Abstract

We numerically study a passive THz source based on difference frequency generation between modes sustained by cylindrical AlGaAs microcavities. We show that ring-like structures are advantageous in that they provide additional degrees of freedom for tuning the nonlinear process and for maximizing the nonlinear overlap integral and conversion efficiency.

© 2012 OSA

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  1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97–105 (2007).
    [CrossRef]
  2. E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
    [CrossRef]
  3. R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
    [CrossRef] [PubMed]
  4. M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
    [CrossRef]
  5. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
    [CrossRef]
  6. J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express15, 16161–16176 (2007).
    [CrossRef] [PubMed]
  7. C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
    [CrossRef]
  8. L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
    [CrossRef]
  9. A. Andronico, J. Claudon, J.-M. Gérard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett.33, 2416–2418 (2008).
    [CrossRef] [PubMed]
  10. J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
    [CrossRef]
  11. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
    [CrossRef]
  12. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  13. R. D. Kekatpure, “First-principles full-vectorial eigenfrequency computations for axially symmetric resonators,” J. Lightwave Technol.29, 253–259 (2011).
    [CrossRef]
  14. F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
    [CrossRef]
  15. M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
    [CrossRef]

2012

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

2011

R. D. Kekatpure, “First-principles full-vectorial eigenfrequency computations for axially symmetric resonators,” J. Lightwave Technol.29, 253–259 (2011).
[CrossRef]

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

2010

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

2008

A. Andronico, J. Claudon, J.-M. Gérard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett.33, 2416–2418 (2008).
[CrossRef] [PubMed]

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

2007

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97–105 (2007).
[CrossRef]

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express15, 16161–16176 (2007).
[CrossRef] [PubMed]

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

2003

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

2002

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

1995

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
[CrossRef]

Albert, F.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Andronico, A.

Bai, Y.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Baker, C.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Bandyopadhyay, N.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Beere, H.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Belkin, M. A.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Beltram, F.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Belyanin, A.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Berger, V.

Bermel, P.

Braun, T.

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Bravo-Abad, J.

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express15, 16161–16176 (2007).
[CrossRef] [PubMed]

Brown, E. R.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
[CrossRef]

Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

Capasso, F.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Claudon, J.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

A. Andronico, J. Claudon, J.-M. Gérard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett.33, 2416–2418 (2008).
[CrossRef] [PubMed]

Davies, A. G.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Dennis, C. L.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
[CrossRef]

Ding, L.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Ducci, S.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Faist, J.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Favero, I.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Fischer, M.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Forchel, A.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Gérard, J.-M.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

A. Andronico, J. Claudon, J.-M. Gérard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett.33, 2416–2418 (2008).
[CrossRef] [PubMed]

Gilbert, K.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Grosse, P.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Heindel, T.

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Hennessy, K.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Höfling, S.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Hu, E.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Hu, Q.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Joannopoulos, J. D.

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express15, 16161–16176 (2007).
[CrossRef] [PubMed]

Johnson, S. G.

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express15, 16161–16176 (2007).
[CrossRef] [PubMed]

Johnson, T. J.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Kamp, M.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Kekatpure, R. D.

Kim, H.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Kumar, S.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

Langer, F.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Lee, K. H.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Lemaître, A.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Leo, G.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

A. Andronico, J. Claudon, J.-M. Gérard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett.33, 2416–2418 (2008).
[CrossRef] [PubMed]

Linfield, E. H.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Lu, Q. Y.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Malik, N. S.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

McIntosh, K. A.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
[CrossRef]

Michael, C. P.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Munsch, M.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Nichols, K. B.

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
[CrossRef]

Painter, O.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Pieczarka, M. M.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Rakich, P. T.

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

Razeghi, M.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Reitzenstein, S.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Reno, J. L.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

Ritchie, D. A.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Rodriguez, A.

Rodriguez, A. W.

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Schlereth, T.

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

Schneider, C.

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Senellart, P.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Slivken, S.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Soljacic, M.

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express15, 16161–16176 (2007).
[CrossRef] [PubMed]

Srinivasan, K.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97–105 (2007).
[CrossRef]

Tredicucci, A.

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Williams, B. S.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

Wittmann, A.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Worschech, L.

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

Xie, F.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Appl. Phys. Lett.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature tera-hertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.92, 201101 (2008).
[CrossRef]

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett.96, 101110 (2010).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ ≈ 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett.83, 2124–2126 (2003).
[CrossRef]

E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett.66, 285–287 (1995).
[CrossRef]

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett.90, 051108 (2007).
[CrossRef]

F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Whispering gallery mode lasing in electrically driven quantum dot micropillars,” Appl. Phys. Lett.97, 101108 (2010).
[CrossRef]

M. Munsch, J. Claudon, N. S. Malik, K. Gilbert, P. Grosse, J.-M. Gérard, F. Albert, F. Langer, T. Schlereth, M. M. Pieczarka, S. Höfling, M. Kamp, A. Forchel, and S. Reitzenstein, “Room temperature, continuous wave lasing in microcylinder and microring quantum dot laser diodes,” Appl. Phys. Lett.100, 031111 (2012).
[CrossRef]

J. Lightwave Technol.

Nat. Photon.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97–105 (2007).
[CrossRef]

Nature

R. Köhler, A. Tredicucci, F. Beltram, H. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417, 156–159 (2002).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

L. Ding, C. Baker, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett.105, 263903 (2010).
[CrossRef]

Other

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (5)

Fig. 1
Fig. 1

Sketch of the nonlinear source studied in text (a). Schematic of the DFG process with pump fields injected via a tapered waveguide (b).

Fig. 2
Fig. 2

THz WGM frequency ν3 (solid black curve) and near-IR mode spacing Δν (dash-dotted blue curves) versus internal radius of the ring. The black dotted line corresponds to the THz resonance frequency for a structure without hole. The inset is a zoomed-in view around Rint = 15.7μm.

Fig. 3
Fig. 3

THz output power (in nW) versus waveguide input power (in mW) calculated for a ring-like structure with internal radius Rint = 15.72 μm and external radius Rext = 17.48 μm. Both pump modes are assumed to be critically coupled to the cavity.

Fig. 4
Fig. 4

Frequency shift of the THz WGM versus: the radius of a metallic tip placed at half pillar height (top panel); the height of a tip with fixed radius RT = 0.9Rint (bottom panel). Inset: sectional view of the tip and AlGaAs microring (the dashed line represents the axis of cylindrical symmetry).

Fig. 5
Fig. 5

Frequency shift of the THz WGM versus the height of a GaAs tip with fixed radius RT = 0.76Rint. The solid black line is a guide to the eye.

Equations (1)

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η = 4 ω 3 ω 1 ω 2 Q 3 rad ( 1 + Q 3 rad / Q 3 mat ) 2 i = 1 , 2 [ Q i cpl ( 1 + Q i cpl / Q i int ) 2 ] | I o v | 2 1 ( 2 Δ ω Q 3 int / ω 3 ) 2 + 1

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