Abstract

In ion-doped solids there is a nonlinear refractive index n2 that is due to the polarizability difference Δα between excited and ground states, the so-called population-lens (PL) effect. In addition, the thermal-lens (TL) effect is particularly important in fluoride materials, owing to their low thermal conductivity. We performed time-resolved Z-scan and mode-mismatched TL measurements at λ=488 nm in SrAlF5:Cr+3. In this crystal the PL effect is faster than that of the TL, owing to its relatively short metastable lifetime (93 µs), and therefore we could temporally discriminate between these two contributions to the nonlinear refractive index. For the PL effect we measured n2=(6.6+1.7i)×10-11 cm2/W-1 and calculated Δα=3.1×10-26 cm3 and Δσ=1.7×10-20 cm2. From the TL measurements we obtained the thermal diffusivity D=6.5×10-3 cm2 s-1 and estimated the thermal conductivity K=1.7×10-2 W cm-1 K-1 and ds/dT=-8.5×10-7 K-1.

© 1999 Optical Society of America

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References

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  1. H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
    [CrossRef]
  2. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).
  3. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
    [CrossRef]
  4. T. Catunda and L. A. Cury, “Transverse self-phase modulation in ruby and GdalO3:Cr+3 crystals,” J. Opt. Soc. Am. B 7, 1445–1455 (1990).
    [CrossRef]
  5. L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 1–3 (1994); L. C. Oliveira, T. Catunda, and S. C. Zílio “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys., Part 1 35, 2649–2652 (1996); V. Pilla, P. R. Impinnisi, and T. Catunda, “Measurement of saturation intensity in ion doped solids by transient nonlinear refraction,” Appl. Phys. Lett. APPLAB 70, 817–819 (1997).
    [CrossRef]
  6. M. L. Baesso, J. Shen, and R. D. Snook, “Mode mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3748 (1994).
    [CrossRef]
  7. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982); J. Shen and R. D. Snook, “A radial finite model of thermal lens spectrometry and the influence of sample radius upon the validity of the radial infinite model,” J. Appl. Phys. 73, 5286–5288 (1993).
    [CrossRef] [PubMed]
  8. S. C. Weaver and S. Payne, “Determination of excited-state polarizabilities of Cr+3 doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989); R. Powell and S. Payne, “Dispersion Effects in four-wave mixing measurements of ion in solids,” Opt. Lett. 15, 1233–1235 (1990).
    [CrossRef] [PubMed]
  9. C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
    [CrossRef]
  10. M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of the resonator of a neodymium glass laser due to a change in the polarizability of excited neodymium ions,” Sov. J. Quantum Electron. 8, 275–278 (1978); R. Powell, S. Payne, L. Chase, and G. Wilke, “Four-wave mixing of Nd+3 doped crystals and glasses,” Phys. Rev. B 41, 8593–8602 (1990).
    [CrossRef]
  11. U. Hömmerich, H. Eilers, E. Strauss, and W. N. Yen, “Optically induced lensing effects in Nd+3-doped laser glass measured by photothermal beam-deflection spectroscopy,” Opt. Lett. 17, 213–214 (1992).
    [CrossRef]
  12. T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
    [CrossRef]
  13. B. W. Woods, S. Payne, J. E. Marion, R. S. Hughes, and L. E. Davies, “Thermomechanical and thermo-optical properties of LiCaAlF6:Cr+3 laser material,” J. Opt. Soc. Am. B 8, 970–977 (1991).
    [CrossRef]
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    [CrossRef]
  15. M. Stalder, M. Bass, and B. H. Chai, “Thermal quenching of fluorescence in chromium-doped fluoride laser crystals,” J. Opt. Soc. Am. B 9, 2271–2273 (1992).
    [CrossRef]

1997 (2)

C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
[CrossRef]

T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
[CrossRef]

1996 (1)

1994 (1)

M. L. Baesso, J. Shen, and R. D. Snook, “Mode mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3748 (1994).
[CrossRef]

1992 (2)

1991 (1)

1990 (2)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

T. Catunda and L. A. Cury, “Transverse self-phase modulation in ruby and GdalO3:Cr+3 crystals,” J. Opt. Soc. Am. B 7, 1445–1455 (1990).
[CrossRef]

Aegerter, M.

T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
[CrossRef]

Baesso, M. L.

T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
[CrossRef]

M. L. Baesso, J. Shen, and R. D. Snook, “Mode mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3748 (1994).
[CrossRef]

Bass, M.

Catunda, T.

T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
[CrossRef]

T. Catunda and L. A. Cury, “Transverse self-phase modulation in ruby and GdalO3:Cr+3 crystals,” J. Opt. Soc. Am. B 7, 1445–1455 (1990).
[CrossRef]

Chai, B. H.

Costa, B. J.

C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
[CrossRef]

Cury, L. A.

Davies, L. E.

Eilers, H.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

Hömmerich, U.

Hughes, R. S.

Jenssen, H. P.

Lai, S. T.

Marion, J. E.

Mendonça, C. R.

C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
[CrossRef]

Messaddeq, Y.

