Abstract

We identify two physical mechanisms which drastically increase the Q/V factor of photonic crystal microcavities. Both mechanisms rely on a fine tuning the geometry of the holes around the cavity defect. The first mechanism relies on engineering the mirrors in order to reduce the out-of-plane far field radiation. The second mechanism is less intuitive and relies on a pure electromagnetism effect based on transient fields at the subwavelength scale, namely a recycling of the mirror losses by radiation modes. The recycling mechanism enables the design of high-performance microresonators with moderate requirements on the mirror reflectivity. Once the geometry around the defect is optimised, both mechanisms are shown to strongly impact the Q and the Purcell factors of the microcavity.

© 2004 Optical Society of America

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  1. E.M. Purcell, “Spontaneous emission probabilities at radio frequencies”, Phys. Rev. 69, 681 (1946)
  2. H. Yokoyama and K. Ujihara, Spontaneous emission and laser oscillation in microcavities, (FL: CRC Press, 1995)
  3. O.J. Painter, A. Husain, A. Scherer, J.D. O’Brien, I. Kim, and P.D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082–2088 (1999).
    [CrossRef]
  4. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
    [CrossRef] [PubMed]
  5. D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
    [CrossRef]
  6. Y. Akahane, T. Asano, B-S Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–47 (2003).
    [CrossRef] [PubMed]
  7. A.S. Jugessur, P. Pottier, and R.M. De La Rue, “One-dimensional periodic photonic crystal microcavity filters with transition mode-matching features, embedded in ridge waveguides,” Electron. Lett. 39, 367–369 (2003).
    [CrossRef]
  8. M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–69 (2001).
    [CrossRef]
  9. Steven G. Johnson, Shanhui Fan, Attila Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high- Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-00 (2001).
    [CrossRef]
  10. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev.E 65, art. #016608 (2002).
  11. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670.
    [CrossRef] [PubMed]
  12. Ph. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high Q’s, small V’s microcavities,” IEEE J. Quantum Electron. 39, 1430–38 (2003)
    [CrossRef]
  13. J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
    [CrossRef]
  14. J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
    [CrossRef]
  15. D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
    [CrossRef]
  16. Ph. Lalanne and E. Silberstein, “Fourier-modal method applied to waveguide computational problems,” Opt. Lett. 25, 1092–94 (2000).
    [CrossRef]
  17. E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A. 18, 2865 (2001).
    [CrossRef]
  18. J.P Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computational. Phys. 114, 185 (1994).
    [CrossRef]
  19. A.W. Snyder and J.D. Love, Optical Waveguide theory (Chapman and Hall, NY, 1983).
  20. P. Benech and D. Khalil, “Rigorous spectral analysis of leaky structures: application to the prism coupling problem,” Opt. Commun. 118, 220 (1995).
    [CrossRef]

2003 (3)

Y. Akahane, T. Asano, B-S Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–47 (2003).
[CrossRef] [PubMed]

A.S. Jugessur, P. Pottier, and R.M. De La Rue, “One-dimensional periodic photonic crystal microcavity filters with transition mode-matching features, embedded in ridge waveguides,” Electron. Lett. 39, 367–369 (2003).
[CrossRef]

Ph. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high Q’s, small V’s microcavities,” IEEE J. Quantum Electron. 39, 1430–38 (2003)
[CrossRef]

2002 (2)

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
[CrossRef]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670.
[CrossRef] [PubMed]

2001 (3)

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–69 (2001).
[CrossRef]

Steven G. Johnson, Shanhui Fan, Attila Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high- Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-00 (2001).
[CrossRef]

E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A. 18, 2865 (2001).
[CrossRef]

2000 (3)

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

Ph. Lalanne and E. Silberstein, “Fourier-modal method applied to waveguide computational problems,” Opt. Lett. 25, 1092–94 (2000).
[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

1996 (1)

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

1995 (1)

P. Benech and D. Khalil, “Rigorous spectral analysis of leaky structures: application to the prism coupling problem,” Opt. Commun. 118, 220 (1995).
[CrossRef]

1994 (1)

J.P Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computational. Phys. 114, 185 (1994).
[CrossRef]

1946 (1)

E.M. Purcell, “Spontaneous emission probabilities at radio frequencies”, Phys. Rev. 69, 681 (1946)

Akahane, Y.

