Abstract

A new technique for measuring third-order susceptibility with a Mach–Zehnder interferometer with a pump–probe system is proposed. The optical setup is combined with a charge-coupled device for image processing. With the proposed method it is possible to resolve the spatial profile of a complex nonlinear variation index with only one laser shot in the nonlinear material. Therefore we can get intensity-resolved information by comparing this profile, pixel per pixel, with that of the incident beam. To verify the validity of the method, we carry out measurements of reference materials illuminated by linearly polarized light. Good agreement is obtained with measurements made by various authors. An advantage of this new technique is that only one laser shot is needed to minimize the risk of damage in fragile nonlinear materials.

© 2001 Optical Society of America

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References

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  1. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23, 2089–2094 (1987).
    [CrossRef]
  2. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
    [CrossRef]
  3. P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index in liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
    [CrossRef]
  4. M. J. Moran, G. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. 11, 259–263 (1975).
    [CrossRef]
  5. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  6. B. M. Patterson, W. R. White, T. A. Robbins, and R. J. Knize, “Linear optical effects in Z-scan measurements of thin films,” Appl. Opt. 37, 1854–1857 (1998).
    [CrossRef]
  7. D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
    [CrossRef]
  8. G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B 13, 1450–1456 (1996).
    [CrossRef]
  9. J. Goodman, Introduction to Fourier Optics, 2nd ed. (Mc-Graw Hill, New York, 1996), Chap. 5, pp. 96–120.
  10. Y. R. Shen, Nonlinear Optics (Wiley, New York, 1984), Chap. 3, pp. 42–52.

1998 (2)

B. M. Patterson, W. R. White, T. A. Robbins, and R. J. Knize, “Linear optical effects in Z-scan measurements of thin films,” Appl. Opt. 37, 1854–1857 (1998).
[CrossRef]

D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
[CrossRef]

1996 (1)

1990 (1)

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

1987 (2)

S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23, 2089–2094 (1987).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
[CrossRef]

1975 (1)

M. J. Moran, G. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. 11, 259–263 (1975).
[CrossRef]

1964 (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index in liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Adair, R.

Boudebs, G.

Bourdin, J. P.

Carman, R. L.

M. J. Moran, G. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. 11, 259–263 (1975).
[CrossRef]

Chase, L. L.

Chis, M.

Friberg, S. R.

S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23, 2089–2094 (1987).
[CrossRef]

Garrido, F.

D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
[CrossRef]

Gonella, F.

D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
[CrossRef]

Hagan, D.

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

Haglund, R. F.

D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
[CrossRef]

Knize, R. J.

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index in liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Moran, M. J.

M. J. Moran, G. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. 11, 259–263 (1975).
[CrossRef]

Osborne, D. H.

D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
[CrossRef]

Patterson, B. M.

Payne, S. A.

Robbins, T. A.

Said, A. A.

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

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index in liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

She, G. Y.

M. J. Moran, G. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. 11, 259–263 (1975).
[CrossRef]

Sheik-Bahae, M.

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

Smith, P. W.

S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23, 2089–2094 (1987).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index in liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Van Stryland, E. W.

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

Wei, T. H.

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

White, W. R.

Appl. Opt. (1)

Appl. Phys. B (1)

D. H. Osborne, R. F. Haglund, F. Gonella, and F. Garrido, “Laser-induced sign reversal of the nonlinear refractive index of Ag nanoclusters in soda-lime glass,” Appl. Phys. B 66, 517–521 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23, 2089–2094 (1987).
[CrossRef]

M. J. Moran, G. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. 11, 259–263 (1975).
[CrossRef]

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

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

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index in liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Other (2)

J. Goodman, Introduction to Fourier Optics, 2nd ed. (Mc-Graw Hill, New York, 1996), Chap. 5, pp. 96–120.

Y. R. Shen, Nonlinear Optics (Wiley, New York, 1984), Chap. 3, pp. 42–52.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: Li, lenses; M’s, mirrors; BS’s, beam splitters; other abbreviations defined in text.

Fig. 2
Fig. 2

Simulation of the local deformation that occurs in the fringe pattern [n2>0; n2=0; (φNL)Max=π/2].

Fig. 3
Fig. 3

Base-10 logarithm power spectrum of the interference pattern shown in Fig. 2. The two symmetrical areas located at the spatial frequency of the cosine function contain the information on the nonlinear dephasing. This figure is shifted by 129 points along the u and v directions.

Fig. 4
Fig. 4

Typical experimental acquisition: the fringe pattern and the pump beam are acquired at the same time with neutral filters of different values.

Fig. 5
Fig. 5

Results of numerical processing corresponding to an experimental acquisition from a 1-mm-thick cell of CS2 (same as shown in Fig. 4). (a) Transmitted numerically filtered pump beam. Note that this beam is twice as large in the x direction as in the y direction. (b) Calculated nonlinear index variation image Δn(x, y). (c) Δn(x, y) versus incident intensity I(x, y). The n2 measurement is the result of calculating the slope of the linear regression line over 1800 pixels in the image. The very broad spread in the data at low Δn is related to the signal-to-noise ratio.

Tables (1)

Tables Icon

Table 1 Results of Measurements with This Method of Classic-Nonlinear Liquid Materialsa

Equations (9)

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Eq(x, y)=Eq(x, y)exp(-j2πϕq),q=1, 2,
E2P(x, y)=E2(x, y)exp(-j2πϕ2)expj 2πλΔn(x, y)L,
Δn(x, y)=n2I(x, y)=(n2+jn2)I(x, y).
T(x, y)=exp-2πλn2I(x, y)Lexpj 2πλn2I(x, y)L.
INL(x, y)=|E1+E2.T|2,
INL(x, y)=I1(x, y)+I2(x, y)T(x, y)2+2T(x, y)×I1I2 cos2πxi+φNL(x, y),
IˆNL(u, v)=[Iˆ1(u, v)+Tˆ(u, v)Tˆ(u, v)Iˆ2(u, v)]+(Tˆ(u, v)FT{[I1(x, y)I2(x, y)]1/2})δ(u-u0, v)+(Tˆ*(u, v)FT{[I1(x, y)I2(x, y)]1/2})δ(u+u0, v),
I1I2.T(x, y)=I1I2T(x, y)exp[jφNL(x, y)],
I(x, y)=Ig(x, y)4.25×10-7τΔs×10-12,

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