Abstract

We report a single-beam, differential z-scan technique with improved sensitivity for the determination of nonlinear absorption and refraction of materials. A sample is scanned in the direction of beam propagation as usual, but, in addition, its longitudinal position is dithered, producing a detector signal proportional to the spatial derivative of only the nonlinear transmission and therefore giving a background-free signal; the nonlinear transmission for any spatial position of the sample can be recovered by simple integration. For both open and closed aperture scans in GaP, we find an improvement in the signal-to-noise ratio of >5× compared with a balanced z-scan setup, but this can be improved with apparatus optimization. Nonlinear phase distortions <λ/1500 are obtained with a 78 MHz, mode-locked Ti:sapphire laser.

© 2007 Optical Society of America

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  1. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
    [CrossRef]
  2. W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
    [CrossRef]
  3. T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, "Eclipsing z-scan measurement of λ/104 wave-front distortion," Opt. Lett. 19, 317-319 (1994).
    [CrossRef] [PubMed]
  4. M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
    [CrossRef]
  5. I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
    [CrossRef]
  6. M. Falconieri, E. Palange, and H. L. Fragnito, "Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique," J. Opt. A 4, 404-407 (2002).
    [CrossRef]
  7. C. R. Mendoça, L. Misoguti, and S. C. Zilio, "Z-scan measurements with Fourier analysis in ton-doped solids," Appl. Phys. Lett. 71, 2094-2096 (1997).
    [CrossRef]
  8. T. Catunda, J. P. Andreeta, and J. C. Castro, "Differential interferometric technique for the measurement of the nonlinear index of refraction of ruby and GdAlO3:Cr+3," Appl. Opt. 25, 2391-2395 (1986).
    [CrossRef] [PubMed]
  9. 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, 1009-1017 (1994).
    [CrossRef]
  10. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, 1996).
  11. W.-P. Zang, J.-G. Tian, Z.-B. Liu, W.-Y. Zhou, F. Song, and C.-P. Zhang, "Analytic solutions to z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption," J. Opt. Soc. Am. B 21, 63-66 (2004).
    [CrossRef]
  12. 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]
  13. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, "High-sensitivity, single-beam N2 measurements," Opt. Lett. 14, 955-957 (1989).
    [CrossRef] [PubMed]
  14. H. Ma, A. S. L. Gomes, and C. B. de Araujo, "Measurements of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
    [CrossRef]

2004 (1)

2002 (1)

M. Falconieri, E. Palange, and H. L. Fragnito, "Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique," J. Opt. A 4, 404-407 (2002).
[CrossRef]

1998 (1)

M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
[CrossRef]

1997 (2)

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

C. R. Mendoça, L. Misoguti, and S. C. Zilio, "Z-scan measurements with Fourier analysis in ton-doped solids," Appl. Phys. Lett. 71, 2094-2096 (1997).
[CrossRef]

1994 (2)

1993 (1)

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

1991 (1)

H. Ma, A. S. L. Gomes, and C. B. de Araujo, "Measurements of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

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]

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

1989 (1)

1986 (1)

Andreeta, J. P.

Bian, S.

M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
[CrossRef]

Blewett, I. J.

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

Castro, J. C.

Catunda, T.

de Araujo, C. B.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, "Measurements of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

Falconieri, M.

M. Falconieri, E. Palange, and H. L. Fragnito, "Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique," J. Opt. A 4, 404-407 (2002).
[CrossRef]

Fragnito, H. L.

M. Falconieri, E. Palange, and H. L. Fragnito, "Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique," J. Opt. A 4, 404-407 (2002).
[CrossRef]

Gomes, A. S. L.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, "Measurements of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

Hagan, D. 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, 1009-1017 (1994).
[CrossRef]

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, "Eclipsing z-scan measurement of λ/104 wave-front distortion," Opt. Lett. 19, 317-319 (1994).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, 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. 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]

Horowicz, R. J.

M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
[CrossRef]

Kar, A. K.

