Abstract

We propose an active waveguide design that provides both low propagation losses (< 20 dB/cm) and the capability for electrical pumping of the photonic crystal waveguide with a vertical contacting scheme. A careful estimation of a large number of parameters is required in order to obtain both properties. The proposed device supports single mode operation at the telecom wavelength λ = 1550 nm and is suitable for the implementation of in-plane active photonic crystal devices, such as semiconductor optical amplifiers and lasers.

© 2012 OSA

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  1. S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
    [CrossRef]
  2. S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
    [CrossRef]
  3. A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
    [CrossRef]
  4. T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
    [CrossRef]
  5. A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
    [CrossRef]
  6. R. Kappeler, P. Kaspar, and H. Jäckel, “Propagation loss computation of W1 photonic crystal waveguides using the cutback technique with the 3D-FDTD method,” Photonics Nanostruct. Fundam. Appl. 9, 235–247 (2011).
    [CrossRef]
  7. Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, and K. Inoue, “Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length,” Opt. Express 12, 1090–1096 (2004).
    [CrossRef] [PubMed]
  8. L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
    [CrossRef]
  9. S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003).
    [CrossRef] [PubMed]
  10. E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005).
    [CrossRef]
  11. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
    [CrossRef]
  12. H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
    [CrossRef] [PubMed]
  13. A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
    [CrossRef]
  14. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the Flow of Light, 2nd ed. (Princeton University Press, 2007).
  15. R. März, Integrated Optics, Design and Modeling (Artech House Publishers, 1994).
  16. P. Kaspar, R. Kappeler, D. Erni, and H. Jäckel, “Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement,” Opt. Express 19, 24344–24353 (2011).
    [CrossRef] [PubMed]
  17. B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of bloch wave propagation in photonic crystals.” J. Opt. Soc. Am. B 22, 1179–1190 (2005).
    [CrossRef]
  18. W. Kuang and J. D. O’Brien, “Reducing the out-of-plane radiation loss of photonic crystal waveguides on high-index substrates,” Opt. Lett. 29, 860–862 (2004).
    [CrossRef] [PubMed]
  19. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]
  20. B. Jiang, W. Zhou, W. Chen, A. Liu, and W. Zheng, “Improved fake mode free plane wave expansion method,” Opt. Lett. 36, 2788–2790 (2011).
    [CrossRef] [PubMed]
  21. R. Kappeler, P. Kaspar, and H. Jäckel, “Loss-relevant structural imperfections in substrate-type photonic crystal waveguides,” IEEE J. Lightwave Technol. 29, 3156–3166 (2011).
    [CrossRef]
  22. G. K. Wachutka, “Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling,” IEEE Trans. Comput.-Aided Des. 9, 1141–1149 (1990).
    [CrossRef]
  23. G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
    [CrossRef]
  24. The non-radiative recombination rate was estimated by solving J = Bn2 +Cn3 using the radiative recombination coefficient B = 0.96 × 10−10cm3/s and the Auger coefficient C = 7 × 10−29cm6/s for In0.53Ga0.47As [25].
  25. M. Levinshtein, S. Rumyantsev, and M. Shureditors, Handbook Series on Semiconductor Parameters (World Scientific, 1999).

2011 (5)

R. Kappeler, P. Kaspar, and H. Jäckel, “Propagation loss computation of W1 photonic crystal waveguides using the cutback technique with the 3D-FDTD method,” Photonics Nanostruct. Fundam. Appl. 9, 235–247 (2011).
[CrossRef]

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

R. Kappeler, P. Kaspar, and H. Jäckel, “Loss-relevant structural imperfections in substrate-type photonic crystal waveguides,” IEEE J. Lightwave Technol. 29, 3156–3166 (2011).
[CrossRef]

B. Jiang, W. Zhou, W. Chen, A. Liu, and W. Zheng, “Improved fake mode free plane wave expansion method,” Opt. Lett. 36, 2788–2790 (2011).
[CrossRef] [PubMed]

