Abstract

We show comparison of four different numerical methods for simulating Photonic-Crystal (PC) VCSELs. We present the theoretical basis behind each method and analyze the differences by studying a benchmark VCSEL structure, where the PC structure penetrates all VCSEL layers, the entire top-mirror DBR, a fraction of the top-mirror DBR or just the VCSEL cavity. The different models are evaluated by comparing the predicted resonance wavelengths and threshold gains for different hole diameters and pitches of the PC. The agreement between the models is relatively good, except for one model, which corresponds to the effective index method. The simulation results elucidate the strength and weaknesses of the analyzed methods; and outline the limits of applicability of the different models.

© 2010 Optical Society of America

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  1. . D. S. Song, S. H. Kim, H. G. Park, c. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic-crystal verticalcavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
    [CrossRef]
  2. . A. J. Danner, T. S. Kim, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity laser with improved output power,” Electron. Lett. 41, 325–326 (2005).
    [CrossRef]
  3. . T. Czyszanowski, M. Dems, and K. Panajotov, “Single mode condition and modes discrimination in photoniccrystal 1.3 μm AlInGaAs/InP VCSEL,” Opt. Express 15, 5604–5609 (2007).
    [CrossRef] [PubMed]
  4. . T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
    [CrossRef]
  5. . S. Bischoff, F. Romstad, M. Juhl, M. H. Madsen, J. Hanberg, and D. Birkedal, “2.5 Gbit/s modulation of 1300 nm single-mode photonic crystal VCSELs,” in “Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD),” (2006), OFA6.
  6. . F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
    [CrossRef]
  7. . D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
    [CrossRef]
  8. . M. Dems, T. Czyszanowski, and K. Panajotov, “Highly birefringent and dichroic photonic-crystal VCSEL design,” Opt. Commun 281, 3149–3152 (2008).
    [CrossRef]
  9. . G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995).
    [CrossRef] [PubMed]
  10. . G. P. Bava, P. Debernardi, and L. Fratta, “Three-dimensional model for vectorial fields in vertical-cavity surfaceemitting lasers,” Phys Rev. A 63, 23816 (2001).
    [CrossRef]
  11. . S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE T. Antenn. Propag. 44, 1630–1639 (1996).
    [CrossRef]
  12. . P. Nyakas, “Full-vectorial three-dimensional finite element optical simulation of vertical-cavity surface-emitting lasers,” IEEE J. Lightwave Techn. 25, 2427–2434 (2007).
    [CrossRef]
  13. . P. Nyakas, G. Varga, Z. Puskás, N. Hashizume, T. Kárpáti, T. Veszprémi, and G. Zsombok, “Self-consistent real three-dimensional simulation of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 23, 1761–1769 (2006).
    [CrossRef]
  14. . M. Dems, R. Kotynski, and K. Panajotov, “Plane-wave admittance method — a novel approach for determining the electromagnetic modes in photonic structures,” Opt. Express 13, 3196–3207 (2005).
    [CrossRef] [PubMed]
  15. . M. Dems, “Plane-wave admittance method and its applications to modeling semiconductor lasers and planar photonic-crystal structures,” Ph.D. thesis, Technical University of Lodz (2007).
  16. . M. Dems and K. Panajotov, “Modeling of single- and multimode photonic-crystal planar waveguides with planewave admittance method,” Appl. Phys. B 89, 19–23 (2007).
    [CrossRef]
  17. . P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
    [CrossRef]

2008 (2)

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

. M. Dems, T. Czyszanowski, and K. Panajotov, “Highly birefringent and dichroic photonic-crystal VCSEL design,” Opt. Commun 281, 3149–3152 (2008).
[CrossRef]

2007 (3)

. P. Nyakas, “Full-vectorial three-dimensional finite element optical simulation of vertical-cavity surface-emitting lasers,” IEEE J. Lightwave Techn. 25, 2427–2434 (2007).
[CrossRef]

