Abstract

Silicon based nonlinear photonics has been extensively researched at telecom wavelengths in recent years. However, studies of Kerr nonlinearity in silicon at mid-infrared wavelengths still remain limited. Here, we report the wavelength dependency of third-order nonlinearity in the spectral range from 1.6 µm to 6 µm, as well as multi-photon absorption coefficients in the same range. The third-order nonlinear coefficient n2 was measured with a peak value of 1.65 × 10−13 cm2/W at a wavelength of 2.1 µm followed by the decay of nonlinear refractive index n2 up to 2.6 µm. Our latest measurements extend the wavelength towards 6 µm, which show a sharp decrement of n2 beyond 2.1 µm and steadily retains above 3 µm. In addition, the analysis of three-photon absorption and four-photon absorption processes are simultaneously performed over the wavelength range from 2.3 µm to 4.4 µm. Furthermore, the effect of multi-photon absorption on nonlinear figure of merit in silicon is discussed in detail.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
    [CrossRef]
  2. 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(2), 021111 (2007).
    [CrossRef]
  3. V. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett.14(20), 1140–1142 (1989).
    [CrossRef] [PubMed]
  4. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
    [CrossRef]
  5. F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
    [CrossRef]
  6. N. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” Appl. Phys. Lett.110, 011301 (2011).
  7. 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(19), 191104 (2007).
    [CrossRef]
  8. N. Venkatram, R. Sathyavathi, and D. N. Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express15(19), 12258–12263 (2007).
    [CrossRef] [PubMed]
  9. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).
  10. R. L. Sutherland, D. G. Mclean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, 2003) p. 528.
  11. W. C. Hurlbut, Y. S. Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett.32(6), 668–670 (2007).
    [CrossRef] [PubMed]
  12. B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B1(1), 67–72 (1984).
    [CrossRef]
  13. Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
    [CrossRef]
  14. D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE Trans. Electron. Dev.25(2), 254–261 (1978).
    [CrossRef]
  15. J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
    [CrossRef]
  16. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett.21(24), 1966–1968 (1996).
    [CrossRef] [PubMed]
  17. T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, “Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light,” Opt. Lett.20(9), 988–990 (1995).
    [CrossRef] [PubMed]
  18. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
    [CrossRef]
  19. 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(1), 96–99 (1990).
    [CrossRef] [PubMed]
  20. C. Bree, A. Demircan, and G. Steinmeyer, “Kramers-Kronig relations and high-order nonlinear susceptibilities,” Phys. Rev. A85(3), 033806 (2012).
    [CrossRef]
  21. T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
    [CrossRef]

2013 (1)

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

2012 (1)

C. Bree, A. Demircan, and G. Steinmeyer, “Kramers-Kronig relations and high-order nonlinear susceptibilities,” Phys. Rev. A85(3), 033806 (2012).
[CrossRef]

2011 (2)

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

N. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” Appl. Phys. Lett.110, 011301 (2011).

2008 (1)

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

2007 (5)

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(2), 021111 (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(19), 191104 (2007).
[CrossRef]

N. Venkatram, R. Sathyavathi, and D. N. Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express15(19), 12258–12263 (2007).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

W. C. Hurlbut, Y. S. Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett.32(6), 668–670 (2007).
[CrossRef] [PubMed]

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
[CrossRef]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[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(1), 96–99 (1990).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

1984 (1)

1978 (1)

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE Trans. Electron. Dev.25(2), 254–261 (1978).
[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(2), 021111 (2007).
[CrossRef]

Alic, N.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Andrejco, M. J.

Boggess, T. F.

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

Bohnert, K.

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

Borlaug, D.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Boskovic, A.

Boyd, I. W.

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[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(2), 021111 (2007).
[CrossRef]

Bree, C.

C. Bree, A. Demircan, and G. Steinmeyer, “Kramers-Kronig relations and high-order nonlinear susceptibilities,” Phys. Rev. A85(3), 033806 (2012).
[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(19), 191104 (2007).
[CrossRef]

Chen, S.

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Chen, X.

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Chernikov, S. V.

Delong, K. W.

Demircan, A.

C. Bree, A. Demircan, and G. Steinmeyer, “Kramers-Kronig relations and high-order nonlinear susceptibilities,” Phys. Rev. A85(3), 033806 (2012).
[CrossRef]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

Fainman, Y.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

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(2), 021111 (2007).
[CrossRef]

Fejer, M. M.

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

Gholami, F.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Gruner-Nielsen, L.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[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(1), 96–99 (1990).
[CrossRef] [PubMed]

Hon, N.

N. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” Appl. Phys. Lett.110, 011301 (2011).

Hurlbut, W. C.

Jalali, B.

N. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” Appl. Phys. Lett.110, 011301 (2011).

Kato, T.

Kuo, P. S.

Lee, Y. S.

Levring, O. A.

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(2), 021111 (2007).
[CrossRef]

Liu, L.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Ma, E.

