Abstract

We simulate the propagation of light in a W1 planar photonic crystal waveguide with the three-dimensional finite-difference time-domain method and apply an inner product against previously calculated mode profiles to the simulated field cross sections. We show that this inner product satisfies mode orthogonality for both photonic crystal waveguides and segmented waveguides and use the obtained data to evaluate waveguide losses.

© 2003 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. T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature (London) 383, 699–702 (1996).
    [CrossRef]
  3. A. Mekis, J. C. Chen, I. Kurand, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  4. T. Baba, N. Fukaya, J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
    [CrossRef]
  5. T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
    [CrossRef]
  6. M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,” J. Lightwave Technol. 17, 2096–2112 (1999).
    [CrossRef]
  7. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. De la Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050–2057 (1999).
    [CrossRef]
  8. M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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. H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
    [CrossRef]
  10. P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
    [CrossRef]
  11. P. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
    [CrossRef]
  12. G. R. Hadley, “Out-of-plane losses of line defect photonic crystal waveguides,” IEEE Photonics Technol. Lett. 14, 642–644 (2002).
    [CrossRef]
  13. L. C. Andreani, M. Agio, “Intrinsic diffraction losses in photonic crystal waveguides with line defects,” Appl. Phys. Lett. 82, 2011–2013 (2003).
    [CrossRef]
  14. Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
    [CrossRef]
  15. A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  16. M. Qiu, B. Jaskorzynska, M. Swillo, H. Benisty, “Time-domain 2D modeling of slab-waveguide-based photonic-crystal devices in the presence of radiation losses,” Microwave Opt. Technol. Lett. 34, 387–393 (2002).
    [CrossRef]
  17. M. Lončar, T. Doll, J. Vučković, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
    [CrossRef]
  18. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London (1983).

2003 (1)

L. C. Andreani, M. Agio, “Intrinsic diffraction losses in photonic crystal waveguides with line defects,” Appl. Phys. Lett. 82, 2011–2013 (2003).
[CrossRef]

2002 (7)

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

M. Qiu, B. Jaskorzynska, M. Swillo, H. Benisty, “Time-domain 2D modeling of slab-waveguide-based photonic-crystal devices in the presence of radiation losses,” Microwave Opt. Technol. Lett. 34, 387–393 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

G. R. Hadley, “Out-of-plane losses of line defect photonic crystal waveguides,” IEEE Photonics Technol. Lett. 14, 642–644 (2002).
[CrossRef]

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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]

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
[CrossRef]

2001 (1)

P. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

2000 (1)

1999 (3)

1996 (2)

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

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

1987 (1)

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

Agio, M.

L. C. Andreani, M. Agio, “Intrinsic diffraction losses in photonic crystal waveguides with line defects,” Appl. Phys. Lett. 82, 2011–2013 (2003).
[CrossRef]

Allan, D. C.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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]

Andreani, L. C.

L. C. Andreani, M. Agio, “Intrinsic diffraction losses in photonic crystal waveguides with line defects,” Appl. Phys. Lett. 82, 2011–2013 (2003).
[CrossRef]

Astratov, V. N.

Baba, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

T. Baba, N. Fukaya, J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Benech, P.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Benisty, H.

M. Qiu, B. Jaskorzynska, M. Swillo, H. Benisty, “Time-domain 2D modeling of slab-waveguide-based photonic-crystal devices in the presence of radiation losses,” Microwave Opt. Technol. Lett. 34, 387–393 (2002).
[CrossRef]

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

P. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Benyattou, T.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Bhat, R.

Boroditsky, M.

Brand, S.

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

Cassagne, D.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

Chen, J. C.

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

Coccioli, R.

Culshaw, I. S.

De la Rue, R. M.

Désières, Y.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Doll, T.

Fan, S.

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

Fukaya, N.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

T. Baba, N. Fukaya, J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Grillet, C.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Hadley, G. R.

G. R. Hadley, “Out-of-plane losses of line defect photonic crystal waveguides,” IEEE Photonics Technol. Lett. 14, 642–644 (2002).
[CrossRef]

Iwai, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Jaskorzynska, B.

M. Qiu, B. Jaskorzynska, M. Swillo, H. Benisty, “Time-domain 2D modeling of slab-waveguide-based photonic-crystal devices in the presence of radiation losses,” Microwave Opt. Technol. Lett. 34, 387–393 (2002).
[CrossRef]

Joannopoulos, J. D.

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

Jouanin, C.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

Krauss, T. F.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. De la Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050–2057 (1999).
[CrossRef]

M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,” J. Lightwave Technol. 17, 2096–2112 (1999).
[CrossRef]

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

Kuchinsky, S.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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]

Kurand, I.

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

Lalanne, P.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
[CrossRef]

P. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Letartre, X.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Loncar, M.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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. Lončar, T. Doll, J. Vučković, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London (1983).

