Abstract

We propose a near-field eclipsing Z-scan technique for the measurement of nonlinear refraction of optical materials. The technique does not require sample displacement as in previous Z-scan and eclipsing Z-scan experiments but preserves the high sensitivity of the eclipsing Z-scan method and the experimental simplicity of the Z-scan technique. As an example of the feasibility of the new technique, the dye solution’s thermal nonlinear refraction is measured with increased sensitivity in comparison with the Z-scan method.

© 1997 Optical Society of America

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References

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  1. 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]
  2. L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 2121–2123 (1994).
    [CrossRef]
  3. K. H. Lee, W. R. Cho, J. H. Park, J. S. Kim, S. H. Park, and 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).
    [CrossRef] [PubMed]
  4. J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of χ(3) of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543–548 (1994).
    [CrossRef]
  5. 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]
  6. L. Yang, R. Dorsinville, Q. Z. Wang, P. X. Ye, and R. R. Alfano, “Excited-state nonlinearity in polythiophene thin films investigated by the Z-scan technique,” Opt. Lett. 17, 323–325 (1992).
    [CrossRef] [PubMed]
  7. G. R. Kumar and F. A. Rajgara, “Z-scan studies and optical limiting in a mode-locking dye,” Appl. Phys. Lett. 67, 3871–3873 (1995).
    [CrossRef]
  8. K. Y. Tseng, K. S. Wong, and G. K. Wong, “Femtosecond time-resolved Z-scan investigations of optical nonlinearities in ZnSe,” Opt. Lett. 21, 180–182 (1996).
    [CrossRef] [PubMed]
  9. M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z-scan,” Opt. Lett. 17, 258–260 (1992).
    [CrossRef] [PubMed]
  10. H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurement of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
    [CrossRef]
  11. V. P. Kozich, A. Marcano O., F. E. Hernández, and J. A. Castillo, “Dual-beam time-resolved Z-scan in liquids to study heating due to linear and nonlinear light absorption,” Appl. Spectrosc. 48, 1506–1512 (1994).
    [CrossRef]
  12. 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]
  13. S. V. Kershaw, “Analysis of EZ scan measurement technique,” J. Mod. Opt. 42, 1361–1366 (1995).
    [CrossRef]
  14. A. Marcano O., G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
    [CrossRef]
  15. A. Marcano O. and J. A. Castillo, “A new approach for a pump-probe photothermal experiment,” Braz. J. Phys. 22, 25–29 (1992).
  16. A. Marcano O. and G. Da Costa, “Microstructure of the laser-induced thermal lens,” Proc. SPIE 1626, 348–353 (1992).
    [CrossRef]
  17. D. Weaire, B. S. Wherret, D. A. Miller, and D. S. Smith, “Effect of low-power nonlinear refraction on laser beam propagation in InSb,” Opt. Lett. 4, 331–333 (1974).
    [CrossRef]

1996

1995

G. R. Kumar and F. A. Rajgara, “Z-scan studies and optical limiting in a mode-locking dye,” Appl. Phys. Lett. 67, 3871–3873 (1995).
[CrossRef]

S. V. Kershaw, “Analysis of EZ scan measurement technique,” J. Mod. Opt. 42, 1361–1366 (1995).
[CrossRef]

1994

1993

A. Marcano O., G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[CrossRef]

1992

1991

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

1990

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]

1974

Appl. Phys. Lett.

G. R. Kumar and F. A. Rajgara, “Z-scan studies and optical limiting in a mode-locking dye,” Appl. Phys. Lett. 67, 3871–3873 (1995).
[CrossRef]

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

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 2121–2123 (1994).
[CrossRef]

Appl. Spectrosc.

Braz. J. Phys.

A. Marcano O. and J. A. Castillo, “A new approach for a pump-probe photothermal experiment,” Braz. J. Phys. 22, 25–29 (1992).

Chem. Phys.

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of χ(3) of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543–548 (1994).
[CrossRef]

IEEE J. Quantum Electron.

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]

J. Mod. Opt.

S. V. Kershaw, “Analysis of EZ scan measurement technique,” J. Mod. Opt. 42, 1361–1366 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng.

A. Marcano O., G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[CrossRef]

Opt. Lett.

Proc. SPIE

A. Marcano O. and G. Da Costa, “Microstructure of the laser-induced thermal lens,” Proc. SPIE 1626, 348–353 (1992).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Scheme of the DZ-scan experiment showing the relevant calculation parameters: pump light beam (curve a) and probe light beam (curve b) have the confocal distance zop and zob, respectively. The pump- and probe-beam waists are at distances zcp and zcb, respectively. The sample cell S of length Le is at distance z=0. The microdisk D of a radius rd is at position z. After the disk, a filter cancels the pump light and a lens focuses the probe light beam onto the detector.

