Abstract

Linear and non-linear thermo-optical dynamical regimes were investigated in a photonic crystal cavity. First, we have measured the thermal relaxation time in an InP-based nano-cavity with quantum dots in the presence of optical pumping. The experimental method presented here allows one to obtain the dynamics of temperature in a nanocavity. It is based on reflectivity measurements of a cw probe beam coupled through an adiabatically tapered fiber. Characteristic times of 1.0±0.2 µs and 0.9±0.2 µs for the heating and the cooling processes were obtained. Finally, thermal dynamics were also investigated in a thermo-optical bistable regime. Switch-on/off times of 2 µs and 4 µs respectively were measured, which could be explained in terms of a simple non-linear dynamical representation.

© 2009 Optical Society of America

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  1. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
    [CrossRef] [PubMed]
  2. M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, M. Morita, "Nonlinear and adiabatic control of high-Q photonic crystal nanocavities," Opt. Express 15, 17458 (2007).
    [CrossRef] [PubMed]
  3. A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
    [CrossRef]
  4. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87, 151112 (2005).
    [CrossRef]
  5. R. Braive, S. Barbay, I. Sagnes, A. Miard, I. Robert-Philip, and A. Beveratos, "Transient chirp in high-speed photonic-crystal quantum-dot lasers with controlled spontaneous emission," Opt. Lett. 34, 554 (2009).
    [CrossRef] [PubMed]
  6. H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Phys. 2, 484 (2006).
    [CrossRef]
  7. Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005).
    [CrossRef] [PubMed]
  8. T. J. Johnson, M. Borselli, and O. Painter, "Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator," Opt. Express 14, 817-831 (2006).
    [CrossRef] [PubMed]
  9. T. Carmon, L. Yang, and K. J. Vahala, "Dynamical thermal behavior and thermal self-stability of microcavities," Opt. Express 12, 4742 (2004).
    [CrossRef] [PubMed]
  10. A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
    [CrossRef] [PubMed]
  11. M. T. Tinker and J-B. Lee, "Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency," Optics Express 18, 7174-7187 (2005).
    [CrossRef]
  12. G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
    [CrossRef]
  13. L. Pottier, "Micrometer scale visualization of thermal waves by photoreflectance microscopy," Appl. Phys. Lett. 64, 1618-1619 (1994).
    [CrossRef]
  14. Y. Akahane, T. Asano, B.-S. Song and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
    [CrossRef] [PubMed]
  15. A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
    [CrossRef]
  16. I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
    [CrossRef]
  17. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85, (2004)
    [CrossRef]
  18. C. Grillet, C. Smith, D. Freeman, S. Madden, B. L-Davies, E. C. Magi, D. J. Moss and B. J. Eggleton, "Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires," Opt. Express 14, 1070 (2006).
    [CrossRef] [PubMed]
  19. See for example B. Maes, P. Bienstman, and R. Baets, "Switching in coupled nonlinear photonic-crystal resonators," J. Opt. Soc. Am. B 22, 1778 (2005).
    [CrossRef]
  20. In Section 5 we study nonlinear thermo-optical effects which are shown to appear for a signal power greater than ~1 mW (see transmission curves as a function of input power in Fig. 4c).
  21. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
    [CrossRef] [PubMed]
  22. P. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13, 801-820 (2005).
    [CrossRef] [PubMed]
  23. Convection within the air gap can be neglected since the Rayleigh number for an air gap of thickness ? between two rigid walls, for a few degrees of temperature increment, is Ra?=g ?T ?3/a?T~10-10, whereas the onset for convection is Ra?~2 103. See for example J. Taine and J. P. Petit, Heat transfert (Prentice-Hall, 1993).
  24. F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, "Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 µm," Appl. Phys. Lett. 77, 1614 (2000).
    [CrossRef]
  25. F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj and A. Levenson, "Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes," Appl. Phys. Lett. 86, 011116 (2005).
    [CrossRef]
  26. The thermal relaxation time for a PhC membrane on oxide can be easily calculated under the hypothesis of 1D vertical heat flow through the oxide layer to the substrate. For instance, for a 250 nm-thick Si membrane (?Si=1.5 W/cm K, ?Si=0.9 cm2/s) in contact with a 1 µm-thick SiO2 layer (?SiO2=0.013 W/cm K, ?SiO2=0.006 cm2/s), a numerical simulation of the 1D heat equation gives tth=950 ns.
  27. A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
    [CrossRef]
  28. We use the estimated ?th from the experimental results, ?th~110 ns (see Section 6.1). This is an approximation since ?th depends on the geometry of the hot spot which, in the resonant case, is given by the cavity volume, different from the pumped region given by the surface illumination.
  29. C. Sauvan, P. Lalanne and J.P. Hugonin, "Slow-wave effect and mode-profile matching in Photonic Crystal microcavities," Phys. Rev. B 71, 165118 (2005).
    [CrossRef]