P. Kaspar, R. Kappeler, D. Erni, and H. Jäckel, “Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement,” Opt. Express 19, 24344–24353 (2011).
[CrossRef] [PubMed]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

2006 (2)

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

2005 (3)

E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005).
[CrossRef]

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of bloch wave propagation in photonic crystals.” J. Opt. Soc. Am. B 22, 1179–1190 (2005).
[CrossRef]

2004 (6)

Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, and K. Inoue, “Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length,” Opt. Express 12, 1090–1096 (2004).
[CrossRef] [PubMed]

W. Kuang and J. D. O’Brien, “Reducing the out-of-plane radiation loss of photonic crystal waveguides on high-index substrates,” Opt. Lett. 29, 860–862 (2004).
[CrossRef] [PubMed]

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

2003 (2)

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003).
[CrossRef] [PubMed]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

1993 (1)

G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
[CrossRef]

1990 (1)

G. K. Wachutka, “Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling,” IEEE Trans. Comput.-Aided Des. 9, 1141–1149 (1990).
[CrossRef]

Agio, M.

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

Anand, S.

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

Asakawa, K.

Baek, J.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Berrier, A.

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

Bewtra, N.

G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
[CrossRef]

Chen, W.

Chong, H.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

De La Rue, R. M.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

de Rossi, S.

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

Duan, Guang-Hua

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

Dulkeith, E.

E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005).
[CrossRef]

Dunbar, L. A.

Ellis, B.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Erni, D.

Ferrini, R.

Forchel, A.

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Gentner, J. L.

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Goldstein, L.

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Haller, E. E.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Happ, T. D.

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Harris, J.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Houdré, R.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Ikeda, N.

Inoue, K.

Jäckel, H.

R. Kappeler, P. Kaspar, and H. Jäckel, “Propagation loss computation of W1 photonic crystal waveguides using the cutback technique with the 3D-FDTD method,” Photonics Nanostruct. Fundam. Appl. 9, 235–247 (2011).
[CrossRef]

R. Kappeler, P. Kaspar, and H. Jäckel, “Loss-relevant structural imperfections in substrate-type photonic crystal waveguides,” IEEE J. Lightwave Technol. 29, 3156–3166 (2011).
[CrossRef]

P. Kaspar, R. Kappeler, D. Erni, and H. Jäckel, “Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement,” Opt. Express 19, 24344–24353 (2011).
[CrossRef] [PubMed]

Jiang, B.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the Flow of Light, 2nd ed. (Princeton University Press, 2007).

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Ju, Y.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Kafesaki, M.

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

Kamp, M.

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Kappeler, R.

P. Kaspar, R. Kappeler, D. Erni, and H. Jäckel, “Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement,” Opt. Express 19, 24344–24353 (2011).
[CrossRef] [PubMed]

R. Kappeler, P. Kaspar, and H. Jäckel, “Propagation loss computation of W1 photonic crystal waveguides using the cutback technique with the 3D-FDTD method,” Photonics Nanostruct. Fundam. Appl. 9, 235–247 (2011).
[CrossRef]

R. Kappeler, P. Kaspar, and H. Jäckel, “Loss-relevant structural imperfections in substrate-type photonic crystal waveguides,” IEEE J. Lightwave Technol. 29, 3156–3166 (2011).
[CrossRef]

Kaspar, P.

R. Kappeler, P. Kaspar, and H. Jäckel, “Loss-relevant structural imperfections in substrate-type photonic crystal waveguides,” IEEE J. Lightwave Technol. 29, 3156–3166 (2011).
[CrossRef]

R. Kappeler, P. Kaspar, and H. Jäckel, “Propagation loss computation of W1 photonic crystal waveguides using the cutback technique with the 3D-FDTD method,” Photonics Nanostruct. Fundam. Appl. 9, 235–247 (2011).
[CrossRef]

P. Kaspar, R. Kappeler, D. Erni, and H. Jäckel, “Relevance of the light line in planar photonic crystal waveguides with weak vertical confinement,” Opt. Express 19, 24344–24353 (2011).
[CrossRef] [PubMed]

Kim, S.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Krauss, T. F.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

Kuang, W.