Mekis, A.

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

Morand, A.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Motegi, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Nedeljkovic, D.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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]

Olivier, S.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

Orobtchouk, R.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Pearsall, T. P.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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, B. Jaskorzynska, M. Swillo, H. Benisty, “Time-domain 2D modeling of slab-waveguide-based photonic-crystal devices in the presence of radiation losses,” Microwave Opt. Technol. Lett. 34, 387–393 (2002).
[CrossRef]

Rattier, M.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

Rojo-Romeo, P.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Sakai, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Scherer, A.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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. Lončar, T. Doll, J. Vučković, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

Seassal, C.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Skolnick, M. S.

Smith, C. J. M.

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London (1983).

Stevenson, R. M.

Swillo, M.

M. Qiu, B. Jaskorzynska, M. Swillo, H. Benisty, “Time-domain 2D modeling of slab-waveguide-based photonic-crystal devices in the presence of radiation losses,” Microwave Opt. Technol. Lett. 34, 387–393 (2002).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

Viktorovitch, P.

Y. Désières, T. Benyattou, R. Orobtchouk, A. Morand, P. Benech, C. Grillet, C. Seassal, X. Letartre, P. Rojo-Romeo, P. Viktorovitch, “Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane,” J. Appl. Phys. 92, 2227–2234 (2002).
[CrossRef]

Villeneuve, P. R.

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

Vrijen, R.

Vuckovic, J.

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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. Lončar, T. Doll, J. Vučković, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

Watanabe, Y.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Whittaker, D. M.

Yablonovitch, E.

Yonekura, J.

T. Baba, N. Fukaya, J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, 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]

L. C. Andreani, M. Agio, “Intrinsic diffraction losses in photonic crystal waveguides with line defects,” Appl. Phys. Lett. 82, 2011–2013 (2003).
[CrossRef]

Electron. Lett. (1)

T. Baba, N. Fukaya, J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

IEEE J. Quantum Electron. (3)

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

H. Benisty, P. Lalanne, S. Olivier, M. Rattier, C. J. M. Smith, T. F. Krauss, C. Jouanin, D. Cassagne, “Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals,” IEEE J. Quantum Electron. 35, 205–215 (2002).
[CrossRef]

P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

G. R. Hadley, “Out-of-plane losses of line defect photonic crystal waveguides,” IEEE Photonics Technol. Lett. 14, 642–644 (2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Cross section of the simulation domain. A dipole source launches a field of symmetry σxy=-1, σyz=+1. Every second lattice period a field probe saves the field.

Fig. 2
Fig. 2

Mode profile for ka=0.07π (lower band of e1). The colormap shows |Bz|. The thick black line shows the high-index region (n=3.43). The two maxima have the same phase (i.e., Bz is even). Units are in micrometers for a pitch of a=0.52µ.

Fig. 3
Fig. 3

20 log10(|ψl|ψka=0.07π|) is plotted with circles, where |ψl is the field profile at the lth probe and |ψka=0.07π is the mode profile at ka=0.07π. 10 log10(|ψl|ψl|) is plotted with crosses. Probes are spaced by two lattice constants.

Fig. 4
Fig. 4

Plot of the phase of ψl|ψka=0.07π. The expected linear behavior is seen.

Fig. 5
Fig. 5

(a) Dispersion diagram of the lower band of e1, (b) losses of the lower band of e1. The straight line in (a) represents the light line. Losses (in dB/mm) correspond to a lattice parameter of a=0.52µ.

Fig. 6
Fig. 6

ka as set in the mode solve versus ka extracted from the phases of ψl|ψka. Away from the mini stop band, in the high-group-velocity regime, there is a good correspondence. However, near the mini stop band the behavior of phase ψl|ψka differs from what would be expected from the dispersion diagram.

Equations (10)

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(Ex, Ey, Ez)(Ex, -Ey, Ez)*, (Bx, By, Bz)(-Bx, By, -Bz)*.
E=ej(x, z)exp(iβjy), H=hj(x, z)exp(iβjy),
E¯=ek(x, z)exp(iβky),H¯=hk(x, z)exp(iβky),
(βj-βk)A{ej×hk*+ek*×hj}yˆdA=0,
E=ej(x, y, z)exp(iβjy), H=hj(x, y, z)exp(iβjy),
E¯=ek(x, y, z)exp(iβky), H¯=hk(x, y, z)exp(iβky),
ψ|ψ¯y0=14A{y=y0}{ej×hk*+ek*×hj}yˆdA.
ψ1|ψ2y0=ψ1|ψ2y0+a,
ψ1|ψ2=ψ1|Ta+Ta|ψ2.
ψ1|Ta+Ta|ψ2=exp[i(k2-k1)a]ψ1|ψ2.

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