. M. Dems and K. Panajotov, “Modeling of single- and multimode photonic-crystal planar waveguides with planewave admittance method,” Appl. Phys. B 89, 19–23 (2007).
[CrossRef]

. T. Czyszanowski, M. Dems, and K. Panajotov, “Single mode condition and modes discrimination in photoniccrystal 1.3 μm AlInGaAs/InP VCSEL,” Opt. Express 15, 5604–5609 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

. M. Dems, R. Kotynski, and K. Panajotov, “Plane-wave admittance method — a novel approach for determining the electromagnetic modes in photonic structures,” Opt. Express 13, 3196–3207 (2005).
[CrossRef] [PubMed]

. A. J. Danner, T. S. Kim, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity laser with improved output power,” Electron. Lett. 41, 325–326 (2005).
[CrossRef]

2004 (1)

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

2003 (1)

. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
[CrossRef]

2002 (1)

. D. S. Song, S. H. Kim, H. G. Park, c. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic-crystal verticalcavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

2001 (2)

. G. P. Bava, P. Debernardi, and L. Fratta, “Three-dimensional model for vectorial fields in vertical-cavity surfaceemitting lasers,” Phys Rev. A 63, 23816 (2001).
[CrossRef]

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

1996 (1)

. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE T. Antenn. Propag. 44, 1630–1639 (1996).
[CrossRef]

1995 (1)

Baets, R.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Bava, G. P.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

. G. P. Bava, P. Debernardi, and L. Fratta, “Three-dimensional model for vectorial fields in vertical-cavity surfaceemitting lasers,” Phys Rev. A 63, 23816 (2001).
[CrossRef]

Bienstman, P.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Birkedal, D.

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

Bischoff, S.

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

Brunner, M.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Choi, H. W.

. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
[CrossRef]

Choquette, K. D.

. A. J. Danner, T. S. Kim, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity laser with improved output power,” Electron. Lett. 41, 325–326 (2005).
[CrossRef]

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

Chuang, S. L.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Conradi, C.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Czyszanowski, T.

. M. Dems, T. Czyszanowski, and K. Panajotov, “Highly birefringent and dichroic photonic-crystal VCSEL design,” Opt. Commun 281, 3149–3152 (2008).
[CrossRef]

. T. Czyszanowski, M. Dems, and K. Panajotov, “Single mode condition and modes discrimination in photoniccrystal 1.3 μm AlInGaAs/InP VCSEL,” Opt. Express 15, 5604–5609 (2007).
[CrossRef] [PubMed]

Danner, A. J.

. A. J. Danner, T. S. Kim, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity laser with improved output power,” Electron. Lett. 41, 325–326 (2005).
[CrossRef]

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

Debernardi, P.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

. G. P. Bava, P. Debernardi, and L. Fratta, “Three-dimensional model for vectorial fields in vertical-cavity surfaceemitting lasers,” Phys Rev. A 63, 23816 (2001).
[CrossRef]

Dems, M.

. M. Dems, T. Czyszanowski, and K. Panajotov, “Highly birefringent and dichroic photonic-crystal VCSEL design,” Opt. Commun 281, 3149–3152 (2008).
[CrossRef]

. M. Dems and K. Panajotov, “Modeling of single- and multimode photonic-crystal planar waveguides with planewave admittance method,” Appl. Phys. B 89, 19–23 (2007).
[CrossRef]

. T. Czyszanowski, M. Dems, and K. Panajotov, “Single mode condition and modes discrimination in photoniccrystal 1.3 μm AlInGaAs/InP VCSEL,” Opt. Express 15, 5604–5609 (2007).
[CrossRef] [PubMed]

. M. Dems, R. Kotynski, and K. Panajotov, “Plane-wave admittance method — a novel approach for determining the electromagnetic modes in photonic structures,” Opt. Express 13, 3196–3207 (2005).
[CrossRef] [PubMed]

Fratta, L.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

. G. P. Bava, P. Debernardi, and L. Fratta, “Three-dimensional model for vectorial fields in vertical-cavity surfaceemitting lasers,” Phys Rev. A 63, 23816 (2001).
[CrossRef]

Gedney, S. D.

. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE T. Antenn. Propag. 44, 1630–1639 (1996).
[CrossRef]

Grasso, D. M.

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

Gulden, K.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Hadley, G. R.

Hashizume, N.

Jacobsen, S.

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

Juhl, M.

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

Kárpáti, T.

Kim, S. H.

. D. S. Song, S. H. Kim, H. G. Park, c. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic-crystal verticalcavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Kim, T. S.

. A. J. Danner, T. S. Kim, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity laser with improved output power,” Electron. Lett. 41, 325–326 (2005).
[CrossRef]

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

Klein, K.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Kotynski, R.

Larsson, A.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Lee, Y. H.

. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
[CrossRef]

Lee, Y. J.

. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
[CrossRef]

Noble, M. J.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Nyakas, P.

. P. Nyakas, “Full-vectorial three-dimensional finite element optical simulation of vertical-cavity surface-emitting lasers,” IEEE J. Lightwave Techn. 25, 2427–2434 (2007).
[CrossRef]

. P. Nyakas, G. Varga, Z. Puskás, N. Hashizume, T. Kárpáti, T. Veszprémi, and G. Zsombok, “Self-consistent real three-dimensional simulation of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 23, 1761–1769 (2006).
[CrossRef]

Panajotov, K.

. M. Dems, T. Czyszanowski, and K. Panajotov, “Highly birefringent and dichroic photonic-crystal VCSEL design,” Opt. Commun 281, 3149–3152 (2008).
[CrossRef]

. M. Dems and K. Panajotov, “Modeling of single- and multimode photonic-crystal planar waveguides with planewave admittance method,” Appl. Phys. B 89, 19–23 (2007).
[CrossRef]

. T. Czyszanowski, M. Dems, and K. Panajotov, “Single mode condition and modes discrimination in photoniccrystal 1.3 μm AlInGaAs/InP VCSEL,” Opt. Express 15, 5604–5609 (2007).
[CrossRef] [PubMed]

. M. Dems, R. Kotynski, and K. Panajotov, “Plane-wave admittance method — a novel approach for determining the electromagnetic modes in photonic structures,” Opt. Express 13, 3196–3207 (2005).
[CrossRef] [PubMed]

Park, H. G.

. D. S. Song, S. H. Kim, H. G. Park, c. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic-crystal verticalcavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Pregla, R.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Puskás, Z.

Riyopoulos, S. A.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Romstad, F.

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

Seurin, J.-F. P.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Song, D. S.

. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
[CrossRef]

. D. S. Song, S. H. Kim, H. G. Park, c. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic-crystal verticalcavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Varga, G.

Veszprémi, T.

Vukusic, J.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Wenzel, W.

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

Young, E. W.

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

Zsombok, G.

Appl. Phys. B (1)

. M. Dems and K. Panajotov, “Modeling of single- and multimode photonic-crystal planar waveguides with planewave admittance method,” Appl. Phys. B 89, 19–23 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photoniccrystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82, 3182–3184 (2003).
[CrossRef]

. D. S. Song, S. H. Kim, H. G. Park, c. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic-crystal verticalcavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Electron. Lett. (2)

. A. J. Danner, T. S. Kim, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity laser with improved output power,” Electron. Lett. 41, 325–326 (2005).
[CrossRef]

. T. S. Kim, A. J. Danner, D. M. Grasso, E. W. Young, and K. D. Choquette, “Single fundamental mode photonic crystal vertical cavity surface emitting laser with 9 GHz bandwidth,” Electron. Lett. 40, 1340–1341 (2004).
[CrossRef]

IEEE J. Lightwave Techn. (1)

