Abstract

High-quality cavities in hybrid material systems have various interesting applications. We perform a comprehensive modeling comparison on such a design, where confinement in the III–V material is provided by gradual photonic crystal tuning, a recently proposed method offering strong resonances. The III–V cavity couples to an underlying silicon waveguide. We report on the device properties using four simulation methods: finite-difference time-domain (FDTD), finite-element method (FEM), bidirectional eigenmode propagation (BEP) and aperiodic rigorous coupled wave analysis (aRCWA). We explain the major confinement and coupling effects, consistent with the simulation results. E.g. for strong waveguide coupling, we find quantitative discrepancies between the methods, which establishes the proposed high-index-contrast, lossy, 3D structure as a challenging modeling benchmark.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express16, 11095–11102 (2008).
    [CrossRef]
  2. E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express18, 15859–15869 (2010).
    [CrossRef]
  3. D. Dai, J. Bauters, and J. Bowers, “Passive technologies for future large-scale photonic integrated circuits on silicon: polarization handling, light non-reciprocity and loss reduction,” Light. Sci. Appl.1, e1 (2012).
    [CrossRef]
  4. G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
    [CrossRef]
  5. G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
    [CrossRef]
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).
  7. 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. Comm.181, 687–702 (2010).
    [CrossRef]
  8. V. A. Mandelstahm and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997).
    [CrossRef]
  9. G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” Photonic Tech. Lett.5, 554–557 (1993).
    [CrossRef]
  10. J. Mu and W. P. Huang, “Simulation of three-dimensional waveguide discontinuities by a full-vector mode-matching method based on finite-difference schemes,” Opt. Express16, 18152–18163 (2008).
    [CrossRef]
  11. P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron.33, 327–341 (2001).
    [CrossRef]
  12. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A13, 1024–1035 (1996).
    [CrossRef]
  13. N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
    [CrossRef]
  14. J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
    [CrossRef]
  15. S. Burger, F. Schmidt, and L. Zschiedrich, “Numerical investigation of photonic crystal microcavities in silicon-on-insulator waveguides,” in Photonic and Phononic Crystal Materials and Devices X, A. Adibi, S. Y. Lin, and A. Scherer, eds., Proc. SPIE7609, 76091Q (2010).
    [CrossRef]
  16. S. Burger, J. Pomplun, F. Schmidt, and L. Zschiedrich, “Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap,” in Physics and Simulation of Optoelectronic Devices XIX, B. Witzigmann, F. Henneberger, Y. Arakawa, and A. Freundlich, eds., Proc. SPIE7933, 79330T (2011).
    [CrossRef]
  17. M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micro-pillar cavity quality factors calculated with finite element methods,” Opt. Express17, 1144–1158 (2009).
    [CrossRef]
  18. L. Li, “Note on the S-matrix propagation algorithm,” J. Opt. Soc. Am. A20, 655–660 (2003).
    [CrossRef]
  19. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A14, 2758–2767 (1997).
    [CrossRef]
  20. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A18, 2865–2875 (2001).
    [CrossRef]
  21. P. Lalanne and J. P. Hugonin, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A22, 1844–1849 (2005).
    [CrossRef]
  22. G. Granet, “Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution,” J. Opt. Soc. Am. A16, 2510–2516 (1999).
    [CrossRef]
  23. J. Čtyroký, P. Kwiecien, and I. Richter, “Fourier series-based bidirectional propagation algorithm with adaptive spatial resolution,” J. Lightwave Technol.28, 2969–2976 (2010).
    [CrossRef]
  24. Z. Y. Li and K. M. Ho, “Application of strucural symmetries in the plane-wave-based transfer-matrix method for 3D photonic crystal waveguides,” Phys. Rev. B24, 245117-1-20 (2003).
  25. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001).
    [CrossRef]
  26. H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express13, 3310–3322 (2005).
    [CrossRef]
  27. Y. Halioua, A. Bazin, P. Monnier, T. J. Karle, G. Roelkens, I. Sagnes, R. Raj, and F. Raineri, “Hybrid III–V semiconductor/silicon nanolaser,” Opt. Express19, 9221–9231 (2011).
    [CrossRef]

