Abstract

We study free-carrier nonlinearities in crystalline silicon at 1.064 µm using the Z-scan technique, with special emphasis on the dependence of their nonlinearities on the width of incident pulses. In the Z-scan experiment, the pulse duration was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in a liquid. At this excitation wavelength, linear absorption is dominant for the creation of electron-hole pairs and the photoexcited carriers can modify the refractive index and absorption coefficient just as a third-order nonlinear effect. The effective nonlinear refractive index n 2eff and nonlinear absorption coefficient β eff are proportional to the pulse duration and optical intensity, i.e. the fluence when the pulse duration is shorter than the carrier recombination lifetime. We can determine the variation of refractive index per unit of photoexcited carrier density σ r and the total carrier absorption cross section σ ab from the dependence of n 2eff and β eff on the pulse width, respectively. In this work we had σ r = -1.0 × 10-21 cm3 and σ ab = 8.4 × 10-18 cm2, which agree well with previous data. We also observed the decrease in the magnitude of n 2eff and β eff at high incident fluence, which is presumably attributed to band filling. This new measurement approach has an advantage of being able to separate an ultrafast Kerr nonlinearity and a cumulative nonlinearity such as the free-carrier nonlinearity treated in this paper and can be utilized to evaluate the optical nonlinearities of other materials.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. R. Soref, "The past, present, and future of silicon photonics," IEEE J. Sel. Top. Quantum Electron. 12, 1678-1687 (2006).
    [CrossRef]
  2. M. Lipson, "Guiding, modulating, and emitting light on silicon - Challenges and opportunities," J. Lightwave Technol. 23, 4222-4238 (2005).
    [CrossRef]
  3. B. Jalali and S. Fathpour, "Silicon photonics," J. Lightwave Technol. 24, 4600-4615 (2006).
    [CrossRef]
  4. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: Modeling and applications," Opt. Express 15, 16604-166444 (2007).
    [CrossRef] [PubMed]
  5. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
    [CrossRef]
  6. 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]
  7. R. A. Soref and B. R. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. 23, 123-129 (1987).
    [CrossRef]
  8. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992).
    [CrossRef]
  9. Ö. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, "All optical switching and continum generation in silicon waveguides," Opt. Express 12, 4094-4102 (2004).
    [CrossRef]
  10. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87, 151112 (2005).
    [CrossRef]
  11. T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, "Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities," Appl. Phys. Lett. 90, 031115 (2007).
    [CrossRef]
  12. Q. Xu and M. Lipson, "Carrier-induced optical bistability in silicon ring resonators," Opt. Lett. 31, 341-343 (2006).
    [CrossRef] [PubMed]
  13. R. K. Jain and M. B. Klien, "Degenerate four-wave mixing near the band gap of semiconductors," Appl. Phys. Lett. 35, 454-456 (1979).
    [CrossRef]
  14. R. K. Jain, "Degenerate four-wave mixing in semiconductors: application to phase conjugation and to picosecond-resolved studies of transient carrier dynamics," Opt. Eng. 21, 199-218 (1982).
  15. T. F. Boggess, K. Bohnert, D. P. Norwood, C. D. Mire, and A. L. Smirl, "Nonlinear refraction in silicon induced by one-micron picosecond pulses," Opt. Commun. 64, 387-392 (1987).
    [CrossRef]
  16. H. J. Eichler, J. Chen, and K. Richter, "Four-wave mixing reflectivity of silicon at 1.06 ?m: Influence of free-carrier absorption," Appl. Phys. B 42, 215-219 (1987).
    [CrossRef]
  17. 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, 760-769 (1990).
    [CrossRef]
  18. K.-H. Lee, W.-R. Cho, J.-H. Park, J.-S. Kim, S.-H. Park, U. Kim, "Measurement of free-carrier nonlinearities in ZnSe based on the Z-scan technique with a nanosecond laser," Opt. Lett. 19, 1116-1118 (1994).
    [PubMed]
  19. H. Yoshida, V. Kmertik, H. Fujita, M. Nakatsuka, T. Yamanaka, and K. Yoshida, "Heavy fluorocarbon liquids for a phase-conjugated stimulated Brillouin scattering mirror," Appl. Opt. 36, 3739-3744 (1997).
    [CrossRef] [PubMed]
  20. V. Kmertik, H. Fiedorowicz, A. A. Andreev, K. J. Witte, H. Daido, H. Fujita, M. Nakatsuka, and T. Yamanaka, "Reliable simulated Brillouin scattering compression of Nd:YAG laser pulses with liquid fluorocarbon for long-time operation at 10 Hz," Appl. Opt. 37, 7085-7090 (1998).
    [CrossRef]
  21. D. Neshev, I. Velchev, W. A. Majewski, W. Hogervorst, and W. Ubachs, "SBS pulse compression to 200 ps in a compact single-cell setup," Appl. Phys. B 68, 671-675 (1999).
    [CrossRef]
  22. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, "Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching," Opt. Lett. 29, 265-267 (2004).
    [CrossRef] [PubMed]
  23. V. G. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggelton, D. Y. Choi, S. Madden, and B. Luther-Davies, "Ultrafast all-optical chalcogenide glass photonic circuits," Opt. Express 15, 9205-9221 (2007).
    [CrossRef] [PubMed]
  24. K. Ogusu, K. Suzuki, and H. Nishio, "Simple and accurate measurement of the absorption coefficient of an absorbing plate by use of the Brewster angle," Opt. Lett. 31, 909-911 (2006).
    [CrossRef] [PubMed]
  25. G. Cocorullo and I. Rendina, "Thermo-optical modulation at 1.5 ?m in silicon etalon," Electron. Lett. 28, 83-85 (1992).
    [CrossRef]
  26. C. H. Lee, P. S. Mak, and A. P. DeFonzo, "Optical control of millimeter-wave propagation in dielectric waveguides," IEEE J. Quantum Electron. 16, 277-288 (1980).
    [CrossRef]
  27. T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," IEEE Photon. Technol. Lett. 15, 36-38 (2003).
    [CrossRef]

