the length of the PhC waveguide is modified. A theoretical model has been used to achieve each cavity generated pulse at the output of the PhC waveguide. The unique parameters needed for these calculations are the propagation constant of the PhC waveguide and the transmission and reflection coefficients at each interface. Numerical simulations based on the eigenmode expansion method are used to obtain these parameters. The time and resources required to calculate the output pulse with this method are significantly reduced in comparison with FDTD simulations and the results are proved to be quite accurate.

© 2006 Optical Society of America

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  1. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  2. S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
    [CrossRef]
  3. 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]
  4. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
    [CrossRef] [PubMed]
  5. S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
    [CrossRef]
  6. S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
    [CrossRef]
  7. M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave Technol. 18, 1402-1411 (2000).
    [CrossRef]
  8. M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
    [CrossRef]
  9. M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
    [CrossRef]
  10. P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
    [CrossRef]
  11. This software can be encountered at http://camfr.sourceforge.net/
  12. S.F. Mingaleev and K. Busch, "Scattering matrix approach to large-scale photonic crystal circuits," Opt. Lett. 28, 619-621 (2003).
    [CrossRef] [PubMed]
  13. E. Istrate, A.A. Green, and E.H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
    [CrossRef]
  14. P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
    [CrossRef]
  15. P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
    [CrossRef]
  16. S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, "Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects," Opt. Lett. 27, 2079-2081 (2002).
    [CrossRef]
  17. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]

2005 (2)

E. Istrate, A.A. Green, and E.H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
[CrossRef]

P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
[CrossRef]

2004 (2)

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

2003 (2)

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

S.F. Mingaleev and K. Busch, "Scattering matrix approach to large-scale photonic crystal circuits," Opt. Lett. 28, 619-621 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, "Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects," Opt. Lett. 27, 2079-2081 (2002).
[CrossRef]

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

2000 (3)

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave Technol. 18, 1402-1411 (2000).
[CrossRef]

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

1999 (1)

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

1998 (1)

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

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]

Allan, D.C.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

Anand, S.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Asakawa, K.

Baets, R.

P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
[CrossRef]

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Beckx, S.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Bienstman, P.

P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
[CrossRef]

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

Biswas, R.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Bogaerts, W.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Bur, J.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Busch, K.

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]

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Doll, T.

Dumon, P.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Fan, S.

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

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]

Fleming, J.G.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Forchel, A.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

García, J.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Green, A.A.

E. Istrate, A.A. Green, and E.H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
[CrossRef]

Hetherington, D.L.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Ho, K.M.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Ikeda, N.

Ishikawa, H.

Istrate, E.

E. Istrate, A.A. Green, and E.H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
[CrossRef]

Jaskorzynska, B.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Joannopoulos, J.D.

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

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]

John, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Johnson, S.G.

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Kamp, M.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Karslsson, A.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Kuchinsky, S.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

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]

Kurtz, S.R.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Lan, S.

Leonard, S.W.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Lin, S.Y.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Loncar, M.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave Technol. 18, 1402-1411 (2000).
[CrossRef]

Lopez, C.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Luyssaert, B.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

Marti, J.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

Martí, J.

P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
[CrossRef]

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[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]

Meseguer, F.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Miguez, H.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Mingaleev, S.F.

Mondia, J.P.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Mulot, M.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Nedeljkovic, D.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

Nishikawa, S.

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Ozin, G.A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Pearsall, T.P.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

Qiu, M.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Sanchis, P.

P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
[CrossRef]

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Sargent, E.H.

E. Istrate, A.A. Green, and E.H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
[CrossRef]

Scherer, A.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave Technol. 18, 1402-1411 (2000).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Sigalas, M.M.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Smith, B.K.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Sugimoto, Y.

Swillo, M.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

Taillaert, D.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Toader, O.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

van Driel, H.M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Villeneuve, P.R.

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

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]

Vuckovic, J.

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave Technol. 18, 1402-1411 (2000).
[CrossRef]

Wiaux, V.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Wouters, J.

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Zubrzycki, W.

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Appl. Phys. Lett. (3)

M. Loncar, D. Nedeljkovic, T.P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D.C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
[CrossRef]

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karslsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003).
[CrossRef]

P. Sanchis, J. Martí, P. Bienstman, and R. Baets, "Semi-analytic approach for analyzing coupling issues in photonic crystal structures," Appl. Phys. Lett. 87, 203107 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, "Analysis of Butt Coupling in Photonic Crystals," IEEE J. Quantum Electron. 40, 541-550 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. Sanchis, J. García, J. Martí, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental Demonstration of High Coupling Efficiency Between Wide Ridge Waveguides and Single-Mode Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

J. Lightwave Technol. (1)

Nature (2)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, and H.M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

S.Y. Lin, J.G. Fleming, D.L. Hetherington, B.K. Smith, R. Biswas, K.M. Ho, M.M. Sigalas, W. Zubrzycki, S.R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (3)

E. Istrate, A.A. Green, and E.H. Sargent, "Behavior of light at photonic crystal interfaces," Phys. Rev. B 71, 195122 (2005).
[CrossRef]

S.G. Johnson, S. Fan, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

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]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Other (2)

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (15)

Fig. 1.
Fig. 1.

Schematic of the theoretical model used to calculate the pulse propagation. The three media depicted represent: 1) input waveguide, 2) PhC waveguide of length L, and 3) output waveguide. The transmission and reflection coefficients at each interface are also depicted (tij , rij ). The expressions of each signal getting out the cavity are shown, as well as the combination of all of them.

Fig. 2.
Fig. 2.