2012 (1)

D. Dai, J. Bauters, and J. Bowers, “Passive technologies for future large-scale photonic integrated circuits on silicon: polarization handling, light non-reciprocity and loss reduction,” Light. Sci. Appl.1, e1 (2012).
[CrossRef]

2011 (1)

2010 (5)

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express18, 15859–15869 (2010).
[CrossRef]

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. Comm.181, 687–702 (2010).
[CrossRef]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

J. Čtyroký, P. Kwiecien, and I. Richter, “Fourier series-based bidirectional propagation algorithm with adaptive spatial resolution,” J. Lightwave Technol.28, 2969–2976 (2010).
[CrossRef]

2009 (1)

2008 (2)

2007 (1)

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
[CrossRef]

2006 (1)

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

2005 (2)

2003 (2)

Z. Y. Li and K. M. Ho, “Application of strucural symmetries in the plane-wave-based transfer-matrix method for 3D photonic crystal waveguides,” Phys. Rev. B24, 245117-1-20 (2003).

L. Li, “Note on the S-matrix propagation algorithm,” J. Opt. Soc. Am. A20, 655–660 (2003).
[CrossRef]

2001 (3)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001).
[CrossRef]

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron.33, 327–341 (2001).
[CrossRef]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A18, 2865–2875 (2001).
[CrossRef]

1999 (1)

1997 (2)

L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A14, 2758–2767 (1997).
[CrossRef]

V. A. Mandelstahm and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997).
[CrossRef]

1996 (1)

1993 (1)

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” Photonic Tech. Lett.5, 554–557 (1993).
[CrossRef]

Baets, R.

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron.33, 327–341 (2001).
[CrossRef]

Bauters, J.

D. Dai, J. Bauters, and J. Bowers, “Passive technologies for future large-scale photonic integrated circuits on silicon: polarization handling, light non-reciprocity and loss reduction,” Light. Sci. Appl.1, e1 (2012).
[CrossRef]

Bazin, A.

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. Comm.181, 687–702 (2010).
[CrossRef]

Bienstman, P.

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron.33, 327–341 (2001).
[CrossRef]

Bowers, J.

D. Dai, J. Bauters, and J. Bowers, “Passive technologies for future large-scale photonic integrated circuits on silicon: polarization handling, light non-reciprocity and loss reduction,” Light. Sci. Appl.1, e1 (2012).
[CrossRef]

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Brouckaert, J.

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

Burger, S.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micro-pillar cavity quality factors calculated with finite element methods,” Opt. Express17, 1144–1158 (2009).
[CrossRef]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
[CrossRef]

S. Burger, F. Schmidt, and L. Zschiedrich, “Numerical investigation of photonic crystal microcavities in silicon-on-insulator waveguides,” in Photonic and Phononic Crystal Materials and Devices X, A. Adibi, S. Y. Lin, and A. Scherer, eds., Proc. SPIE7609, 76091Q (2010).
[CrossRef]

S. Burger, J. Pomplun, F. Schmidt, and L. Zschiedrich, “Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap,” in Physics and Simulation of Optoelectronic Devices XIX, B. Witzigmann, F. Henneberger, Y. Arakawa, and A. Freundlich, eds., Proc. SPIE7933, 79330T (2011).
[CrossRef]

Cao, Q.

Ctyroký, J.

Dai, D.

D. Dai, J. Bauters, and J. Bowers, “Passive technologies for future large-scale photonic integrated circuits on silicon: polarization handling, light non-reciprocity and loss reduction,” Light. Sci. Appl.1, e1 (2012).
[CrossRef]

di Cioccio, L.

El Melhaoui, L.

Fang, A.

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Fedeli, J. M.

Forchel, A.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Gérard, J. M.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Granet, G.

Gregersen, N.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

Halioua, Y.

Hattori, H. T.

Hetterich, M.

Ho, K. M.

Z. Y. Li and K. M. Ho, “Application of strucural symmetries in the plane-wave-based transfer-matrix method for 3D photonic crystal waveguides,” Phys. Rev. B24, 245117-1-20 (2003).

Höfling, S.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Huang, W. P.