C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
[CrossRef]

T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
[CrossRef]

Payne, S.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

Shen, J.

M. L. Baesso, J. Shen, and R. D. Snook, “Mode mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3748 (1994).
[CrossRef]

Snook, R. D.

M. L. Baesso, J. Shen, and R. D. Snook, “Mode mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3748 (1994).
[CrossRef]

Stalder, M.

Strauss, E.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

Woods, B. W.

Yen, W. N.

Zilio, S. C.

C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–768 (1990).
[CrossRef]

J. Appl. Phys. (1)

M. L. Baesso, J. Shen, and R. D. Snook, “Mode mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3748 (1994).
[CrossRef]

J. Non-Cryst. Solids (1)

T. Catunda, M. L. Baesso, Y. Messaddeq, and M. Aegerter, “Measurement of the complex nonlinear refractive index of Er and Nd doped glasses,” J. Non-Cryst. Solids 213/214, 225–230 (1997).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Lett. (1)

Phys. Rev. B (1)

C. R. Mendonça, B. J. Costa, Y. Messaddeq, and S. C. Zilio, “Optical properties of chromium-doped fluoroindate glasses,” Phys. Rev. B 56, 2483–2487 (1997).
[CrossRef]

Other (6)

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of the resonator of a neodymium glass laser due to a change in the polarizability of excited neodymium ions,” Sov. J. Quantum Electron. 8, 275–278 (1978); R. Powell, S. Payne, L. Chase, and G. Wilke, “Four-wave mixing of Nd+3 doped crystals and glasses,” Phys. Rev. B 41, 8593–8602 (1990).
[CrossRef]

S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982); J. Shen and R. D. Snook, “A radial finite model of thermal lens spectrometry and the influence of sample radius upon the validity of the radial infinite model,” J. Appl. Phys. 73, 5286–5288 (1993).
[CrossRef] [PubMed]

S. C. Weaver and S. Payne, “Determination of excited-state polarizabilities of Cr+3 doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989); R. Powell and S. Payne, “Dispersion Effects in four-wave mixing measurements of ion in solids,” Opt. Lett. 15, 1233–1235 (1990).
[CrossRef] [PubMed]

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 1–3 (1994); L. C. Oliveira, T. Catunda, and S. C. Zílio “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys., Part 1 35, 2649–2652 (1996); V. Pilla, P. R. Impinnisi, and T. Catunda, “Measurement of saturation intensity in ion doped solids by transient nonlinear refraction,” Appl. Phys. Lett. APPLAB 70, 817–819 (1997).
[CrossRef]

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
[CrossRef]

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).

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Figures (5)

Fig. 1
Fig. 1

Normalized transmittance obtained in a SrAlF5:Cr+3 sample for laser power (P=227 mW) and chopper frequency (f=822 Hz). (a) Open- and closed-aperture data represented by S1=100% (circles) and S2=50% (squares), respectively. (b) Division curve S2/S1 (circles) with the theoretical fit.

Fig. 2
Fig. 2

Signal time dependence with the SrAlF5:Cr+3 sample at valley position (z=-0.85z0), with laser power P=335 mW and chopper frequency f=822 Hz. (a) Open aperture S1=100% (open circles) transmittance and the iris transmittance S2=50% aperture (squares). (b) Ratio S2/S1 (filled circles). Curves, single exponential decays with τ=80 µs for open circles and τ=67 µs for filled circles.

Fig. 3
Fig. 3

Normalized transmittance obtained in a SrAlF5:Cr+3 sample for laser power (P=175 mW) and chopper frequency (f=186 Hz), where S1=100% (open circles) and S2=50% (filled circles). The theoretical fit with equation LT gives z0=(2.3±0.05) mm.

Fig. 4
Fig. 4

Schematic diagram of the time-resolved thermal lens apparatus with an Ar+–ion laser (λ=488 nm) as excitation beam and a He–Ne laser (λ=633 nm) as probe beam. M is mirror, L is lens, F is neutral density filter, and Ph is photodiode detector.

Fig. 5
Fig. 5

Time development of the probe signal in a SrAlF5:Cr+3 sample for laser power (P=600 mW). With the theoretical fit we obtain θ=-0.089 rad and tc=1.6 ms, which was used to calculate the thermal diffusitivity (D=6.5×10-3 cm2 s-1), with w0=6.5×10-3 cm.

Equations (12)

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Nex(t)=N0 [1-exp(-t/τ)]I/Is(1+I/Is),
τ-1=τ0-1(1+I/Is),
Δϕ=2πλΔ(nL),
n2=(2π/n0)fL2N0Δα/Is,
n2=(λ/4π)N0Δσ/Is,
Δϕp=(2π/λ)n2I0Leff,
θ=-PALKλφ dsdT,
dsdT=n0-1L0LTT0+nTT0,
dsdT=(n0-1)(1+ν)γ+dndT.
tc=w2/4D,
Δϕth=-3.2PALKλφ dsdT.
ΔϕpΔϕth=7.85λexcφw02chfL2τ0Δαn0Kds/dT.

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