Abstract

We present a systematic study of ultrafast all-optical switching of Si photonic bandgap woodpile crystals using broadband tunable nondegenerate pump-probe spectroscopy. At pump-probe coincidence, we investigate the behavior of the differential reflectivity at the blue edge of the stop band for a wide range of pump and probe frequencies. Both dispersive and absorptive features are observed from the probe spectra at coincidence. As the pump frequency is tuned through half the electronic bandgap of Si, the magnitude of both these features increases. For the first time, to the best of our knowledge, we unambiguously identify this dispersive effect with the electronic Kerr effect in photonic crystals and attribute the absorptive features to nondegenerate two photon absorption. The dispersive and absorptive nonlinear coefficients are extracted and are found to agree well with the literature. Finally, we propose a nondegenerate figure of merit, which defines the quality of switching for all nondegenerate optical switching processes.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B 66, 081102(R) (2002).
    [CrossRef]
  2. B. P. J. Bret, T. L. Sonnemans, and T. W. Hijmans, “Capturing a light pulse in a short high-finesse cavity,” Phys. Rev. A 68, 023807 (2003).
    [CrossRef]
  3. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
    [CrossRef] [PubMed]
  4. Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30, 2733-2735 (2005).
    [CrossRef] [PubMed]
  5. S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293-296 (2007).
    [CrossRef]
  6. P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
    [CrossRef]
  7. S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
    [CrossRef]
  8. C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
    [CrossRef]
  9. T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
    [CrossRef]
  10. A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
    [CrossRef]
  11. M. Först, J. Niehusmann, T. Plötzing, J. Bolten, T. Wahlbrink, C. Moormann, and H. Kurz, “High-speed all-optical switching in ion-implanted silicon-on-insulator microring resonators,” Opt. Lett. 32, 2046-2048 (2007).
    [CrossRef] [PubMed]
  12. T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
    [CrossRef]
  13. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954-2956 (2003).
    [CrossRef]
  14. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
    [CrossRef]
  15. Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
    [CrossRef]
  16. A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089-4091 (2000).
    [CrossRef]
  17. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
    [CrossRef] [PubMed]
  18. S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
    [CrossRef]
  19. J. P. Mondia, H. W. Tan, S. Linden, H. M. van Driel, and J. F. Young, “Ultrafast tuning of two-dimensional planar photonic-crystal waveguides via free-carrier injection and the optical Kerr effect,” J. Opt. Soc. Am. B 22, 2480-2486 (2005).
    [CrossRef]
  20. Indeed, this Kerr nonlinearity was also claimed by our group , but was later corrected .
  21. T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
    [CrossRef]
  22. T. G. Euser, “Ultrafast optical switching of photonic crystals,” Ph.D. dissertation (University of Twente, 2007), ISBN 978-90-365-2471-1, www.photonicbandgaps.com.
  23. J. G. Fleming and S. Lin, “Three-dimensional photonic crystal with a stop band from 1.35to1.95 μm,” Opt. Lett. 24, 49-51 (1999).
    [CrossRef]
  24. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  25. B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
    [CrossRef]
  26. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
    [CrossRef]
  27. W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).
  28. A. F. Koenderink, “Emission and transport of light in photonic crystals,” Ph.D. dissertation, (University of Amsterdam, 2003), ISBN 90-9016903-2, www.photonicbandgaps.com.
  29. M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
    [CrossRef]
  30. T. G. Euser and W. L. Vos, “Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors,” J. Appl. Phys. 97, 043102 (2005).
    [CrossRef]
  31. J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in Si at 1.06 μm,” Phys. Rev. Lett. 30, 901-903 (1973).
    [CrossRef]
  32. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
    [CrossRef]
  33. K. W.-K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11265-11269 (1993).
    [CrossRef]
  34. M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
    [CrossRef]
  35. Variable Angle Spectroscopic Ellipsometry Handbook (WVASE32) (J. A. Woollam Co., Inc., 1987).
  36. C. Rotaru, S. Nastase, and N. Tomozeiu, “Amorphous phase influence on the optical bandgap of polysilicon,” Phys. Status Solidi A 171, 365-370 (1999).
    [CrossRef]
  37. H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz-Keldysch effect in indirect gap semiconductors,” J. Phys. B 39, 2737-2746 (2006).
    [CrossRef]
  38. Higher probe intensities do not influence the magnitude of the nondegenerate absorption: in the absence of linear absorption, as in our case, the differential equation governing nondegenerate two photon absorption is dIProbedz=−2β12(EProbe,EPump)IPumpIProbe(z).Here, β12 is the nondegenerate two-photon absorption coefficient. From Eq. we see that higher probe intensities do not increase absorption: The coefficient of −IProbe(z) is 2β12(EProbe+EPump)IPump=αeff, which is an effective absorption coefficient. Higher probe intensities merely lead to a higher absorbance, commensurate to the number of absorbed photons.
  39. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
    [CrossRef] [PubMed]
  40. K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643-2650 (2000).
    [CrossRef]
  41. K. Ikeda, Y. Shen, and Y. Fainman, “Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices,” Opt. Express 15, 17761-17771 (2007).
    [CrossRef] [PubMed]
  42. I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
    [CrossRef]
  43. We had independently measured the radius of the beam waist at the focus, and had confirmed that the radius is diffraction limited.
  44. E. Garmire, “Nonlinear optics in semiconductors,” Phys. Today 47, 42-48 (1994).
    [CrossRef]
  45. We note that the n2 in Eq. depends on EPump only. Measurements of nondegenerate n2 are still lacking in the literature.
  46. C. Klingshirn, Semiconductor Optics (Springer, 2005).
  47. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
    [CrossRef]
  48. A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
    [CrossRef]
  49. M. Sheik-Bahae, J. Wang, and E. W. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30, 249-255 (1994).
    [CrossRef]
  50. P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B 61, 2090-2101 (2000).
    [CrossRef]
  51. T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).
  52. D. C. Hutchins and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065-2074 (1992).
    [CrossRef]