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

Leite, J. R.

M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
[CrossRef]

Liu, Z.-B.

Ma, H.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, "Measurements of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

Martinelli, M.

M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
[CrossRef]

Mendoça, C. R.

C. R. Mendoça, L. Misoguti, and S. C. Zilio, "Z-scan measurements with Fourier analysis in ton-doped solids," Appl. Phys. Lett. 71, 2094-2096 (1997).
[CrossRef]

Misoguti, L.

C. R. Mendoça, L. Misoguti, and S. C. Zilio, "Z-scan measurements with Fourier analysis in ton-doped solids," Appl. Phys. Lett. 71, 2094-2096 (1997).
[CrossRef]

Palange, E.

M. Falconieri, E. Palange, and H. L. Fragnito, "Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique," J. Opt. A 4, 404-407 (2002).
[CrossRef]

Palffy-Muhoray, P.

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

Said, A. A.

Shah, J.

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, 1996).

Sheik-Bahae, M.

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, 1009-1017 (1994).
[CrossRef]

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, "Eclipsing z-scan measurement of λ/104 wave-front distortion," Opt. Lett. 19, 317-319 (1994).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, 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. 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]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, "High-sensitivity, single-beam N2 measurements," Opt. Lett. 14, 955-957 (1989).
[CrossRef] [PubMed]

Song, F.

Stokes, J.

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

Tian, J.-G.

Tookey, A.

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

Van Stryland, E. W.

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, "Eclipsing z-scan measurement of λ/104 wave-front distortion," Opt. Lett. 19, 317-319 (1994).
[CrossRef] [PubMed]

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, 1009-1017 (1994).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, 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. 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]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, "High-sensitivity, single-beam N2 measurements," Opt. Lett. 14, 955-957 (1989).
[CrossRef] [PubMed]

Wang, J.

Wei, T.-H.

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

Wherrett, B. S.

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

Xia, T.

Zang, W.-P.

Zhang, C.-P.

Zhao, W.

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

Zhou, W.-Y.

Zilio, S. C.

C. R. Mendoça, L. Misoguti, and S. C. Zilio, "Z-scan measurements with Fourier analysis in ton-doped solids," Appl. Phys. Lett. 71, 2094-2096 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

M. Martinelli, S. Bian, J. R. Leite, and R. J. Horowicz, "Sensitivity-enhanced reflection z-scan by oblique incidence of a polarized beam," Appl. Phys. Lett. 72, 1427-1429 (1998).
[CrossRef]

C. R. Mendoça, L. Misoguti, and S. C. Zilio, "Z-scan measurements with Fourier analysis in ton-doped solids," Appl. Phys. Lett. 71, 2094-2096 (1997).
[CrossRef]

H. Ma, A. S. L. Gomes, and C. B. de Araujo, "Measurements of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Opt. A (1)

M. Falconieri, E. Palange, and H. L. Fragnito, "Achievement of λ/4000 phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated z-scan technique," J. Opt. A 4, 404-407 (2002).
[CrossRef]

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

Opt. Laser Technol. (1)

I. J. Blewett, J. Stokes, A. Tookey, A. K. Kar, and B. S. Wherrett, "Fastscan z-scan system for determining optical non-linearities in semiconductors," Opt. Laser Technol. 29, 355-358 (1997).
[CrossRef]

Opt. Lett. (2)

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]

Other (1)

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, 1996).

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Figures (3)

Fig. 1
Fig. 1

Differential z-scan experimental setup.

Fig. 2
Fig. 2

Open aperture differential z-scan transmission of GaP. (a) Output from lock-in amplifier. (b) Integrated signal (transmission) as a function of the displacement (circles) and numerical fit (curve) based on Ref. 11.

Fig. 3
Fig. 3

Normalized transmission for closed aperture integrated differential z scan (circles) and conventional z scan (squares). The two experimental traces are displaced by + 1 % and 1 % along the y axis for clarity. The numerical fit (curve) is based on Ref. 11.

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