Fig. 2
Fig. 2

DZ-scan nonlinear signal calculated with Eqs. (2) and (3) and parameters λb=632 nm, λp=530 nm, zob=4 mm, zop=4 mm, rd=80 µm, ΔΦo=-0.1, and zcp=zcb=-4 mm for curve a, zcp=zcb=8 mm for curve b, and zcp=zcb=0 mm for curve c.

Fig. 3
Fig. 3

Schemes for the explanation of the shape of the nonlinear DZ-scan signal when the sample cell is (a) after, (b) before, and (c) at the beam waists. The schemes correspond to the calculations shown by curves a, b, and c in Fig. 2, respectively.

Fig. 4
Fig. 4

Dependence of the nonlinear DZ-scan signal on the phase-shift values. The curves a, b, and c correspond to the situations depicted by curves a, b, and c in Fig. 2, respectively.

Fig. 5
Fig. 5

DZ-scan experimental setup consisting of a pump laser (double-frequency 7-ns Nd:YAG laser working at λp=530 nm), a probe laser (cw He–Ne laser working at λb=632 nm), focusing lenses L1 and L2, beam splitter B, 1-mm-long glass sample cell S containing a 10-µm ethanol solution of Rhodamine 6G, microdisk of radius rd, diffraction grating R, focusing lens L3, filter F for canceling the remaining pump light, and the detector De. To perform a Z-scan experiment with the same setup, one removes the disk and the lens L3 and locates a small aperture A before the detector.

Fig. 6
Fig. 6

Z-scan nonlinear signal of the 0.98-µm ethanol solution of Rhodamine 6G. The continuous line is a theoretical fit to the data with the GDM approximation and the parameters Δϕo =-0.27, λp=530 nm, λb=632.5 nm, zop=3.9 mm, zob =3.8 mm, and zcp=zcb=0.

Fig. 7
Fig. 7

DZ-scan nonlinear signals performed with the same sample and with the same experimental conditions as in Fig. 6. The curve a, b, and c correspond to the situations when the sample cell is after, before, and at the beam waists, respectively. The continuous lines are theoretical fits to the data by Eqs. (2) and (3) with parameters Δϕo=-0.28, λp=530 nm, λb=632.5 nm, zop=4 mm, zob=4 mm, rd=130 µm, and zcp=zcb=-5.3 mm for curve a, Δϕo=-0.28, λp=530 nm, λb=632.5 nm, zop=8 mm, zob=4 mm, rd=70 µm, and zcp=zcb=16 mm for curve b, and Δϕo=-0.28, λp=530 nm, λb=632.5 nm, zop=8 mm, zob=4 mm, rd=70 µm, and zcp=zcb=0 for curve c.

Fig. 8
Fig. 8

Z-scan and DZ-scan nonlinear signals measured at low phase values. The continuous lines are theoretical fits to the data with the parameters Δϕo=-0.06, zop=4 mm, zob=4 mm, rd=70 µm, and zcp=zcb=0.

Equations (15)

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E(z, r)=Eom=0[(-iΔϕ)m/m!](ωom/ωm)×exp[-r2/ωm2-iπr2/(λbRm)+iθm],
Δϕ=Δϕ0/(1+zcp2/zop2),
ωm=ωom(g2+z2/dm2)1/2,g=1+z/R,
R=(zcb2+zob2)/(-zcb),
ωom={[ωob2(1+zcb2/zob2)]-1+2m[ωop2(1+zcp2/zop2)]-1}-1/2,
ωop=λpzop/π,
ωob=λbzob/π,
dm=ωπom2/λb,
Rm=z[1-g/(g2+z2/dm2)]-1,
θm=arctan(z/gdm).
S(z)=[T(z)-T0(z)]/T0(z),
T(z)=|Eo|2/2n=0m=0[(Δϕ)m+n/(m!n!)]×exp(-αmnrd2)cos(ψmn+βmnrd2)×[(g2+z2/dm2)(g2+z2/dn2)×(αmn2+βmn2)]-1/2,
αmn=1/ωm2+1/ωn2,
βmn=πgz(dn2-dm2)/[λb(g2dm2+z2)×(g2dn2+z2)],
ψmn=arctg[gz(dm-dn)/(g2dmdn+z2)]+arctg(βmn/αmn)+(m-n)π/2.

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