2008 (3)

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[CrossRef]

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

2007 (10)

T. G. Euser, “Ultrafast optical switching of photonic crystals,” Ph.D. dissertation (University of Twente, 2007), ISBN 978-90-365-2471-1, www.photonicbandgaps.com.

M. Först, J. Niehusmann, T. Plötzing, J. Bolten, T. Wahlbrink, C. Moormann, and H. Kurz, “High-speed all-optical switching in ion-implanted silicon-on-insulator microring resonators,” Opt. Lett. 32, 2046-2048 (2007).
[CrossRef] [PubMed]

K. Ikeda, Y. Shen, and Y. Fainman, “Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices,” Opt. Express 15, 17761-17771 (2007).
[CrossRef] [PubMed]

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293-296 (2007).
[CrossRef]

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

2006 (2)

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz-Keldysch effect in indirect gap semiconductors,” J. Phys. B 39, 2737-2746 (2006).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

2005 (7)

C. Klingshirn, Semiconductor Optics (Springer, 2005).

Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30, 2733-2735 (2005).
[CrossRef] [PubMed]

J. P. Mondia, H. W. Tan, S. Linden, H. M. van Driel, and J. F. Young, “Ultrafast tuning of two-dimensional planar photonic-crystal waveguides via free-carrier injection and the optical Kerr effect,” J. Opt. Soc. Am. B 22, 2480-2486 (2005).
[CrossRef]

M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
[CrossRef]

T. G. Euser and W. L. Vos, “Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors,” J. Appl. Phys. 97, 043102 (2005).
[CrossRef]

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

2004 (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

2003 (6)

B. P. J. Bret, T. L. Sonnemans, and T. W. Hijmans, “Capturing a light pulse in a short high-finesse cavity,” Phys. Rev. A 68, 023807 (2003).
[CrossRef]

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

A. F. Koenderink, “Emission and transport of light in photonic crystals,” Ph.D. dissertation, (University of Amsterdam, 2003), ISBN 90-9016903-2, www.photonicbandgaps.com.