2009

2008

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
[CrossRef]

2007

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, M. Morita, "Nonlinear and adiabatic control of high-Q photonic crystal nanocavities," Opt. Express 15, 17458 (2007).
[CrossRef] [PubMed]

2006

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Phys. 2, 484 (2006).
[CrossRef]

T. J. Johnson, M. Borselli, and O. Painter, "Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator," Opt. Express 14, 817-831 (2006).
[CrossRef] [PubMed]

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

C. Grillet, C. Smith, D. Freeman, S. Madden, B. L-Davies, E. C. Magi, D. J. Moss and B. J. Eggleton, "Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires," Opt. Express 14, 1070 (2006).
[CrossRef] [PubMed]

2005

See for example B. Maes, P. Bienstman, and R. Baets, "Switching in coupled nonlinear photonic-crystal resonators," J. Opt. Soc. Am. B 22, 1778 (2005).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

P. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13, 801-820 (2005).
[CrossRef] [PubMed]

M. T. Tinker and J-B. Lee, "Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency," Optics Express 18, 7174-7187 (2005).
[CrossRef]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

C. Sauvan, P. Lalanne and J.P. Hugonin, "Slow-wave effect and mode-profile matching in Photonic Crystal microcavities," Phys. Rev. B 71, 165118 (2005).
[CrossRef]

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
[CrossRef]

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj and A. Levenson, "Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes," Appl. Phys. Lett. 86, 011116 (2005).
[CrossRef]

2004

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85, (2004)
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, "Dynamical thermal behavior and thermal self-stability of microcavities," Opt. Express 12, 4742 (2004).
[CrossRef] [PubMed]

2003

G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
[CrossRef]

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

2000

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, "Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 µm," Appl. Phys. Lett. 77, 1614 (2000).
[CrossRef]

1994

L. Pottier, "Micrometer scale visualization of thermal waves by photoreflectance microscopy," Appl. Phys. Lett. 64, 1618-1619 (1994).
[CrossRef]

Abram, I.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Akahane, Y.

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

Altug, H.

H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Phys. 2, 484 (2006).
[CrossRef]

Asano, T.

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

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Barbay, S.

Barclay, P.

Barclay, P. E.

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85, (2004)
[CrossRef]

Beaudoin, G.

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
[CrossRef]

Ben Bakir, B.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

Beveratos, A.

R. Braive, S. Barbay, I. Sagnes, A. Miard, I. Robert-Philip, and A. Beveratos, "Transient chirp in high-speed photonic-crystal quantum-dot lasers with controlled spontaneous emission," Opt. Lett. 34, 554 (2009).
[CrossRef] [PubMed]

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
[CrossRef]

Borselli, M.

T. J. Johnson, M. Borselli, and O. Painter, "Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator," Opt. Express 14, 817-831 (2006).
[CrossRef] [PubMed]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85, (2004)
[CrossRef]

Boucaud, P.

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
[CrossRef]

Braive, R.

Carmon, T.

Chalcraft, A. R. A.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Cocorullo, G.

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, "Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 µm," Appl. Phys. Lett. 77, 1614 (2000).
[CrossRef]

Della Corte, F. G.

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, "Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 µm," Appl. Phys. Lett. 77, 1614 (2000).
[CrossRef]

Di Cioccio, L.

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

Englund, D.

H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Phys. 2, 484 (2006).
[CrossRef]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Fedeli, J.-M.

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

Filloy, C.

G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
[CrossRef]

Fournier, D.

G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
[CrossRef]

Fox, A. M.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Freeman, D.

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
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A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
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Grillet, C.

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005).
[CrossRef] [PubMed]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

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G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
[CrossRef]

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A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
[CrossRef]

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

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C. Sauvan, P. Lalanne and J.P. Hugonin, "Slow-wave effect and mode-profile matching in Photonic Crystal microcavities," Phys. Rev. B 71, 165118 (2005).
[CrossRef]

Hwang, I.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
[CrossRef]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Iodice, M.

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, "Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 µm," Appl. Phys. Lett. 77, 1614 (2000).
[CrossRef]

Jerosolimski, G.

G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
[CrossRef]

Johnson, T. J.

Kim, S.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
[CrossRef]

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
[CrossRef]

Kira, G.

Krauss, T. F.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Kuramochi, E.

Lalanne, P.