. P. Nyakas, “Full-vectorial three-dimensional finite element optical simulation of vertical-cavity surface-emitting lasers,” IEEE J. Lightwave Techn. 25, 2427–2434 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, W. Wenzel, K. Klein, C. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models on the simulation of oxide-confined devices,” IEEE J. Quantum Electron. 37, 1618–1631 (2001).
[CrossRef]

IEEE T. Antenn. Propag. (1)

. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE T. Antenn. Propag. 44, 1630–1639 (1996).
[CrossRef]

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

Opt. Commun (1)

. M. Dems, T. Czyszanowski, and K. Panajotov, “Highly birefringent and dichroic photonic-crystal VCSEL design,” Opt. Commun 281, 3149–3152 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys Rev. A (1)

. G. P. Bava, P. Debernardi, and L. Fratta, “Three-dimensional model for vectorial fields in vertical-cavity surfaceemitting lasers,” Phys Rev. A 63, 23816 (2001).
[CrossRef]

Proc. SPIE (1)

. F. Romstad, S. Bischoff, M. Juhl, S. Jacobsen, and D. Birkedal, “Photonic crystals for long-wavelength singlemode VCSELs,” Proc. SPIE 6908, 69080C (2008).
[CrossRef]

Other (2)

. M. Dems, “Plane-wave admittance method and its applications to modeling semiconductor lasers and planar photonic-crystal structures,” Ph.D. thesis, Technical University of Lodz (2007).

. S. Bischoff, F. Romstad, M. Juhl, M. H. Madsen, J. Hanberg, and D. Birkedal, “2.5 Gbit/s modulation of 1300 nm single-mode photonic crystal VCSELs,” in “Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD),” (2006), OFA6.

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic structure of the analyzed PC-VCSEL. (b) Top view of photonic crystal arrangement.

Fig. 2.
Fig. 2.

(a) A schematic profile of a VCSEL structure. (b) A modeling of the structure of (a) in CMM.

Fig. 3.
Fig. 3.

Sample triangular lateral mesh for a single-defect PC-VCSEL. In order to exploit symmetry conditions, only a quarter cross-section is meshed for vectorial, and a 30-degree section for scalar solutions. Etched regions are shown with blue colors, and can be matched to various hole diameters. Finer mesh is created around the defect to focus on the most important part of the laser.

Fig. 4.
Fig. 4.

Resonant wavelengths of PC-VCSELs with photonic crystals etched in different parts of the structure as a function of the hole diameters.

Fig. 5.
Fig. 5.

Threshold gains of PC-VCSELs with photonic crystals etched in different parts of the structure as a function of the hole diameters.

Fig. 6.
Fig. 6.

Resonant wavelengths of PC-VCSELs with photonic crystals etched in different parts of the structure as a function of the photonic crystal pitch.

Fig. 7.
Fig. 7.

Threshold gains of PC-VCSELs with photonic crystals etched in different parts of the structure as a function of the photonic crystal pitch.

Fig. 8.
Fig. 8.

Electric field intensity profiles in the vertical cross-section of the PC-VCSEL, computed for Λ = 4µm, d/Λ = 0.5 with holes etched in the cavity only. (a) xyz profile in dB scale obtained using the CMM, (b) xz profile in log scale obtained using the FEM, and (c) xz profile in dB scale obtained using PWAT.

Tables (3)

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Table 1. Details of the layer structure of the analyzed VCSEL.

Tables Icon

Table 2. The results summary computed for Λ = 4.0µm.

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Table 3. The results summary computed for d/Λ = 0.5.

Equations (4)

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A · c = ω 2 c 2 B · c ,
2 E z 2 = Q E E , 2 H z 2 = Q H H
2 E ˜ z 2 = Γ 2 E ˜ , 2 H ˜ z 2 = Γ 2 H ˜ ,
E ( x , y , z ) = f E ( z ) E ( x , y ) .

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