M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
[CrossRef]

2002 (3)

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B 66, 081102(R) (2002).
[CrossRef]

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
[CrossRef]

2001 (1)

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

2000 (3)

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643-2650 (2000).
[CrossRef]

A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089-4091 (2000).
[CrossRef]

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B 61, 2090-2101 (2000).
[CrossRef]

1999 (2)

J. G. Fleming and S. Lin, “Three-dimensional photonic crystal with a stop band from 1.35to1.95 μm,” Opt. Lett. 24, 49-51 (1999).
[CrossRef]

C. Rotaru, S. Nastase, and N. Tomozeiu, “Amorphous phase influence on the optical bandgap of polysilicon,” Phys. Status Solidi A 171, 365-370 (1999).
[CrossRef]

1996 (1)

A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
[CrossRef]

1994 (3)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Garmire, “Nonlinear optics in semiconductors,” Phys. Today 47, 42-48 (1994).
[CrossRef]

M. Sheik-Bahae, J. Wang, and E. W. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30, 249-255 (1994).
[CrossRef]

1993 (1)

K. W.-K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11265-11269 (1993).
[CrossRef]

1992 (1)

1990 (2)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1987 (1)

Variable Angle Spectroscopic Ellipsometry Handbook (WVASE32) (J. A. Woollam Co., Inc., 1987).

1973 (1)

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in Si at 1.06 μm,” Phys. Rev. Lett. 30, 901-903 (1973).
[CrossRef]

Agrawal, G. P.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Akimov, A. V.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Almeida, V. R.

Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30, 2733-2735 (2005).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Becker, C.

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Bolten, J.

Bourgeois, M.

A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089-4091 (2000).
[CrossRef]

Bouwmeester, D.

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

Boyd, R. W.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Bret, B. P. J.

B. P. J. Bret, T. L. Sonnemans, and T. W. Hijmans, “Capturing a light pulse in a short high-finesse cavity,” Phys. Rev. A 68, 023807 (2003).
[CrossRef]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chin, A.

A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
[CrossRef]

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

de Dood, M. J. A.

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
[CrossRef]

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Deubel, M.

M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
[CrossRef]

Dijkhuis, J. I.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Eisenberg, H. S.

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

Englund, D.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

Enoch, S.

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Euser, T. G.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

T. G. Euser, “Ultrafast optical switching of photonic crystals,” Ph.D. dissertation (University of Twente, 2007), ISBN 978-90-365-2471-1, www.photonicbandgaps.com.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

T. G. Euser and W. L. Vos, “Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors,” J. Appl. Phys. 97, 043102 (2005).
[CrossRef]

Fainman, Y.

Fauchet, P. M.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Fleming, J. G.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
[CrossRef]

J. G. Fleming and S. Lin, “Three-dimensional photonic crystal with a stop band from 1.35to1.95 μm,” Opt. Lett. 24, 49-51 (1999).
[CrossRef]

Först, M.

Fushman, I.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

Garcia, H.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz-Keldysch effect in indirect gap semiconductors,” J. Phys. B 39, 2737-2746 (2006).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Garmire, E.

E. Garmire, “Nonlinear optics in semiconductors,” Phys. Today 47, 42-48 (1994).
[CrossRef]

Gérard, J.-M.

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Golubev, V. G.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Gralak, B.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
[CrossRef]

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Haché, A.

A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089-4091 (2000).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Harding, P. J.

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Hartsuiker, A.

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

Hastings, S. R.

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

Hijmans, T. W.

B. P. J. Bret, T. L. Sonnemans, and T. W. Hijmans, “Capturing a light pulse in a short high-finesse cavity,” Phys. Rev. A 68, 023807 (2003).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Horng, S.

A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
[CrossRef]

Hutchins, D. C.

Ikeda, K.

Imhof, A.

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

Inokawa, H.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Johnson, P. M.

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B 66, 081102(R) (2002).
[CrossRef]

Jun, Y.

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

Kalkman, J.

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

Kalyanaraman, R.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz-Keldysch effect in indirect gap semiconductors,” J. Phys. B 39, 2737-2746 (2006).
[CrossRef]

Kerst, R.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Kim, H.

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

Kitaev, V.

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

Klingshirn, C.

C. Klingshirn, Semiconductor Optics (Springer, 2005).

Koenderink, A. F.

A. F. Koenderink, “Emission and transport of light in photonic crystals,” Ph.D. dissertation, (University of Amsterdam, 2003), ISBN 90-9016903-2, www.photonicbandgaps.com.

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B 66, 081102(R) (2002).
[CrossRef]

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

Kuramochi, E.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Kurdyukov, D. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Kurz, H.

Lee, K. Y.

A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
[CrossRef]

Leonard, S. W.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
[CrossRef]

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Lin, B. C.

A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
[CrossRef]

Lin, Q.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Lin, S.