C. Sauvan, P. Lalanne and J.P. Hugonin, "Slow-wave effect and mode-profile matching in Photonic Crystal microcavities," Phys. Rev. B 71, 165118 (2005).
[CrossRef]

Lam, S.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
[CrossRef]

Laurent, S.

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Le Gratiet, L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Lee, J-B.

M. T. Tinker and J-B. Lee, "Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency," Optics Express 18, 7174-7187 (2005).
[CrossRef]

Lee, S.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
[CrossRef]

Lee, Y.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, "Curved-microfiber photon coupling for photonic crystal light emitter," Appl. Phys. Lett. 87, 131107 (2005)
[CrossRef]

Lemaître, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Letartre, X.

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

Levenson, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj and A. Levenson, "Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes," Appl. Phys. Lett. 86, 011116 (2005).
[CrossRef]

Levenson, J. A.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
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A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
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Madden, S.

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005).
[CrossRef] [PubMed]

Miard, A.

Michon, A.

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
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Mitsugi, S.

Monnier, P.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
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Morita, M.

Noda, S.

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

Notomi, M.

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65 (2005).
[CrossRef] [PubMed]

O'Brien, D.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
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A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
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Painter, O.

Patriarche, G.

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj and A. Levenson, "Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes," Appl. Phys. Lett. 86, 011116 (2005).
[CrossRef]

Raj, R.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
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F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj and A. Levenson, "Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes," Appl. Phys. Lett. 86, 011116 (2005).
[CrossRef]

Rendina, I.

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, "Temperature dependence of the thermo-optic coefficient of InP, GaAs, and SiC from room temperature to 600 K at the wavelength of 1.5 µm," Appl. Phys. Lett. 77, 1614 (2000).
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R. Braive, S. Barbay, I. Sagnes, A. Miard, I. Robert-Philip, and A. Beveratos, "Transient chirp in high-speed photonic-crystal quantum-dot lasers with controlled spontaneous emission," Opt. Lett. 34, 554 (2009).
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A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Sagnes, I.

R. Braive, S. Barbay, I. Sagnes, A. Miard, I. Robert-Philip, and A. Beveratos, "Transient chirp in high-speed photonic-crystal quantum-dot lasers with controlled spontaneous emission," Opt. Lett. 34, 554 (2009).
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A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
[CrossRef] [PubMed]

Sahin, M.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
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Sanvitto, D.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
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Sauvage, S.

A. Michon, R. Hostein, G. Patriarche, N. Gogneau, G. Beaudoin, A. Beveratos, I. Robert?Philip, S. Laurent, S. Sauvage, P. Boucaud, I. Sagnes, "Metal organic vapor phase epitaxy of InAsP/InP(001) quantum dots for 1.55 ?m applications: Growth, structural, and optical properties," J. Appl. Phys. 104, 043504 (2008).
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C. Sauvan, P. Lalanne and J.P. Hugonin, "Slow-wave effect and mode-profile matching in Photonic Crystal microcavities," Phys. Rev. B 71, 165118 (2005).
[CrossRef]

Seassal, C.

A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
[CrossRef]

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo-Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj and A. Levenson, "Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes," Appl. Phys. Lett. 86, 011116 (2005).
[CrossRef]

Shinya, A.

Skolnick, M. S.

A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
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Smith, C.

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
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P. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13, 801-820 (2005).
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M. T. Tinker and J-B. Lee, "Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency," Optics Express 18, 7174-7187 (2005).
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A. M. Yacomotti, F. Raineri, G. Vecchi, P. Monnier, R. Raj, J. A. Levenson, B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, L. Di Cioccio, J.-M. Fedeli, "All-optical bistable band-edge Bloch modes in a two-dimensional photonic cristal," Appl. Phys. Lett. 88, 231107 (2006).
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A. R. A. Chalcraft, S. Lam, D. O'Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, and D. M. Whittaker, "Mode structure of the L3 photonic crystal cavity," Appl. Phys. Lett. 90, 241117 (2007).
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[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007);S. Laurent, S. Varoutsis, L. Le Gratiet, A. Lemaître, I. Sagnes, F. Raineri, A. Levenson, I. Robert-Philip and I. Abram, "Indistinguishable single photons from a single quantum dot in two-dimensional Photonic Crystal cavity," Appl. Phys. Lett. 87, 163107 (2005).
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G. Tessier, G. Jerosolimski, S. Hole, D. Fournier, and C. Filloy, "Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials," Rev. Sci. Instrum. 74 (1), 495 (2003).
[CrossRef]

Other

In Section 5 we study nonlinear thermo-optical effects which are shown to appear for a signal power greater than ~1 mW (see transmission curves as a function of input power in Fig. 4c).

