Abstract

We report a systematic investigation of both three-photon absorption (3PA) spectra and wavelength dispersions of Kerr-type nonlinear refraction in wide-gap semiconductors. The Z-scan measurements are recorded for both ZnO and ZnS with femtosecond laser pulses. While the wavelength dispersions of the Kerr nonlinearity are in agreement with a two-band model, the wavelength dependences of the 3PA are found to be given by (3E photon/Eg -1)5/2(3E photon/Eg )-9. We also evaluate higher-order nonlinear optical effects including the fifth-order instantaneous nonlinear refraction associated with virtual three-photon transitions, and effectively seventh-order nonlinear processes induced by three-photon-excited free charge carriers. These higher-order nonlinear effects are insignificant with laser excitation irradiances up to 40 GW/cm2. Both pump-probe measurements and three-photon figures of merits demonstrate that ZnO and ZnS should be a promising candidate for optical switching applications at telecommunication wavelengths.

© 2005 Optical Society of America

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  1. U. Ozgur, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Dogan, V. Avrutin, S.-J. Cho, and H. Morkoc, �??A comprehensive review of ZnO materials and devices,�?? J. Appl. Phys. 98, 041301 (2005).
    [CrossRef]
  2. D. Noda, K. Hagiwara, T. Yamamoto, and S. Okamoto, �??Electron emission properties of ZnS-based thin-film cold cathode for field emission display,�?? Jpn. J. Appl. Phys. 44 4108-4111 (2005).
    [CrossRef]
  3. L. X. Shao, K. H. Chang, and H. L. Hwang, �??Zinc sulfide thin films deposited by RF reactive sputtering for photovoltaic applications,�?? Appl. Surf. Sci. 212, 305-310 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. J. C. Johnson, K. P. Knutsen, H. Q. Yan, M. Law, Y. F. Zhang, P. D. Yang, and R. J. Saykally, �??Ultrafast carrier dynamics in single ZnO nanowire and nanoribbon lasers,�?? Nano Lett. 4, 197-204 (2004).
    [CrossRef]
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    [CrossRef]
  10. J.-H. Lin, Y.-J. Chen, H.-Y. Lin, and W.-F. Hsieh, �??Two-photon resonance assisted huge nonlinear refraction and absorption in ZnO thin films,�?? J. Appl. Phys. 97, 033526 (2005).
    [CrossRef]
  11. A. Miller, K. R. Welford, and B. Baino, Nonlinear Optical Materials for Applications in Information Technology, (Kluwer, Dordrecht, 1995).
  12. A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, �??Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,�?? Appl. Phys. Lett. 61, 147-149 (1992).
    [CrossRef]
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    [CrossRef]
  15. A. Major, F. Yoshino, J. S. Aitchison, P. W. E. Smith, E. Sorokin, and I. T. Sorokina, �??Ultrafast nonresonant third-order optical nonlinearities in ZnSe for photonic switching at telecom wavelengths,�?? Appl. Phys. Lett. 85, 4606-4608 (2004).
    [CrossRef]
  16. J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, �??Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,�?? Appl. Phys. Lett. 84, 4472-4474 (2004).
    [CrossRef]
  17. I. M. Catalano, A. Cingolani, and A. Minafra, �??Multiphoton impurity luminescence in zinc sulphide,�?? Opt. Commun. 7, 270-271 (1973).
    [CrossRef]
  18. V. Pacebutas, A. Krotkus, T. Suski, P. Perlin, and M. Leszczynski, �??Photoconductive Z-scan measurement of multiphoton absoption in GaN,�?? J. Appl. Phys. 92, 6930-6932 (2002).
    [CrossRef]
  19. H. S. Brandi and C. B. de Araujo, �??Multiphoton absorption coefficients in solids: a universal curve,�?? J. Phys. C: Solid State Phys. 16, 5929-5936 (1983).
    [CrossRef]
  20. 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]
  21. 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]
  22. G. H. Ma, L. J. Guo, J. Mi, Y. Liu, S. X. Qian, D. C. Pan, and Y. Huang, �??Femtosecond nonlinear optical response of metallophthalocyanine films,�?? Solid State Commun. 118, 633-638 (2001).
    [CrossRef]
  23. R. L. Sutherland with contributions by D. G. McLean and S. Kirkpatrick, Handbook of Nonlinear Optics, Second Edition, Revised and Expanded (New York, NY: Marcel Dekker, 2003).
    [CrossRef]
  24. K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, �??Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,�?? Appl. Phys. Lett. 79, 1939-1941 (2001).
    [CrossRef]
  25. B. S. Wherrett, �??Scaling rules for multiphoton interband absorption in semiconductors,�?? J. Opt. Soc. Am B 1, 67-72 (1984).
    [CrossRef]
  26. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, �??Dispersion of bound electronic nonlinear refraction in solids,�?? IEEE J. Quantum Electron. 27, 1296-1309 (1991).
    [CrossRef]
  27. M. Sheik-Bahae, J. Wang, E. and W. Van Stryland, �??Nondegenerate optical Kerr effect in semiconductors,�?? IEEE J. Quantum Electron. 30, 249-255 (1994).
    [CrossRef]
  28. 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]