Kwon, S.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Lee, K.

G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
[CrossRef]

Lee, Y.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Legratiet, L.

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

Lelarge, F.

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

Liu, A.

Lombardet, B.

Macintyre, D.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

Mahnkopf, S.

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

Malm, G.

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

März, R.

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

R. März, Integrated Optics, Design and Modeling (Artech House Publishers, 1994).

Mayer, M. A.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

McNab, S. J.

E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005).
[CrossRef]

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003).
[CrossRef] [PubMed]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the Flow of Light, 2nd ed. (Princeton University Press, 2007).

Moll, N.

Mulot, M.

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

Nakamura, Y.

O’Brien, J. D.

O’Faolain, L.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

Oestling, M.

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

Olivier, S.

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Park, H.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Sagnes, I.

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

Sarmiento, T.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Shambat, G.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Soukoulis, C. M.

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

Sugimoto, Y.

Talneau, A.

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

Tan, G. L.

G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
[CrossRef]

Tanaka, Y.

Thoms, S.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

Vlasov, Y. A.

E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005).
[CrossRef]

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Wachutka, G. K.

G. K. Wachutka, “Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling,” IEEE Trans. Comput.-Aided Des. 9, 1141–1149 (1990).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the Flow of Light, 2nd ed. (Princeton University Press, 2007).

Xu, J. M.

G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
[CrossRef]

Yang, J.

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Yuan, X.

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

Zheng, W.

Zhou, W.

Appl. Phys. Lett. (2)

A. Talneau, L. LeGratiet, J. L. Gentner, A. Berrier, M. Mulot, S. Anand, and S. Olivier, “High external efficiency in a monomode full-photonic-crystal laser under continuous wave electrical injection,” Appl. Phys. Lett. 85, 1913–1915 (2004).
[CrossRef]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Electron. Lett. (1)

L. O’Faolain, X. Yuan, D. Macintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 421454–1455 (2006).
[CrossRef]

IEEE J. Lightwave Technol. (2)

R. Kappeler, P. Kaspar, and H. Jäckel, “Loss-relevant structural imperfections in substrate-type photonic crystal waveguides,” IEEE J. Lightwave Technol. 29, 3156–3166 (2011).
[CrossRef]

S. de Rossi, I. Sagnes, L. Legratiet, A. Talneau, A. Berrier, M. Mulot, S. Anand, and J. L. Gentner, “Longitudinal mode selection in constricted photonic crystal guides and electrically injected lasers,” IEEE J. Lightwave Technol. 23, 1363–1368 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

S. Mahnkopf, R. März, M. Kamp, Guang-Hua Duan, F. Lelarge, and A. Forchel, “Tunable photonic crystal coupled-cavity laser.” IEEE J. Quantum Electron. 40, 1306–1314 (2004).
[CrossRef]

G. L. Tan, N. Bewtra, K. Lee, and J. M. Xu, “A two-dimensional nonisothermal finite element simulation of laser diodes,” IEEE J. Quantum Electron. 29, 822–835 (1993).
[CrossRef]

IEEE Trans. Comput.-Aided Des. (1)

G. K. Wachutka, “Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling,” IEEE Trans. Comput.-Aided Des. 9, 1141–1149 (1990).
[CrossRef]

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

Nat. Photonics (1)

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučkovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Photonics Nanostruct. Fundam. Appl. (2)

A. Talneau, M. Mulot, S. Anand, S. Olivier, M. Agio, M. Kafesaki, and C. M. Soukoulis, “Modal behavior of single-line photonic crystal guiding structures on InP substrate,” Photonics Nanostruct. Fundam. Appl. 2, 1–10 (2004).
[CrossRef]