Hugonin, J. P.

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. Comm.181, 687–702 (2010).
[CrossRef]

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. Comm.181, 687–702 (2010).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001).
[CrossRef]

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. Comm.181, 687–702 (2010).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001).
[CrossRef]

Jones, R.

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Kalt, H.

Karl, M.

Karle, T. J.

Kawasaki, K.

Kettner, B.

Kistner, C.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Koch, B.

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Kuramochi, E.

Kwiecien, P.

Lalanne, P.

Leclercq, J. L.

Letartre, X.

Li, L.

Li, Z. Y.

Z. Y. Li and K. M. Ho, “Application of strucural symmetries in the plane-wave-based transfer-matrix method for 3D photonic crystal waveguides,” Phys. Rev. B24, 245117-1-20 (2003).

Liang, D.

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Liu, L.

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Mandelstahm, V. A.

V. A. Mandelstahm and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997).
[CrossRef]

Monnier, P.

Mørk, J.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Mu, J.

Nielsen, T. R.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Nolting, H. P.

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” Photonic Tech. Lett.5, 554–557 (1993).
[CrossRef]

Notomi, M.

Notzel, R.

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[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. Comm.181, 687–702 (2010).
[CrossRef]

Pomplun, J.

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
[CrossRef]

S. Burger, J. Pomplun, F. Schmidt, and L. Zschiedrich, “Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap,” in Physics and Simulation of Optoelectronic Devices XIX, B. Witzigmann, F. Henneberger, Y. Arakawa, and A. Freundlich, eds., Proc. SPIE7933, 79330T (2011).
[CrossRef]

Raineri, F.

Raj, R.

Reitzenstein, S.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Richter, I.

Roelkens, G.

Y. Halioua, A. Bazin, P. Monnier, T. J. Karle, G. Roelkens, I. Sagnes, R. Raj, and F. Raineri, “Hybrid III–V semiconductor/silicon nanolaser,” Opt. Express19, 9221–9231 (2011).
[CrossRef]

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

Roh, Y. G.

Rojo-Romeo, P.

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. Comm.181, 687–702 (2010).
[CrossRef]

Sagnes, I.

Schmidt, F.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micro-pillar cavity quality factors calculated with finite element methods,” Opt. Express17, 1144–1158 (2009).
[CrossRef]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
[CrossRef]

S. Burger, F. Schmidt, and L. Zschiedrich, “Numerical investigation of photonic crystal microcavities in silicon-on-insulator waveguides,” in Photonic and Phononic Crystal Materials and Devices X, A. Adibi, S. Y. Lin, and A. Scherer, eds., Proc. SPIE7609, 76091Q (2010).
[CrossRef]

S. Burger, J. Pomplun, F. Schmidt, and L. Zschiedrich, “Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap,” in Physics and Simulation of Optoelectronic Devices XIX, B. Witzigmann, F. Henneberger, Y. Arakawa, and A. Freundlich, eds., Proc. SPIE7933, 79330T (2011).
[CrossRef]

Schneider, C.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Seassal, C.

Silberstein, E.

Smit, M.

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

Strauss, M.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Sztefka, G.

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” Photonic Tech. Lett.5, 554–557 (1993).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

Tanabe, T.

Taniyama, H.

Taylor, H. S.

V. A. Mandelstahm and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997).
[CrossRef]

Van Thourhout, D.

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

Viktorovitch, P.

Worschech, L.

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

Zschiedrich, L.

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
[CrossRef]

S. Burger, F. Schmidt, and L. Zschiedrich, “Numerical investigation of photonic crystal microcavities in silicon-on-insulator waveguides,” in Photonic and Phononic Crystal Materials and Devices X, A. Adibi, S. Y. Lin, and A. Scherer, eds., Proc. SPIE7609, 76091Q (2010).
[CrossRef]

S. Burger, J. Pomplun, F. Schmidt, and L. Zschiedrich, “Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap,” in Physics and Simulation of Optoelectronic Devices XIX, B. Witzigmann, F. Henneberger, Y. Arakawa, and A. Freundlich, eds., Proc. SPIE7933, 79330T (2011).
[CrossRef]

Zussy, M.