Linden, S.

M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
[CrossRef]

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

J. P. Mondia, H. W. Tan, S. Linden, H. M. van Driel, and J. F. Young, “Ultrafast tuning of two-dimensional planar photonic-crystal waveguides via free-carrier injection and the optical Kerr effect,” J. Opt. Soc. Am. B 22, 2480-2486 (2005).
[CrossRef]

Lipson, M.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293-296 (2007).
[CrossRef]

Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30, 2733-2735 (2005).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Marshall, W.

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

Maystre, D.

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Mazurenko, D. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

McGroddy, J. C.

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in Si at 1.06 μm,” Phys. Rev. Lett. 30, 901-903 (1973).
[CrossRef]

Megens, M.

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

Molenaar, A. J.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

Mondia, J. P.

Moormann, C.

Nastase, S.

C. Rotaru, S. Nastase, and N. Tomozeiu, “Amorphous phase influence on the optical bandgap of polysilicon,” Phys. Status Solidi A 171, 365-370 (1999).
[CrossRef]

Niehusmann, J.

Nishiguchi, K.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Norris, D. J.

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

Notomi, M.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Nowicki-Bringuier, Y. R.

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Nowicki-Bringuier, Y.-R.

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

Ozin, G. A.

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

Paddon, P.

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B 61, 2090-2101 (2000).
[CrossRef]

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Pearl, S.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[CrossRef]

Petroff, P.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

Pevtsov, A. B.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Piredda, G.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Plötzing, T.

Polman, A.

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
[CrossRef]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293-296 (2007).
[CrossRef]

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Reintjes, J. F.

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in Si at 1.06 μm,” Phys. Rev. Lett. 30, 901-903 (1973).
[CrossRef]

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Rotaru, C.

C. Rotaru, S. Nastase, and N. Tomozeiu, “Amorphous phase influence on the optical bandgap of polysilicon,” Phys. Status Solidi A 171, 365-370 (1999).
[CrossRef]

Rotenberg, N.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Schilling, J.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
[CrossRef]

Sel'kin, A. V.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, J. Wang, and E. W. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30, 249-255 (1994).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Shen, Y.

Shinya, A.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Shung, K. W.-K.

K. W.-K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11265-11269 (1993).
[CrossRef]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Sokolowski-Tinten, K.

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643-2650 (2000).
[CrossRef]

Sonnemans, T. L.

B. P. J. Bret, T. L. Sonnemans, and T. W. Hijmans, “Capturing a light pulse in a short high-finesse cavity,” Phys. Rev. A 68, 023807 (2003).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Stoltz, N.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

Tan, H. W.

Tanabe, T.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Tayeb, G.

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Tétreault, N.

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

Tomozeiu, N.

C. Rotaru, S. Nastase, and N. Tomozeiu, “Amorphous phase influence on the optical bandgap of polysilicon,” Phys. Status Solidi A 171, 365-370 (1999).
[CrossRef]

Tsai, Y. C.

K. W.-K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11265-11269 (1993).
[CrossRef]

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

van Driel, H. M.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

J. P. Mondia, H. W. Tan, S. Linden, H. M. van Driel, and J. F. Young, “Ultrafast tuning of two-dimensional planar photonic-crystal waveguides via free-carrier injection and the optical Kerr effect,” J. Opt. Soc. Am. B 22, 2480-2486 (2005).
[CrossRef]

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
[CrossRef]

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

Van Stryland, E. W.

M. Sheik-Bahae, J. Wang, and E. W. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30, 249-255 (1994).
[CrossRef]

D. C. Hutchins and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065-2074 (1992).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Vekris, E.

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

von der Linde, D.

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643-2650 (2000).
[CrossRef]

von Freymann, G.

M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
[CrossRef]

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

Vos, W. L.

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

T. G. Euser and W. L. Vos, “Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors,” J. Appl. Phys. 97, 043102 (2005).
[CrossRef]

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B 66, 081102(R) (2002).
[CrossRef]

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

Vuckovic, J.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

Wahlbrink, T.

Waks, E.

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

Wang, J.

M. Sheik-Bahae, J. Wang, and E. W. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30, 249-255 (1994).
[CrossRef]

Wegener, M.

M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
[CrossRef]

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

Wehrspohn, R. B.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
[CrossRef]

Wei, H.

