Abstract

We demonstrate a theoretical model and the experimental proof of a new method for n2 measurements using single pulses. The advantage of the method is fast measurement, a simple setup, and independence from small nonlinear absorptions and thermal effects. We report on first n2 measurements with the new technique on carbon disulfide, toluene, and a polymer dissolved in toluene to demonstrate the measurement of positive and negative third-order nonlinearities. We achieved a sensitivity of greater than λ/200 phase-front distortion using picosecond Nd:YLF laser pulses. The given theory shows that attainment of higher sensitivities is possible.

© 1997 Optical Society of America

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References

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  1. M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  2. 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]
  3. E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
    [CrossRef]
  4. T. Xia, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
    [CrossRef] [PubMed]
  5. T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.
  6. G. A. Swartzlander, A. E. Kaplan, “Self-deflection of laser beams in a thin nonlinear film,” J. Opt. Soc. Am. B 5, 765–768 (1988).
    [CrossRef]
  7. G. A. Swartzlander, H. Yin, A. E. Kaplan, “Continuous-wave self-deflection effect in sodium vapor,” J. Opt. Soc. Am. B 6, 1317–1325 (1989).
    [CrossRef]
  8. H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
    [CrossRef]
  9. D. Weaire, B. S. Wherrett, D. A. B. Miller, S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4, 331–333 (1979).
    [CrossRef] [PubMed]
  10. A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).
  11. P. P. Ho, R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
    [CrossRef]
  12. M. Terazima, “Ultrafast transient Kerr lens in solution detected by the dual-beam thermal-lens method,” Opt. Lett. 20, 25–27 (1995).
    [CrossRef] [PubMed]
  13. M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color z-scan,” Opt. Lett. 17, 258–260 (1992).
    [CrossRef] [PubMed]

1995 (2)

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

M. Terazima, “Ultrafast transient Kerr lens in solution detected by the dual-beam thermal-lens method,” Opt. Lett. 20, 25–27 (1995).
[CrossRef] [PubMed]

1994 (2)

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

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

1993 (1)

H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[CrossRef]

1992 (1)

1990 (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]

1989 (2)

1988 (1)

1979 (2)

Albrecht, H.-S.

H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[CrossRef]

Alfano, R. R.

P. P. Ho, R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Blau, W.

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

Burbridge, S.

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

Davey, P.

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

DeSalvo, R.

Drury, A.

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

Hagan, D. J.

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

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color z-scan,” Opt. Lett. 17, 258–260 (1992).
[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]

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Heist, P.

H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[CrossRef]

Ho, P. P.

P. P. Ho, R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Kaplan, A. E.

Kleinschmidt, J.

H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[CrossRef]

Lap, D. V.

H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[CrossRef]

Miller, D. A. B.

Page, H.

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

Said, A. A.

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (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, A. A. Said, E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Sheik-Bahae, M.

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

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color z-scan,” Opt. Lett. 17, 258–260 (1992).
[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, A. A. Said, E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Smith, S. D.

Swartzlander, G. A.

Terazima, M.

Van Stryland, E. W.

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

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color z-scan,” Opt. Lett. 17, 258–260 (1992).
[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, A. A. Said, E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Wamsley, C.

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Wang, J.

Wang, Z.

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Weaire, D.

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.

Xia, T.

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

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

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

Yin, H.

Appl. Phys. B (1)

H.-S. Albrecht, P. Heist, J. Kleinschmidt, D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[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]

Int. J. Nonlinear Opt. Phys. (1)

E. W. Van Stryland, M. Sheik-Bahae, T. Xia, C. Wamsley, Z. Wang, A. A. Said, D. J. Hagan, “Z-scan and EZ-scan measurements of optical nonlinearities,” Int. J. Nonlinear Opt. Phys. 3, 489–500 (1994).
[CrossRef]

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

Nonlinear Opt. (1)

A. Drury, P. Davey, S. Burbridge, H. Page, W. Blau, “The synthesis of the narrow-gap, nonlinear, organic polymer poly(tertbutylisothionaphthene),” Nonlinear Opt. 10(1–4), 167–171 (1995).

Opt. Lett. (5)

Phys. Rev. A (1)

P. P. Ho, R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Other (1)

T. Xia, C. Wamsley, Z. Wang, A. A. Said, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “EZ-scan—a method to achieve a sensitivity to induced phase distortions of λ/3000,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 612–614.

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Figures (4)

Fig. 1
Fig. 1

Experimental results of single-pulse measurements with a pulse energy of 5.6 µJ at 1047 nm. The solid curves represent the calculated curves with the on-axis phase shift as the sole fit parameter. PTBITN, poly(tertbutylisothionaphthene).

Fig. 2
Fig. 2

Calculated dependence of ΔI (rmax) on the on-axis phase shift including fifth-order terms of the sum of relation (8) (dotted curve) and a calculation neglecting higher-order terms (solid curve).

Fig. 3
Fig. 3

Experimental setup for single-pulse n2 measurements with the SP method.

Fig. 4
Fig. 4

Dependence of the maximum measured signal Δ I(rmax) on the laser-pulse energy with linear fits (solid curves).

Equations (11)

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EinI0expik2x2qx+y2qy.
Eout=ILI0expiΔΦLEin,
ΔΦz, x, y, zz=n2kIz, x, y, z,Iz, x, y, zz=-αIz, x, y, z-βI2z, x, y, z.
Eout=exp-αL21+βIx, y, zLeffikn2β-12Ein,
Eout=exp-αL2n=0m=1niΔΦ0-2m-1ΔT0m×EinEin*I0nEin,
ΔΦ0=kn2I0Leff
ΔT0=βI0Leff2
EinEin*I0nEinI0expik2x22n+1qx-2nqx*+y22n+1qy-2nqy*
Eoutz=DI0exp-αL2n=0m=1niΔΦ0-2m-1ΔT0m×Qxn0Qyn0QxnDQynD1/2 expik2x2QxnD+y2QynD.
ΔIr=IMx=r-IMy=rIM=0, y=0-IRx=r-IRy=rIRx=0, y=0.
ΔΦ0=-ΔΦ0tI0tdt-I0tdt.

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