Appl. Phys. Lett. (7)

T. D. Krauss and F. W. Wise, �??Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,�?? Appl. Phys. Lett. 65, 1739-1741 (1994).
[CrossRef]

C. K. Sun, S. Z. Sun, K. H. Lin, K. Y. J. Zhang, H. L. Liu, S. C. Liu, and J. J. Wu, �??Ultrafast carrier dynamics in ZnO nanorods,�?? Appl. Phys. Lett. 87, 023106 (2005).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, �??Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,�?? Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Ai-hemyari, J. S. Aitchison, and C. N. Ironside, �??Limitation of three-photon absorption on the usual spectral range for nonlinear optics in AlGaAs below half band gap,�?? Appl. Phys. Lett. 65, 147-149 (1994).
[CrossRef]

A. Major, F. Yoshino, J. S. Aitchison, P. W. E. Smith, E. Sorokin, and I. T. Sorokina, �??Ultrafast nonresonant third-order optical nonlinearities in ZnSe for photonic switching at telecom wavelengths,�?? Appl. Phys. Lett. 85, 4606-4608 (2004).
[CrossRef]

J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, �??Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,�?? Appl. Phys. Lett. 84, 4472-4474 (2004).
[CrossRef]

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, �??Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,�?? Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

Appl. Surf. Sci. (1)

L. X. Shao, K. H. Chang, and H. L. Hwang, �??Zinc sulfide thin films deposited by RF reactive sputtering for photovoltaic applications,�?? Appl. Surf. Sci. 212, 305-310 (2003).
[CrossRef]

IEEE J. Quantum Electron. (3)

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]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, �??Dispersion of bound electronic nonlinear refraction in solids,�?? IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

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

J. Appl. Phys. (3)

V. Pacebutas, A. Krotkus, T. Suski, P. Perlin, and M. Leszczynski, �??Photoconductive Z-scan measurement of multiphoton absoption in GaN,�?? J. Appl. Phys. 92, 6930-6932 (2002).
[CrossRef]

U. Ozgur, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Dogan, V. Avrutin, S.-J. Cho, and H. Morkoc, �??A comprehensive review of ZnO materials and devices,�?? J. Appl. Phys. 98, 041301 (2005).
[CrossRef]

J.-H. Lin, Y.-J. Chen, H.-Y. Lin, and W.-F. Hsieh, �??Two-photon resonance assisted huge nonlinear refraction and absorption in ZnO thin films,�?? J. Appl. Phys. 97, 033526 (2005).
[CrossRef]

J. Opt. Soc. Am B (1)

B. S. Wherrett, �??Scaling rules for multiphoton interband absorption in semiconductors,�?? J. Opt. Soc. Am B 1, 67-72 (1984).
[CrossRef]

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

J. Phys. C: Solid State Phys. (1)

H. S. Brandi and C. B. de Araujo, �??Multiphoton absorption coefficients in solids: a universal curve,�?? J. Phys. C: Solid State Phys. 16, 5929-5936 (1983).
[CrossRef]

Jpn. J. Appl. Phys. (1)

D. Noda, K. Hagiwara, T. Yamamoto, and S. Okamoto, �??Electron emission properties of ZnS-based thin-film cold cathode for field emission display,�?? Jpn. J. Appl. Phys. 44 4108-4111 (2005).
[CrossRef]

Nano Lett. (1)

J. C. Johnson, K. P. Knutsen, H. Q. Yan, M. Law, Y. F. Zhang, P. D. Yang, and R. J. Saykally, �??Ultrafast carrier dynamics in single ZnO nanowire and nanoribbon lasers,�?? Nano Lett. 4, 197-204 (2004).
[CrossRef]

Opt. Commun. (1)

I. M. Catalano, A. Cingolani, and A. Minafra, �??Multiphoton impurity luminescence in zinc sulphide,�?? Opt. Commun. 7, 270-271 (1973).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

R. Adair, L. L. Chase, and S. A. Payne, �??Nonlinear refractive index of optical crystals,�?? Phys. Rev. B 39, 3337-3350 (1989).
[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, 96-99 (1990).
[CrossRef] [PubMed]

Phys. Stat. Sol. (b) (1)

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, �??ZnS-based photonic crystals,�?? Phys. Stat. Sol. (b) 229, 949-960 (2002).
[CrossRef]

Solid State Commun. (1)

G. H. Ma, L. J. Guo, J. Mi, Y. Liu, S. X. Qian, D. C. Pan, and Y. Huang, �??Femtosecond nonlinear optical response of metallophthalocyanine films,�?? Solid State Commun. 118, 633-638 (2001).
[CrossRef]

Other (2)

R. L. Sutherland with contributions by D. G. McLean and S. Kirkpatrick, Handbook of Nonlinear Optics, Second Edition, Revised and Expanded (New York, NY: Marcel Dekker, 2003).
[CrossRef]

A. Miller, K. R. Welford, and B. Baino, Nonlinear Optical Materials for Applications in Information Technology, (Kluwer, Dordrecht, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

(a) OA Z-scans measured with different excitation irradiances at a wavelength of 780 nm and a pulse repetition rate of 90 MHz. The solid and dashed lines are the fitting curves by employing the Z-scan theory, described in the text, on 3PA and 2PA respectively. (b) Plots of Ln(1-T OA) vs. Ln(I 0) at different wavelengths, the solid lines are the examples of the linear fit at 740 nm with a slope of s = 0.86 and at 840 nm with a slope of s = 1.96.