We use the estimated ?th from the experimental results, ?th~110 ns (see Section 6.1). This is an approximation since ?th depends on the geometry of the hot spot which, in the resonant case, is given by the cavity volume, different from the pumped region given by the surface illumination.

Convection within the air gap can be neglected since the Rayleigh number for an air gap of thickness ? between two rigid walls, for a few degrees of temperature increment, is Ra?=g ?T ?3/a?T~10-10, whereas the onset for convection is Ra?~2 103. See for example J. Taine and J. P. Petit, Heat transfert (Prentice-Hall, 1993).

The thermal relaxation time for a PhC membrane on oxide can be easily calculated under the hypothesis of 1D vertical heat flow through the oxide layer to the substrate. For instance, for a 250 nm-thick Si membrane (?Si=1.5 W/cm K, ?Si=0.9 cm2/s) in contact with a 1 µm-thick SiO2 layer (?SiO2=0.013 W/cm K, ?SiO2=0.006 cm2/s), a numerical simulation of the 1D heat equation gives tth=950 ns.

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Figures (5)

Fig. 1.
Fig. 1.

(a). Sketch of the photonic crystal-membrane sample. (b). SEM cross-section image of a 5µm-width membrane showing the ~1µm-thickness air gap. (c). Tapered fiber optical coupling scheme for transmission and reflectivity measurements. A SEM image of the L3 cavity is shown.

Fig. 2.
Fig. 2.

(a). Reflectivity spectrum of the cavity resonance without pump (black line), and with 165µW pump (red line). (b). Simultaneous transmission and reflection. The thick arrow indicates the out-of-resonance transmitted power used to estimate the coupling efficiency (see text).

Fig. 3.
Fig. 3.

Time dependence of the reflected cw probe upon squared pump modulation (red lines on top) for different detuning: a) Δλ0=0; b) Δλ0=-0.08 nm; c) Δλ0=-0.21 nm; d) Δλ0=-0.33 nm. (e)–(f) Thermal dynamics obtained from (a)–(d), taking into account the lorentzian shape of the resonance. The arrow in (c) indicates a small amplitude short peak corresponding to electronic blue-shift dynamics before the slow thermal dynamics takes place.

Fig. 4.
Fig. 4.

Thermo-optical bistability. a) Reflectivity spectrum of the linear cavity resonance, and the wavelength range for the cw injection. b) Time traces of input (blue line) and transmitted output (green line) powers for a detuning of Δλ0=-0.56; durations of the switch processes are 1.8 µs and 4 µs for the on/off switches respectively. c) Hysteresis cycles putting into evidence bistable behavior. Detuning-values with respect to the cavity resonance are, from ΔλA to ΔλK: -0.11, -0.27, -0.36, -0.46, -0.52, -0.56, -0.6, -0.64, -0.66, -0.68 and -0.72 nm. The input power is measured at the fiber taper input.

Fig. 5.
Fig. 5.

(a). Sketch of the sample cross section, showing the direction of the heat flow. (b). Simplified model for cylindrical 2D heat conduction in a membrane; κeff represents the effective thermal conductivity of the photonic crystal membrane (see the definition of the other parameters in the text). (c). Rectangular geometry for the calculation of transient dynamics in a 2D membrane. (d). Phase space for bistability conditions. Blue, green and red lines: stationary solutions of the intracavity power (P) as a function of the normalized wavelength shift (q) for: bistable conditions (Pin,input=2 mW, blue), switch on conditions (Pin,input=3.3 mW, green) and switch off conditions (Pin,input=1.55 mW, red). Black line: stationary solutions of θ. The intersections of the black line with the curves give the steady states: θst +(-) is the stable state for the switch on (off) process. The direction of the dynamical flow is indicated by the arrows. The opposite slopes of dP/dθ at the fixed points mathematically explain the difference in relaxation times (see text). Parameters are: P0=2 mW (calculated with Vc=0.08 µm3, tth=186 ns, G=0.015, Qloaded=4520, η1500=0.00057 and a=100 cm-1), Pin=0.263 Pin,input (Pin,input is injected power into the fiber), ξ=16.2 (using vg=c/10, taken from Ref. [29]) and θ0=3.4.

Equations (5)

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f t 2 f i 2 = 1 ( 1 + τ 0 τ c ) 2
T h ( r , t ) = n , m = 0 A nm e σ nm t cos ( k xn x ) cos ( k ym y )
d θ ( t ) dt = 1 t th [ θ ( t ) θ 0 + P ( t ) P 0 ]
P ( t ) = ξ P in 1 + θ ( t ) 2 ,
τ ± 1 = t th 1 [ 1 + 1 P 0 dP θ st ± ] .

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