Abstract

Single-gate boxcar-integrator time-domain photothermal radiometry (PTR) is proposed as a noncontact remote technique with a high signal-to-noise ratio that can evaluate the optical quality of the surface in a solid-state laser-gain medium such as Ti:sapphire. It was found that immediately after the boxcar-averaged laser-pulse cutoff, the PTR signal is dominated by the laser metastable-level transition lifetime. A PTR theoretical model was formulated to account for this effect and to deconvolute its contribution to the signal from surface absorption of the laser radiation. With the theoretical model, the surface contribution to experimental boxcar PTR signals was deconvoluted and the surface quality was quantified in terms of the surface nonradiative energy generation rate, as the percentage of the input optical power that is converted to heat.

© 1998 Optical Society of America

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References

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  1. W. Koechner, Solid State Laser Engineering, 3rd ed. (Springer-Verlag, New York, 1992).
  2. J. F. Pinto, L. Esterowitz, G. H. Rosenblatt, M. Kokta, and D. Peressini, “Improved Ti:sapphire laser performance with new high figure of merit crystals,” IEEE J. Quantum Electron. 30, 2612–2616 (1994).
    [CrossRef]
  3. N. Bloembergen, “Role of cracks, pores, and absorbing inclusions on laser induced damage threshold at surfaces of transparent dielectrics,” Appl. Opt. 12, 661–664 (1973).
    [CrossRef] [PubMed]
  4. W. Lowdermilk and D. Milam, “Laser-induced surface and coating damage,” IEEE J. Quantum Electron. 17, 1888–1903 (1981).
    [CrossRef]
  5. P. E. Nordal and S. O. Kanstad, “New developments in photothermal radiometry,” Infrared Phys. 25, 295–304 (1985).
    [CrossRef]
  6. A. C. Tam, “Pulsed photothermal radiometry for noncontact spectroscopy, material testing and inspection measurements,” Infrared Phys. 25, 305–313 (1985).
    [CrossRef]
  7. W. P. Leung and A. C. Tam, “Techniques of flash radiometry,” J. Appl. Phys. 56, 153–161 (1984).
    [CrossRef]
  8. R. D. Tom, E. P. O’Hara, and D. Benin, “A generalized model of photothermal radiometry,” J. Appl. Phys. 53, 5392–5400 (1982).
    [CrossRef]
  9. R. Santos and L. C. M. Miranda, “Theory of the photothermal radiometry with solids,” J. Appl. Phys. 52, 4194–4198 (1981).
    [CrossRef]
  10. A. Mandelis and J. Vanniasinkam, “Theory of nonradiative decay dynamics in solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
    [CrossRef]
  11. A. Mandelis, “Signal-to-noise ratio in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency, time, and hybrid (rate window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
    [CrossRef]
  12. J. Vanniasinkam, M. Munidasa, A. Othonos, M. Kokta, and A. Mandelis, “Diagnostics of nonradiative defects in the bulk and surface of brewster-cut Ti:sapphire laser materials using photothermal radiometry,” IEEE J. Quantum Electron. 33, 2301–2310 (1997).
    [CrossRef]
  13. B. F. Gachter and J. A. Koningstein, “Zero phonon transitions and interacting Jahn-Teller phonon energies from the fluorescence spectrum of Ti:sapphire,” J. Chem. Phys. 60, 2003–2006 (1974).
    [CrossRef]
  14. J. Vanniasinkam, A. Mandelis, S. Buddhudu, and M. Kokta, “Photopyroelectric deconvolution of bulk and surface optical absorption and nonradiative energy conversion efficiency spectra in Ti:sapphire crystals,” J. Appl. Phys. 75, 8090–8097 (1994).
    [CrossRef]
  15. A. Mandelis, J. Vanniasinkam, S. Buddhudu, A. Othonos, and M. Kokta, “Absolute nonradiative energy-conversion-efficiency spectra in Ti:sapphire crystals measured by noncontact quadrature photopyroelectric spectroscopy,” Phys. Rev. B 48, 6808–6821 (1993).
    [CrossRef]
  16. P. A. Schultz and S. R. Henion, “Liquid-nitrogen-cooled Ti:sapphire laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
    [CrossRef]