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Xu, Q.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293-296 (2007).
[CrossRef]

Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30, 2733-2735 (2005).
[CrossRef] [PubMed]

Young, J. F.

Zhang, J.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Appl. Phys. Lett. (13)

P. J. Harding, T. G. Euser, Y. R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Ultrafast optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

C. Becker, S. Linden, G. von Freymann, M. Wegener, N. Tétreault, E. Vekris, V. Kitaev, and G. A. Ozin, “Two-color pump-probe experiments on silicon inverse opals,” Appl. Phys. Lett. 87, 091111 (2005).
[CrossRef]

A. Chin, K. Y. Lee, B. C. Lin, and S. Horng, “Picosecond photoresponse of carriers in Si ion-implanted Si,” Appl. Phys. Lett. 69, 653655 (1996).
[CrossRef]

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089-4091 (2000).
[CrossRef]

S. R. Hastings, M. J. A. de Dood, H. Kim, W. Marshall, H. S. Eisenberg, and D. Bouwmeester, “Ultrafast optical response of a high-reflectivity GaAs/AlAs Bragg mirror,” Appl. Phys. Lett. 86, 031109 (2005).
[CrossRef]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Angle-resolved transmission spectroscopy of three-dimensional photonic crystals fabricated by direct laser writing,” Appl. Phys. Lett. 87, 221104 (2005).
[CrossRef]

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Ultrafast nonlinear optical tuning of photonic crystal cavities,” Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93, 131102 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, J. Wang, and E. W. Van Stryland, “Nondegenerate optical Kerr effect in semiconductors,” IEEE J. Quantum Electron. 30, 249-255 (1994).
[CrossRef]

J. Appl. Phys. (3)

A. Hartsuiker, P. J. Harding, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, “Kerr and free-carrier ultrafast all-optical switching of GaAs/AlAs nanostructures near the three-photon edge of GaAs,” J. Appl. Phys. 104, 083105 (2008).
[CrossRef]

T. G. Euser and W. L. Vos, “Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors,” J. Appl. Phys. 97, 043102 (2005).
[CrossRef]

T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, “Ultrafast optical switching of three-dimensional Si inverse opal photonic band gap crystals,” J. Appl. Phys. 102, 053111 (2007).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz-Keldysch effect in indirect gap semiconductors,” J. Phys. B 39, 2737-2746 (2006).
[CrossRef]

Nat. Photonics (1)

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 293-296 (2007).
[CrossRef]

Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

B. P. J. Bret, T. L. Sonnemans, and T. W. Hijmans, “Capturing a light pulse in a short high-finesse cavity,” Phys. Rev. A 68, 023807 (2003).
[CrossRef]

Phys. Rev. B (7)

P. M. Johnson, A. F. Koenderink, and W. L. Vos, “Ultrafast switching of photonic density of states in photonic crystals,” Phys. Rev. B 66, 081102(R) (2002).
[CrossRef]

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, “Ultrafast band-edge tuning of a two-dimensional silicon photonic crystal via free-carrier injection,” Phys. Rev. B 66, 161102(R) (2002).
[CrossRef]

M. J. A. de Dood, B. Gralak, A. Polman, and J. G. Fleming, “Superstructure and finite-size effects in a Si photonic woodpile crystal,” Phys. Rev. B 67, 035322 (2003).
[CrossRef]

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643-2650 (2000).
[CrossRef]

K. W.-K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11265-11269 (1993).
[CrossRef]

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical octave-broad ultrafast switching of Si woodpile photonic band gap crystals,” Phys. Rev. B 77, 115214 (2008).
[CrossRef]

P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode theory for textured planar waveguides,” Phys. Rev. B 61, 2090-2101 (2000).
[CrossRef]

Phys. Rev. E (1)

B. Gralak, M. J. A. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel'kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[CrossRef] [PubMed]

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in Si at 1.06 μm,” Phys. Rev. Lett. 30, 901-903 (1973).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

C. Rotaru, S. Nastase, and N. Tomozeiu, “Amorphous phase influence on the optical bandgap of polysilicon,” Phys. Status Solidi A 171, 365-370 (1999).
[CrossRef]

Phys. Today (1)

E. Garmire, “Nonlinear optics in semiconductors,” Phys. Today 47, 42-48 (1994).
[CrossRef]

Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Other (10)

W. L. Vos, H. M. van Driel, M. Megens, A. F. Koenderink, and A. Imhof, “Experimental probes of the optical properties of photonic crystals,” in Proceedings of the NATO ASI Photonic Crystals and Light Localization in the 21st Century, C.M.Soukoulis, ed. (Kluwer, 2001).