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Mansour, K.

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

Mizrahi, V.

Moss, S. C.

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

Nezhad, M.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Nishimura, M.

Pearl, S.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

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(2), 021111 (2007).
[CrossRef]

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[CrossRef]

Radic, S.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Rao, D. N.

Rotenberg, N.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 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(19), 191104 (2007).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[CrossRef]

Saifi, M. A.

Sasaoka, E.

Sathyavathi, R.

Schroder, D. K.

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE Trans. Electron. Dev.25(2), 254–261 (1978).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[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(1), 96–99 (1990).
[CrossRef] [PubMed]

Simic, A.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Smirl, A. L.

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

Soref, R.

N. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” Appl. Phys. Lett.110, 011301 (2011).

Stegeman, G. I.

Steinmeyer, G.

C. Bree, A. Demircan, and G. Steinmeyer, “Kramers-Kronig relations and high-order nonlinear susceptibilities,” Phys. Rev. A85(3), 033806 (2012).
[CrossRef]

Suetsugu, Y.

Swartz, J. C.

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE Trans. Electron. Dev.25(2), 254–261 (1978).
[CrossRef]

Takagi, M.

Tang, C.

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Taylor, J. R.

Thomas, R. N.

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE Trans. Electron. Dev.25(2), 254–261 (1978).
[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(13), 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(19), 191104 (2007).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (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(1), 96–99 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[CrossRef]

Venkatram, N.

Vodopyanov, K. L.

Wang, J.

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
[CrossRef]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[CrossRef]

Wherrett, B. S.

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(2), 021111 (2007).
[CrossRef]

Zheng, Q.

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Zhu, H.

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Zlatanovic, S.

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

Appl. Phys. Lett. (6)

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

F. Gholami, S. Zlatanovic, A. Simic, L. Liu, D. Borlaug, N. Alic, M. Nezhad, Y. Fainman, and S. Radic, “Third-order nonlinearity in silicon beyond 2350 nm,” Appl. Phys. Lett.99(8), 081102 (2011).
[CrossRef]

N. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” Appl. Phys. Lett.110, 011301 (2011).

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(19), 191104 (2007).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003).
[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(2), 021111 (2007).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
[CrossRef]

T. F. Boggess, K. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon,” IEEE J. Quantum Electron.22(2), 360–368 (1986).
[CrossRef]

IEEE LEOS Newsletter (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Special 30th anniversary feature: sensitive measurement of optical nonlinearities using a single beam,” IEEE LEOS Newsletter21, 17–35 (2007).

IEEE Trans. Electron. Dev. (1)

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free carrier absorption in silicon,” IEEE Trans. Electron. Dev.25(2), 254–261 (1978).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Am. B. (1)

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B.11(6), 1009–1017 (1994).
[CrossRef]

Nat. Photonics (1)

Q. Zheng, H. Zhu, S. Chen, C. Tang, E. Ma, and X. Chen, “Frequency-upconverted stimulated emission by simultaneous five-photon absorption,” Nat. Photonics7(3), 234–239 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

C. Bree, A. Demircan, and G. Steinmeyer, “Kramers-Kronig relations and high-order nonlinear susceptibilities,” Phys. Rev. A85(3), 033806 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

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(1), 96–99 (1990).
[CrossRef] [PubMed]

Other (1)

R. L. Sutherland, D. G. Mclean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, 2003) p. 528.

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 (4)

Fig. 1
Fig. 1

Variation of the MPA coefficients in silicon at mid-IR wavelengths (2.6-4.4 µm).

Fig. 2
Fig. 2

a) Closed and b) open aperture Z-scan curve of a 675µm-thick Si at 2.6 µm; c) Closed aperture Z-scan curve of a 1mm-thick SiO2 substrate at 1.55 µm; d)Closed aperture Z-scan curve of a 675µm-thick Si at 3.8 µm.

Fig. 3
Fig. 3

Variation of n2 in silicon at mid-IR wavelengths from 1.6 to 6 µm: crosses (data from ref. 7) and diamonds (data measured by SUTD-NUS).

Fig. 4
Fig. 4

Nonlinear figure of merit (FOM) with presence of MPA: crosses (data from ref. 7) and stars (data measured by SUTD-NUS).

Equations (5)

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

T OA( nPA ) = 1 {1+(n1) α n L[ I 00 / (1+ ( z/ z 0 ) 2 )] n1 } 1 n1
T OA( 3PA ) = 1 {1+2 α 3 L eff ' [ I 00 / (1+ ( z/ z 0 ) 2 )] 2 } 1 2
T OA( 4PA ) = 1 {1+3 α 4 L eff '' [ I 00 / (1+ ( z/ z 0 ) 2 )] 3 } 1 3
T CA =1+ 4Δ φ 0 (z/ z 0 ) [1+ (z/ z 0 ) 2 ][9+ (z/ z 0 ) 2 ]
n 2 = Δ φ 0 λ 2π I 00 L eff

Metrics