Y. Akahane, T. Asano, B-S Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–47 (2003).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B-S Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–47 (2003).
[CrossRef] [PubMed]

Benech, P.

P. Benech and D. Khalil, “Rigorous spectral analysis of leaky structures: application to the prism coupling problem,” Opt. Commun. 118, 220 (1995).
[CrossRef]

Bérenger, J.P

J.P Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computational. Phys. 114, 185 (1994).
[CrossRef]

Bi, W.G.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Cao, Q.

E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A. 18, 2865 (2001).
[CrossRef]

Chen, Y.

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
[CrossRef]

Chu, D.Y.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Dapkus, P.D.

De La Rue, R.M.

A.S. Jugessur, P. Pottier, and R.M. De La Rue, “One-dimensional periodic photonic crystal microcavity filters with transition mode-matching features, embedded in ridge waveguides,” Electron. Lett. 39, 367–369 (2003).
[CrossRef]

Fan, S.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Fan, Shanhui

Steven G. Johnson, Shanhui Fan, Attila Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high- Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-00 (2001).
[CrossRef]

Ferrera, J.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Foresi, J.S.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Ho, S.T.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Hugonin, J. P.

Ph. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high Q’s, small V’s microcavities,” IEEE J. Quantum Electron. 39, 1430–38 (2003)
[CrossRef]

Hugonin, J.P.

E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A. 18, 2865 (2001).
[CrossRef]

Husain, A.

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Ippen, E.P.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Joannopoulos, J. D.

Steven G. Johnson, Shanhui Fan, Attila Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high- Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-00 (2001).
[CrossRef]

Joannopoulos, J.D.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Johnson, Steven G.

Steven G. Johnson, Shanhui Fan, Attila Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high- Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-00 (2001).
[CrossRef]

Joseph, R.M.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Jugessur, A.S.

A.S. Jugessur, P. Pottier, and R.M. De La Rue, “One-dimensional periodic photonic crystal microcavity filters with transition mode-matching features, embedded in ridge waveguides,” Electron. Lett. 39, 367–369 (2003).
[CrossRef]

Khalil, D.

P. Benech and D. Khalil, “Rigorous spectral analysis of leaky structures: application to the prism coupling problem,” Opt. Commun. 118, 220 (1995).
[CrossRef]

Kim, I.

Kimerling, L.C.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Kolodziejski, L.A.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

Lalanne, P.

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
[CrossRef]

Lalanne, Ph.

Ph. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high Q’s, small V’s microcavities,” IEEE J. Quantum Electron. 39, 1430–38 (2003)
[CrossRef]

E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A. 18, 2865 (2001).
[CrossRef]

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–69 (2001).
[CrossRef]

Ph. Lalanne and E. Silberstein, “Fourier-modal method applied to waveguide computational problems,” Opt. Lett. 25, 1092–94 (2000).
[CrossRef]

Lim, K.Y.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev.E 65, art. #016608 (2002).

Love, J.D.

A.W. Snyder and J.D. Love, Optical Waveguide theory (Chapman and Hall, NY, 1983).

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev.E 65, art. #016608 (2002).

Mekis, Attila

Steven G. Johnson, Shanhui Fan, Attila Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high- Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-00 (2001).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B-S Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–47 (2003).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

O’Brien, J.D.

Painter, O.

Painter, O.J.

Palamaru, M.

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–69 (2001).
[CrossRef]

Petrich, G.S.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

Peyrade, D.

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
[CrossRef]

Pottier, P.

A.S. Jugessur, P. Pottier, and R.M. De La Rue, “One-dimensional periodic photonic crystal microcavity filters with transition mode-matching features, embedded in ridge waveguides,” Electron. Lett. 39, 367–369 (2003).
[CrossRef]

Purcell, E.M.

E.M. Purcell, “Spontaneous emission probabilities at radio frequencies”, Phys. Rev. 69, 681 (1946)

Ripin, D.J.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

Scherer, A.

O.J. Painter, A. Husain, A. Scherer, J.D. O’Brien, I. Kim, and P.D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082–2088 (1999).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev.E 65, art. #016608 (2002).

Silberstein, E.