A. F. Koenderink, “Emission and transport of light in photonic crystals,” Ph.D. dissertation, (University of Amsterdam, 2003), ISBN 90-9016903-2, www.photonicbandgaps.com.

Higher probe intensities do not influence the magnitude of the nondegenerate absorption: in the absence of linear absorption, as in our case, the differential equation governing nondegenerate two photon absorption is dIProbedz=−2β12(EProbe,EPump)IPumpIProbe(z).Here, β12 is the nondegenerate two-photon absorption coefficient. From Eq. we see that higher probe intensities do not increase absorption: The coefficient of −IProbe(z) is 2β12(EProbe+EPump)IPump=αeff, which is an effective absorption coefficient. Higher probe intensities merely lead to a higher absorbance, commensurate to the number of absorbed photons.

We had independently measured the radius of the beam waist at the focus, and had confirmed that the radius is diffraction limited.

Variable Angle Spectroscopic Ellipsometry Handbook (WVASE32) (J. A. Woollam Co., Inc., 1987).

We note that the n2 in Eq. depends on EPump only. Measurements of nondegenerate n2 are still lacking in the literature.

C. Klingshirn, Semiconductor Optics (Springer, 2005).

T. G. Euser, A. J. Molenaar, J. G. Fleming, B. Gralak, A. Polman, and W. L. Vos, “All-optical ultrafast switching of Si woodpile photonic band gap crystals,” arXiv:physics p.0603045v1 (2006).

Indeed, this Kerr nonlinearity was also claimed by our group , but was later corrected .

T. G. Euser, “Ultrafast optical switching of photonic crystals,” Ph.D. dissertation (University of Twente, 2007), ISBN 978-90-365-2471-1, www.photonicbandgaps.com.

Cited By

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

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

High resolution scanning electron micrograph of the surface normal to [001] of a Si woodpile crystal at domain D4. The width and thickness of each rod is 175 ± 10 and 155 ± 10 nm , respectively.

Fig. 2
Fig. 2

Linear reflectivity spectrum of the woodpile photonic crystal measured normal to the [001] direction at a sample domain D4 shown in Fig. 1. The E field is perpendicular to the first row of rods. A stopgap near 0.9 eV gives rise to a high maximum reflectivity of 95 % ± 2 % and has a broad relative width of 47%, indicating a high photonic strength. At high frequencies > 1.2 eV , the spectral features are attributed to Fabry–Pérot-type fringes. The pump frequencies (shaded box) were tuned at the red edge through half the electronic band gap E G = 1.12 eV of silicon (vertical dashed line), and the probe frequencies at the blue edge of the stop band. The dashed curve is a calculation with the SWA in the region of interest.

Fig. 3
Fig. 3

Differential reflectivity Δ R R versus probe delay Δ t taken at different pump frequencies E Pump and at probe frequency E Probe = 1.13 eV , sample domain A1. At Δ t = 0 ps , the pump and probe are coincident, and the differential reflectivity ( Δ R R ) coinc decreases. At Δ t = 1 ps , the differential reflectivity ( Δ R R ) FC has increased due to the dispersion of the FCs. The peak pump intensity varies between I Pump = 10 ± 1 GW cm 2 ( E Pump = 0.516 eV ) and I Pump = 25 ± 2 GW cm 2 ( E Pump = 0.75 eV ) , and the probe intensity was I Probe = 3 ± 2 GW cm 2 .

Fig. 4
Fig. 4

(a) Measured linear reflectivity versus probe frequency (open squares) on domain D4 compared to the scalar wave approximation (solid curve). (b) The differential reflectivity ( Δ R R ) FC at delay Δ t = 1 ps caused by the FCs shows mostly dispersive features, as seen from the symmetric variation of Δ R R around 0. When increasing the pump frequency from 0.54 (solid triangles) to 0.62 eV (open triangles), these dispersive features increase in magnitude. (c) At Δ t = 0 ps , dispersive as well as absorptive features are observed in ( Δ R R ) coinc , increasingly so when increasing the pump frequency from E Pump = 0.54 to 0.62 eV . For E Pump = 0.54 eV , we find Δ n = 0.44 × 10 3 and n = 0.46 × 10 3 , while for E Pump = 0.62 eV the fits give Δ n = 1.1 × 10 3 and n = 1.1 × 10 2 . The pump intensity was I Pump = 36 ± 4 GW cm 2 ( E Pump = 0.54 eV ) and I Pump = 46 ± 5 GW cm 2 ( E Pump = 0.62 eV ) .