PhC waveguide created by removing a row of air holes. The structure is accessed at its ends by means of two Silicon waveguides of width √3a.

Fig. 3.
Fig. 3.

Dispersion diagram for TE-polarized modes of the selected single-line-defect waveguide.

Fig. 4.
Fig. 4.

Transmission and reflection coefficients for the interface between the Silicon and the PhC waveguides.

Fig. 5.
Fig. 5.

Propagation for a PhC waveguide of length L = 15a. a) Input pulse. b) Output pulses generated in the cavity. Each subsequent pulse has smaller amplitude, so each one has been scaled by an appropriate factor in order to achieve a better representation. c) Total output pulse obtained by combining the contributions shown in b) (solid line). The output pulse obtained by directly applying the Fabry-Perot formula of Eq. 2 is also shown (dashed line), but it perfectly matches the solid curve. The output pulse for the FDTD simulation is also plotted with dotted line in c).

Fig. 6.
Fig. 6.

Transmission spectrum of a PhC waveguide with length L = 21a for a FDTD simulation (solid line). The beginning of the band is determined by the projection of the edge slope (dotted line) as 0.21947 (c/a). The theoretical transmission spectrum for the EME calculations obtained from Eq. 2 for L = 21a has also been depicted with dashed line.

Fig. 7.
Fig. 7.

(a) Input pulse, (b) output pulses generated in the cavity and c) total output pulse when a length of the waveguide L = 12a is selected (solid - theoretical propagation, dotted - FDTD simulation).

Fig. 8.
Fig. 8.

(a) Input pulse, (b) output pulses generated in the cavity and c) total output pulse when a length of the waveguide L = 18a is selected (solid - theoretical propagation, dotted - FDTD simulation).

Fig. 9.
Fig. 9.

Evolution of the pulse shape after each contribution is taken into account. Each row depicts the evolution for a PhC waveguide length: a) L = 12a, b) L = 15a, c) L = 18a. Each column depicts the pulse shape after each subsequent contribution is taken into account, i.e., column 1 depicts the pulse shape when only the first contribution is considered, column 2 depicts the pulse shape when the second contribution is also considered, and column 3 depicts the pulse shape when the third contribution is also considered. The pulse shapes corresponding to the previous column are also depicted with dashed line in order to compare their evolution (obviously, this is only made for columns 2 and 3).

Fig. 10.
Fig. 10.

(a) Pulse amplitude, (b) temporal width, (c) time delay and (d) group velocity of the output pulse versus the PhC waveguide length. Solid lines depict the results obtained when the pulses are theoretically propagated. Dashed lines depict the theoretical evolution of the parameters when no reflections are considered at the waveguide interfaces. Dotted lines depict the results obtained with FDTD for PhC waveguide lengths between a and 21a. The dashed-dotted line in plot d) depicts the “instantaneous” group velocity obtained by derivating the time delay results of the FDTD simulations.

Fig. 11.
Fig. 11.

(a) Pulse amplitude, (b) temporal width, (c) time delay and (d) group velocity of the output pulse versus the PhC waveguide length for different working frequencies. f = 0.2176 (c/a) - solid line; f = 0.218 (c/a) - dashed line; f = 0.21823 (c/a) - dotted line; f = 0.2185 (c/a) -dash-dotted line.

Fig. 12.
Fig. 12.

Spectra of the four input pulses simulated. f = 0.2176 (c/a) - solid line; f = 0.218 (c/a) - dashed line; f = 0.21823 (c/a) - dotted line; f = 0.2185 (c/a) - dash-dotted line. The transmission and reflection coefficients have been also depicted.

Fig. 13.
Fig. 13.

(a) Pulse amplitude, (b) temporal broadening, (c) time delay and (d) group velocity of the output pulse versus the PhC waveguide length for a central frequency 0.218 (c/a) and pulse widths T (T = 2138 (a/c), solid line), 2T (dashed line) and 0.5T (dotted line).

Fig. 14.
Fig. 14.

Propagation over a PhC waveguide of length 20a for two pulses with central frequency 0.218 (c/a) and different widths: 0.5T and 2T (where T =2138 (a/c)). (a) Input pulses for both widths (dashed - 2T, dotted - 0.5T), (b) output pulses generated in the cavity for the 2T case and (c) output pulses generated in the cavity for the 0.5T case.

Fig. 15.
Fig. 15.

Evolution of the pulse shape after each contribution is taken into account for a case where a higher reflection coefficient exists (f = 0.218 (c/a), 2T) . Each row depicts the evolution for a PhC waveguide length: a) L = 11a, b) L = 14a, c) L = 18a. Each column depicts the pulse shape after each subsequent contribution is taken into account. The pulse shapes corresponding to the previous column are also depicted with dashed line.

Tables (1)

Tables Icon

Table 1. Amplitude, temporal width and time delay of the output pulse for different PhC waveguide lengths. Two values are shown for each length, the first corresponding to the FDTD simulations and the second corresponding to the theoretical calculations carried out by means of Eq. 1. The input pulse has normalized amplitude and a temporal FWHM of 2138 (c/a).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E n = E 0 t 12 t 23 ( r 23 r 21 ) n 1 exp [ ( 2 n 1 ) jβL ] ,
E T = n = 1 E n = E 0 t 12 t 23 exp ( jβL ) 1 r 23 r 21 exp ( 2 jβL ) .
O n = ( i = 1 n E 0 t 2 r 2 ( i 1 ) ) 2 ,
Q n = O n O n 1 O 2 O 1 × 100 < threshold
Q n = r 2 ( n 2 ) r 2 ( n 1 ) + 2 i = 1 n 1 r 2 ( i 1 ) r 2 + 2 × 100 < threshold

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