Other (27)

R. Soref, "The past, present, and future of silicon photonics," IEEE J. Sel. Top. Quantum Electron. 12, 1678-1687 (2006).
[CrossRef]

M. Lipson, "Guiding, modulating, and emitting light on silicon - Challenges and opportunities," J. Lightwave Technol. 23, 4222-4238 (2005).
[CrossRef]

B. Jalali and S. Fathpour, "Silicon photonics," J. Lightwave Technol. 24, 4600-4615 (2006).
[CrossRef]

Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: Modeling and applications," Opt. Express 15, 16604-166444 (2007).
[CrossRef] [PubMed]

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]

R. A. Soref and B. R. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. 23, 123-129 (1987).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992).
[CrossRef]

Ö. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, "All optical switching and continum generation in silicon waveguides," Opt. Express 12, 4094-4102 (2004).
[CrossRef]

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

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, "Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities," Appl. Phys. Lett. 90, 031115 (2007).
[CrossRef]

Q. Xu and M. Lipson, "Carrier-induced optical bistability in silicon ring resonators," Opt. Lett. 31, 341-343 (2006).
[CrossRef] [PubMed]

R. K. Jain and M. B. Klien, "Degenerate four-wave mixing near the band gap of semiconductors," Appl. Phys. Lett. 35, 454-456 (1979).
[CrossRef]

R. K. Jain, "Degenerate four-wave mixing in semiconductors: application to phase conjugation and to picosecond-resolved studies of transient carrier dynamics," Opt. Eng. 21, 199-218 (1982).

T. F. Boggess, K. Bohnert, D. P. Norwood, C. D. Mire, and A. L. Smirl, "Nonlinear refraction in silicon induced by one-micron picosecond pulses," Opt. Commun. 64, 387-392 (1987).
[CrossRef]

H. J. Eichler, J. Chen, and K. Richter, "Four-wave mixing reflectivity of silicon at 1.06 ?m: Influence of free-carrier absorption," Appl. Phys. B 42, 215-219 (1987).
[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, 760-769 (1990).
[CrossRef]

K.-H. Lee, W.-R. Cho, J.-H. Park, J.-S. Kim, S.-H. Park, U. Kim, "Measurement of free-carrier nonlinearities in ZnSe based on the Z-scan technique with a nanosecond laser," Opt. Lett. 19, 1116-1118 (1994).
[PubMed]

H. Yoshida, V. Kmertik, H. Fujita, M. Nakatsuka, T. Yamanaka, and K. Yoshida, "Heavy fluorocarbon liquids for a phase-conjugated stimulated Brillouin scattering mirror," Appl. Opt. 36, 3739-3744 (1997).
[CrossRef] [PubMed]

V. Kmertik, H. Fiedorowicz, A. A. Andreev, K. J. Witte, H. Daido, H. Fujita, M. Nakatsuka, and T. Yamanaka, "Reliable simulated Brillouin scattering compression of Nd:YAG laser pulses with liquid fluorocarbon for long-time operation at 10 Hz," Appl. Opt. 37, 7085-7090 (1998).
[CrossRef]

D. Neshev, I. Velchev, W. A. Majewski, W. Hogervorst, and W. Ubachs, "SBS pulse compression to 200 ps in a compact single-cell setup," Appl. Phys. B 68, 671-675 (1999).
[CrossRef]

K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, "Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching," Opt. Lett. 29, 265-267 (2004).
[CrossRef] [PubMed]

V. G. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggelton, D. Y. Choi, S. Madden, and B. Luther-Davies, "Ultrafast all-optical chalcogenide glass photonic circuits," Opt. Express 15, 9205-9221 (2007).
[CrossRef] [PubMed]

K. Ogusu, K. Suzuki, and H. Nishio, "Simple and accurate measurement of the absorption coefficient of an absorbing plate by use of the Brewster angle," Opt. Lett. 31, 909-911 (2006).
[CrossRef] [PubMed]

G. Cocorullo and I. Rendina, "Thermo-optical modulation at 1.5 ?m in silicon etalon," Electron. Lett. 28, 83-85 (1992).
[CrossRef]

C. H. Lee, P. S. Mak, and A. P. DeFonzo, "Optical control of millimeter-wave propagation in dielectric waveguides," IEEE J. Quantum Electron. 16, 277-288 (1980).
[CrossRef]

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," IEEE Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

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 (6)

Fig. 1.
Fig. 1.