Fig. 5
Fig. 5

Instantaneous changes of the complex refractive index. (a) Imaginary refractive index ( n , solid squares) versus pump frequency E Pump (lower axis) obtained from fits in Fig. 4. The dashed curve is a fit of n to an exponential. The right scale shows the corresponding absorption coefficient. For comparison, we plot the absorption coefficient for low pressure chemical vapor deposited p - Si (solid curve) annealed at 545 ° C , similar to the backbone of our woodpile crystals. Upper abscissa is the sum of the pump and probe frequencies E Total . (b) Change in real refractive index Δ n (left scale, solid squares) versus pump frequency E Pump from our nondegenerate measurements. The theoretical relation predicted by [39] is also shown (solid curve, right scale). We plot degenerate measurements for comparison: open squares from [13] and open circles from [15]. Data from [14] exceed the scale by one order of magnitude.

Fig. 6
Fig. 6

Nonlinear coefficient β 11 versus pump frequency (solid squares) obtained from data as in Fig. 4. Dashed curve is a calculation from [39] for c - Si . Other data are from [13] ( c - Si , open squares), [15] ( c - Si , open circles), [14] ( c - Si , triangles), and [41] ( p - Si , diamonds).

Fig. 7
Fig. 7

Differential reflectivity at coincidence versus pump frequency extracted from Fig. 3 (domain A1) and corrected for pump beam parameters (squares, left scale). Circles are complex values of n extracted from Fig. 5 (domain D4) and reinserted in the extended SWA at domain A1. We have calculated the differential reflectivity expected from a nonlinear, purely dispersive direct bandgap material (solid curve) [39] by inserting the theoretical relation for n 2 into the extended SWA. The “purely dispersive assumption” deviates from the data for pump frequencies above E Pump = 0.69 eV , or E Total = 1.82 eV .

Fig. 8
Fig. 8

NFOM for instantaneous switching versus pump and probe frequency for polysilicon [see Eq. (6)]. For E Pump < 1 2 E G ( = 0.56 eV ) , pump absorption is absent as we do not consider more than second-order photon absorption. If in addition E Pump + E Probe < E Opt = 1.5 eV , the total absorption is zero leading to large NFOM outside of the scale of graph (crosshatched area). The black curve indicates the parameter space for which a maximum NFOM is reached if three-photon absorption is neglected. At E Pump = 0.8 eV , n 2 ( E Pump ) crosses 0 cm 2 GW 1 , and so the NFOM vanishes. For E Total E Opt , the NFOM is < 1 × 10 5 (hatched area). The parameter space in our present measurements is bounded by the box (square). The only other measurement of n 2 on a Si based photonic structure is [16] (circle).

Fig. 9
Fig. 9

(a) Relative change in frequency Δ E E 0 for a given change in the relative average refractive index Δ n av n av . For comparison, the change according to Bragg’s law is Δ E E 0 = Δ n av n av . (b) Change in reflectivity for a given change in the imaginary part of the refractive index n .

Fig. 10
Fig. 10

Reflectivity calculated with the SWA with and without the thin layer of SiN.

Equations (7)

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

L B = λ π S ,
U G = Δ ϵ f G , G 0 ,
N = I Pump 2 τ P β 11 2 E Pump e ,
Δ ϵ fc = ( ω P ω ) 2 ( 1 i ( ω τ D ) 1 ) ,
FOM ( E Pump ) = n 2 ( E Pump ) λ Pump β 11 ( E Pump ) ,
NFOM ( E Pump , E Probe ) = n 2 ( E Pump ) λ Pump β 11 ( E Pump ) + λ Probe β 12 ( E Pump , E Probe ) .
d I Probe d z = 2 β 12 ( E Probe , E Pump ) I Pump I Probe ( z ) .

Metrics