Comput. Phys. Comm. (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. Comm.181, 687–702 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Höfling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J. M. Gérard, “Numerical and experimental study of the Q factor of high-Q micropillar cavities,” IEEE J. Quantum Electron.46, 1470–1483 (2010).
[CrossRef]

J. Chem. Phys. (1)

V. A. Mandelstahm and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys.107, 6756–6769 (1997).
[CrossRef]

J. Electrochem. Soc. (1)

G. Roelkens, J. Brouckaert, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Adhesive bonding of InP/InGaAsP dies to processed silicon-on-insulator wafers using DVS-bis-benzocyclobutene,” J. Electrochem. Soc.153, G1015–G1019 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (6)

Laser Photonics Rev. (1)

G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III–V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photonics Rev.4, 751–779 (2010).
[CrossRef]

Light. Sci. Appl. (1)

D. Dai, J. Bauters, and J. Bowers, “Passive technologies for future large-scale photonic integrated circuits on silicon: polarization handling, light non-reciprocity and loss reduction,” Light. Sci. Appl.1, e1 (2012).
[CrossRef]

Opt. Express (1)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001).
[CrossRef]

Opt. Express (6)

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron.33, 327–341 (2001).
[CrossRef]

Photonic Tech. Lett. (1)

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode propagation for large refractive index steps,” Photonic Tech. Lett.5, 554–557 (1993).
[CrossRef]

Phys. Rev. B (1)

Z. Y. Li and K. M. Ho, “Application of strucural symmetries in the plane-wave-based transfer-matrix method for 3D photonic crystal waveguides,” Phys. Rev. B24, 245117-1-20 (2003).

Phys. Stat. Sol. (b) (1)

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Stat. Sol. (b)244, 3419–3434 (2007).
[CrossRef]

Other (3)

S. Burger, F. Schmidt, and L. Zschiedrich, “Numerical investigation of photonic crystal microcavities in silicon-on-insulator waveguides,” in Photonic and Phononic Crystal Materials and Devices X, A. Adibi, S. Y. Lin, and A. Scherer, eds., Proc. SPIE7609, 76091Q (2010).
[CrossRef]

S. Burger, J. Pomplun, F. Schmidt, and L. Zschiedrich, “Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap,” in Physics and Simulation of Optoelectronic Devices XIX, B. Witzigmann, F. Henneberger, Y. Arakawa, and A. Freundlich, eds., Proc. SPIE7933, 79330T (2011).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Geometry of the simulated device, with parameters and axes indicated. (a) xz-side view. (b) yz-side view. (c) Top view. (d) Perspective view with only InP and Si shown.

Fig. 2
Fig. 2

Simulation results for the cavity without nearby waveguide. (a) Quality factor Q and (b) normalized resonance frequency a/λ versus Ncav.

Fig. 3
Fig. 3

Electric field of the cavity mode (lower part). Shown is the Ey-component in a horizontal plane (parallel to xy), through the cavity center. The upper part depicts the cavity geometry.

Fig. 4
Fig. 4

Quality factor Q versus Si waveguide width Siy, at various constant values of Ncav.

Fig. 5
Fig. 5

Bloch and waveguide dispersion relations. The horizontal dotted line indicates the cavity resonance frequency. The long-dashed line shows the (folded) Si waveguide dispersion, for the indicated widths. The solid lines are identical in the three graphs, and provide the Bloch mode propagation constant with period as in the center of the cavity (upper mode), and with period as in the mirror sections (lower mode), respectively.

Fig. 6
Fig. 6

Cavity with waveguide. Q versus Ncav for different values of Siy.

Fig. 7
Fig. 7

Cavity with waveguide. Quality factor Q versus waveguide thickness Siy for different values of the buffer thickness BCBz. Here, Ncav = 5, other parameters are as in Fig. 4. To be compared with Fig. 4 (BCBz = 1.0μm), case Ncav = 5.

Fig. 8
Fig. 8

Cavity Q as a function of waveguide offset in the y-direction, for Ncav = 5.

Equations (1)

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

w ( i ) = w cav [ 1 + ( i 1 ) 2 3 N cav 2 ] ,

Metrics