R. Kappeler, P. Kaspar, and H. Jäckel, “Propagation loss computation of W1 photonic crystal waveguides using the cutback technique with the 3D-FDTD method,” Photonics Nanostruct. Fundam. Appl. 9, 235–247 (2011).
[CrossRef]

Phys. Rev. B (1)

E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005).
[CrossRef]

Proceedings of SPIE (1)

A. Berrier, M. Mulot, G. Malm, M. Oestling, and S. Anand, “Electrical conduction through a 2D InP-based photonic crystal,” Proceedings of SPIE 6322, J1–J10 (2006).
[CrossRef]

Science (1)

H. Park, S. Kim, S. Kwon, Y. Ju, J. Yang, J. Baek, and Y. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the Flow of Light, 2nd ed. (Princeton University Press, 2007).

R. März, Integrated Optics, Design and Modeling (Artech House Publishers, 1994).

The non-radiative recombination rate was estimated by solving J = Bn2 +Cn3 using the radiative recombination coefficient B = 0.96 × 10−10cm3/s and the Auger coefficient C = 7 × 10−29cm6/s for In0.53Ga0.47As [25].

M. Levinshtein, S. Rumyantsev, and M. Shureditors, Handbook Series on Semiconductor Parameters (World Scientific, 1999).

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Figures (6)

Fig. 1
Fig. 1

The proposed device consists of a PhC waveguide membrane containing a quantum well. The membrane is pumped vertically through two narrow connecting channels. The InGaAs capping-layer is highly doped to allow for a low contact resistance to the metal contact. Furthermore the capping-layer is needed to cover the holes with SiNx for the formation of the contact.

Fig. 2
Fig. 2

Left: band diagram obtained with MPB and a 3D supercell. The size of the dot corresponds to the energy confinement within the core of the PhC waveguide. The straight black line represents the air light line, the dotted red (orange) line represents the dispersion curve obtained from the vertical slab operated in TM (TE) mode.

Fig. 3
Fig. 3

The influences of the separatrices on the transmission properties. The top figure shows the dispersion curves of the modes of the system in the Fourier representation. The modes are schematically drawn for each of the four points (A–D) that are marked in the dispersion diagram. The PhC waveguide mode is only guided if all Fourier components are below the background line (TE mode of the vertical slab).

Fig. 4
Fig. 4

Definitions of the polarization in 2D PhC structures (left) and in slab waveguides (right).

Fig. 5
Fig. 5

Left: A simplified 2D model of the device to estimate the height of the contact channel htop that minimizes the losses originating from the metallic contact and the doped cladding layers. Right: The propagation losses of the TE mode for λ = 1550 nm and for four different core layer thicknesses tcore as a function of channel height htop computed with Lumerical, a commercial mode solver.

Fig. 6
Fig. 6

A: Measured resistance for 320 μm long trenches of various widths w. The smallest measurable channel width was w = 200 nm. B: schematic of the etched trench waveguides.

Tables (2)

Tables Icon

Table 1 Parameters for the proposed design of Fig. 1. This table summarizes the results from Sec. 4 and Sec. 5. The values given in nm are scaled, such that the best obtained propagation loss value (ωa/(2πc) = 0.253) coincides with a operation wavelength of λ = 1550 nm.

Tables Icon

Table 2 The frequency band width Δωa/(2πc), where the PhC waveguide with a contact channel width w = 0.526a has a propagation loss lower than 100dB/cm and 20dB/cm, respectively, is listed below.

Equations (5)

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

ε m = max ( ε ( r b ) ) ,
g = N g 0 ln ( J / ( N J 0 ) ) .
J tr = N J 0 e α W G / ( N g 0 ) .
( k T ) = H ,
T ( z ) = H 2 k z ( z h total ) + T sink .

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