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
[CrossRef]

E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A. 18, 2865 (2001).
[CrossRef]

Ph. Lalanne and E. Silberstein, “Fourier-modal method applied to waveguide computational problems,” Opt. Lett. 25, 1092–94 (2000).
[CrossRef]

Smith, H.I.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Snyder, A.W.

A.W. Snyder and J.D. Love, Optical Waveguide theory (Chapman and Hall, NY, 1983).

Song, B-S

Y. Akahane, T. Asano, B-S Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–47 (2003).
[CrossRef] [PubMed]

Srinivasan, K.

Steinmeyer, G.

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Taflove, A.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Talneau, A.

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, and Y. Chen, “Short Bragg mirrors with adiabatic modal conversion,” Appl. Phys. Lett. 81, 829–831 (2002).
[CrossRef]

Thoen, E.R.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith, and E.P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997).
[CrossRef]

Tiberio, R.C.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Tu, C.W.

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, and S.T. Ho, “Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,” IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

Ujihara, K.

H. Yokoyama and K. Ujihara, Spontaneous emission and laser oscillation in microcavities, (FL: CRC Press, 1995)

Villeneuve, P.R.

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen, and L.A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” J. Appl. Phys. 87, 1578–80 (2000).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Air-bridge cavity geometry. The cavity is defined by two sets of four holes (diameter 250 nm, lattice constant 450 nm) separated by a defect of length h. The holes are assumed to be fully etched into a semiconductor (n=3.48) air-bridge waveguide 340-nm thick and 500-nm wide. (b) Red curve : calculated modal mirror reflectivity spectrum. Blue curve : cavity transmission spectrum for h=0.3 µm. (c) Calculated modal transmission as a function of wavelength and geometric cavity length h.

Fig. 2.
Fig. 2.

Minimal model for recycling radiation in microcavities. Black and red arrows correspond to the fundamental and leaky modes, respectively. The cavity being symmetrical, the coupling coefficients rm and r’ are the same for both mirrors.

Fig. 3.
Fig. 3.

Validation of the model. (a) Comparison between calculated data (black) and model predictions (blue) for the modulus of the cavity transmission coefficients |t| for six different wavelengths covering the full band-gap region. The t values for λ=1.45, 1.6 and 1.75 µm values are vertically shifted by 1 and the model predictions are horizontally shifted by 0.05 (otherwise undistinguishable). The inset in the top center shows an enlarged view of the second resonance (h=0.5 µm) (b) Q’s as a function of the number N of holes for λ=1.56 µm; black circles : calculated data, bold blue curve: model predictions. The horizontal dashed line represents the intrinsic QFP factor in the absence of recycling. For all curves, the model parameters are θ=0.82π, f=0.5 and n’+in”=0.5+i0.1.

Fig. 4.
Fig. 4.

Calculated modal transmission as a function of wavelength and cavity length h for the engineered cavity (N=4).

Fig. 5.
Fig. 5.

Q factor as a function of the number of holes for the cavity with optimised recycling. Circles represent calculated data. The horizontal dashed line represents the cavity intrinsic QFP factor in the absence of recycling.

Fig. 6.
Fig. 6.

Engineered mirrors. (a) Cavity with engineered mirrors. (b) Comparaison between the modal reflectivity spectra of a classical mirror (dotted curve) and that of the engineered mirror (solid curve). Vertical lines indicate the bandgap edges.

Tables (1)

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Table 1. Cavity performance

Equations (10)

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α 1 = t m + r m β 1 + r β 2
α 2 = r β 1
r = r m + t m β 1
t = t m α 1 exp ( i ϕ 1 )
β 1 exp ( i ϕ 1 ) = r m α 1 exp ( i ϕ 1 ) + r α 2 exp ( i ϕ 2 )
β 2 exp ( i ϕ 2 ) = r α 1 exp ( i ϕ 1 ) ,
r eff = r m [ 1 + 2 ( r r m ) 2 exp ( i ϕ 2 i ϕ 1 ) ] 1 2 .
t = t m 2 exp ( i ϕ 1 ) 1 r eff 2 exp ( 2 i ϕ 1 ) ,
r eff r m = 1 + f L r m 2 exp ( k 0 n h ) exp [ i k 0 ( n n eff ) h + 2 i θ ] ,
Q = m π r eff ( 1 r eff 2 ) ,

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