Schematic diagram of a SBS compressor and a Z-scan experiment.

Fig. 2.
Fig. 2.

(a). Stokes pulse duration t FWHM versus the pump pulse energy. (b) Temporal intensity profiles of the pump and Stokes pulses.

Fig. 3.
Fig. 3.

Typical normalized open- and closed-aperture Z-scan data of crystalline silicon at λ = 1.064 µm with an incident energy of 1 µJ. The incident pulse width is (a) t FWHM = 11.5 ns and (b) t FWHM = 1.6 ns. The solid lines are the best fits based on Eqs. (15) and (12).

Fig. 4.
Fig. 4.

Dependence of n 2eff (<0) and β eff of the incident pulse energy at the pulse width t FWHM = 11.5 ns. The white circles show ΔΦ0≥π.

Fig. 5.
Fig. 5.

Dependence of n 2eff (<0) and β eff of the incident pulse energy at the pulse width t FWHM = 1.6 ns. The white circles show ΔΦ0≥π.

Fig. 6.
Fig. 6.

(a). Dependence of n 2eff (<0) on the incident pulse width t FWHM at an incident energy of 1 µJ. (b)Dependence of β eff on t FWHM. The straight lines are the best fits to extract the coefficients σ r and σ ab.

Equations (19)

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

d Δ ϕ d z = k 0 Δ n = k 0 ( γ I + σ r N ( I ) ) ,
d I d z = ( α + β I + σ ab N ( I ) ) I ,
d N ( t ) d t = N ( t ) τ + α I ( t ) ω ,
I ( t ) = I 0 e x p ( t 2 t 0 2 ) ,
N ( t ) = α I 0 ω · π t 0 2 · exp ( t 0 2 4 τ 2 ) [ 1 + erf ( t t 0 t 0 2 τ ) ] · exp ( t τ ) .
N ( t ) = { α I 0 ω · τ exp ( t 2 t 0 2 ) t 0 > > τ , α I 0 ω · π t 0 2 [ 1 + erf ( t t 0 ) ] τ > > t 0 ,
N ( t ) = β I 0 2 2 ω · π t 0 8 · exp ( t 0 2 8 τ 2 ) [ 1 + erf ( 2 t 0 t t 0 8 τ ) ] · exp ( t τ ) .
N ( t ) = { β I 0 2 2 ω · τ exp ( 2 t 2 t 0 2 ) t 0 > > τ , β I 0 2 2 ω · π t 0 8 [ 1 + erf ( 2 t 0 t ) ] τ > > t 0 ,
Δ Φ 0 ( t ) = k 0 Δ n ( t ) L eff ,
Δ Φ 0 < Φ 0 ( t ) > = k 0 ( γ I 0 2 + σ r α I 0 ω π t 0 2 ) L eff k 0 n 2 eff I 0 2 L eff ,
n 2 eff = { γ + σ r α τ ω t 0 > > τ , γ + σ r α ω π t 0 2 τ > > t 0 ,
T ( z ) = 1 4 ( z z 0 ) Δ Φ 0 ( 1 + z 2 z 0 2 ) ( 9 + z 2 z 0 2 ) ,
T ( z ) < T ( z , t ) > = 1 1 2 < q 0 ( z , t ) > + 1 3 < q 0 ( z , t ) 2 > 1 4 < q 0 ( z , t ) 3 > + . . . . ,
q 0 ( z , t ) = β I ( t ) L eff 1 + z 2 z 0 2 ,
T ( z ) = 1 1 2 < β I ( t ) + σ ab N ( t ) > L eff 1 + z 2 z 0 2 = 1 1 2 ( β 2 + σ ab α ω π t 0 2 ) I 0 L eff 1 + z 2 z 0 2
1 1 2 2 β eff I 0 L eff 1 + z 2 z 0 2 .
β eff = { β + σ ab α τ ω t 0 > > τ , β + σ ab α ω π t 0 2 τ > > t 0 .
n 2 eff = γ + σ r ( α ω π t 0 2 + C β ω π t 0 I 0 4 ) ,
β eff = β + σ ab ( α ω π t 0 2 + β ω π t 0 I 0 4 ) ,

Metrics