Fig. 2.
Fig. 2.

3PA coefficients plotted as a function of E photon/Eg , where E photon is the photon energy and Eg is the band-gap energy. The solid stars and squares are the experimental data, while the solid and dashed lines are calculated from the theory of Brandi and de Araujo [19] and the theory of Wherrett [25], respectively. For comparison, the experimental result (the empty square) of Catalano et al. is also displayed [17].

Fig. 3.
Fig. 3.

(a) OA Z-scans and (b) CA Z-scans divided by OA Z-scans measured with 1-kHz repetition rate laser pulses at various excitation irradiances. The inset in (a) and (b) shows the irradiance dependence of the 3PA coefficient and the irradiance dependence of the n 2 value, respectively.

Fig. 4.
Fig. 4.

(a) OA Z-scan, CA Z-scan and CA Z-scan divided by OA Z-scan; and (b) Kerr-type nonlinear refraction plotted as a function of E photon/Eg . The solid scatters are the experimental data, while the solid lines are calculated from the theory of Sheik-Bahae et al. [26]. For comparison, the experimental results of Adair et al. (the empty triangles) [5], Zhang et al. (the empty square) [6], and Krauss et al. (the empty circles) [7], are also displayed.

Fig. 5.
Fig. 5.

Calculated nonlinear refraction n 4 plotted against E photon/Eg , for both ZnO (the dashed line) and ZnS (the solid line).

Fig. 6.
Fig. 6.

Calculated nonlinear refraction changes (n 2 I, n 4 I 2, σ r N e-h) vs. the irradiance for (a) ZnO and (b) ZnS; and calculated changes in nonlinear absorption (α 3 I 2, σ a N e-h) vs. the irradiance for (c) ZnO and (d) ZnS. Herein, wavelength is 780 nm, n 2 is 1.0 × 10-5 cm2/GW (0.69 × 10-5 cm2/GW), n 4 is -1.4 × 10-26 cm4/W2 (3.1 × 10-27 cm4/W2), α 3 is 0.016 cm3/GW2 (0.0021 cm3/GW2) for ZnO (ZnS) crystal, and α r = -1.1×10-21 cm3 and σ a = 6.5×10-18 cm2 are assumed for both ZnO and ZnS crystals [6].

Fig. 7.
Fig. 7.

Normalized OKE signal (the solid squares for ZnO) and pump-probe signals (the solid stars for ZnO and the solid circles for ZnS) measured at a wavelength of 780 nm as a function of the delay time. The experiment data were measured under the same excitation irradiance (~ 9.0 GW/cm2) with 1-kHz pulse repetition rate. The dashed line and solid lines are the 2PA and 3PA intensity autocorrelation functions of the laser pulses, respectively.

Tables (1)

Tables Icon

Table 1. Measured 3PA or 2PA coefficient, Kerr-type refractive nonlinearity, and calculated nonlinear FOM for ZnO and ZnS. The relative errors are estimated as ±20%

Equations (12)

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

d Δ ϕ dz = k m = 2 n 2 m 2 I m 1 + r N e h
dI dz = ( α 0 + m = 2 α m I m 1 + σ a N e h ) I
T OA ( z ) = 1 π 1 2 q 0 ln [ 1 + q 0 exp ( x 2 ) ] dx
T OA ( z ) = 1 π 1 2 p 0 ln { [ 1 + p 0 2 exp ( 2 x 2 ) ] 1 2 + p 0 exp ( x 2 ) } dx
T OA = m = 0 ( 1 ) m q 0 m ( m + 1 ) 3 2
T OA = m = 1 ( 1 ) m 1 p 0 2 m 2 ( 2 m 1 ) ! ( 2 m 1 ) 1 2
T OA = 1 α 2 I 0 L eff 2 3 2
T OA = 1 α 3 I 0 2 L eff 3 3 2
α 3 = 3 10 2 1 2 8 π 2 ( e 2 ħc ) 3 ħ 2 P 3 n 0 3 E g 7 ( 3 E photon E g 1 ) 1 2 ( 3 E photon E g ) 9
α 3 = 2 9 2 3 10 π 2 5 ( e 2 ħc ) 3 ħ 2 S 3 ( 3 E photon E g 1 ) 5 2 ( 3 E photon E g ) 9
n 4 ω 1 ω 2 ω 3 = c π 0 α 3 ( Ω ; ω 2 , ω 3 ) Ω 2 ω 1 2 d Ω
dN e h dt = α 3 I 3 3 ħω N e h τ

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