1997

J. Vanniasinkam, M. Munidasa, A. Othonos, M. Kokta, and A. Mandelis, “Diagnostics of nonradiative defects in the bulk and surface of brewster-cut Ti:sapphire laser materials using photothermal radiometry,” IEEE J. Quantum Electron. 33, 2301–2310 (1997).
[CrossRef]

1996

A. Mandelis and J. Vanniasinkam, “Theory of nonradiative decay dynamics in solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
[CrossRef]

1994

A. Mandelis, “Signal-to-noise ratio in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency, time, and hybrid (rate window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
[CrossRef]

J. F. Pinto, L. Esterowitz, G. H. Rosenblatt, M. Kokta, and D. Peressini, “Improved Ti:sapphire laser performance with new high figure of merit crystals,” IEEE J. Quantum Electron. 30, 2612–2616 (1994).
[CrossRef]

J. Vanniasinkam, A. Mandelis, S. Buddhudu, and M. Kokta, “Photopyroelectric deconvolution of bulk and surface optical absorption and nonradiative energy conversion efficiency spectra in Ti:sapphire crystals,” J. Appl. Phys. 75, 8090–8097 (1994).
[CrossRef]

1993

A. Mandelis, J. Vanniasinkam, S. Buddhudu, A. Othonos, and M. Kokta, “Absolute nonradiative energy-conversion-efficiency spectra in Ti:sapphire crystals measured by noncontact quadrature photopyroelectric spectroscopy,” Phys. Rev. B 48, 6808–6821 (1993).
[CrossRef]

1991

P. A. Schultz and S. R. Henion, “Liquid-nitrogen-cooled Ti:sapphire laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
[CrossRef]

1985

P. E. Nordal and S. O. Kanstad, “New developments in photothermal radiometry,” Infrared Phys. 25, 295–304 (1985).
[CrossRef]

A. C. Tam, “Pulsed photothermal radiometry for noncontact spectroscopy, material testing and inspection measurements,” Infrared Phys. 25, 305–313 (1985).
[CrossRef]

1984

W. P. Leung and A. C. Tam, “Techniques of flash radiometry,” J. Appl. Phys. 56, 153–161 (1984).
[CrossRef]

1982

R. D. Tom, E. P. O’Hara, and D. Benin, “A generalized model of photothermal radiometry,” J. Appl. Phys. 53, 5392–5400 (1982).
[CrossRef]

1981

R. Santos and L. C. M. Miranda, “Theory of the photothermal radiometry with solids,” J. Appl. Phys. 52, 4194–4198 (1981).
[CrossRef]

W. Lowdermilk and D. Milam, “Laser-induced surface and coating damage,” IEEE J. Quantum Electron. 17, 1888–1903 (1981).
[CrossRef]

1974

B. F. Gachter and J. A. Koningstein, “Zero phonon transitions and interacting Jahn-Teller phonon energies from the fluorescence spectrum of Ti:sapphire,” J. Chem. Phys. 60, 2003–2006 (1974).
[CrossRef]

1973

Appl. Opt.

IEEE J. Quantum Electron.

W. Lowdermilk and D. Milam, “Laser-induced surface and coating damage,” IEEE J. Quantum Electron. 17, 1888–1903 (1981).
[CrossRef]

J. F. Pinto, L. Esterowitz, G. H. Rosenblatt, M. Kokta, and D. Peressini, “Improved Ti:sapphire laser performance with new high figure of merit crystals,” IEEE J. Quantum Electron. 30, 2612–2616 (1994).
[CrossRef]

J. Vanniasinkam, M. Munidasa, A. Othonos, M. Kokta, and A. Mandelis, “Diagnostics of nonradiative defects in the bulk and surface of brewster-cut Ti:sapphire laser materials using photothermal radiometry,” IEEE J. Quantum Electron. 33, 2301–2310 (1997).
[CrossRef]

P. A. Schultz and S. R. Henion, “Liquid-nitrogen-cooled Ti:sapphire laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
[CrossRef]

Infrared Phys.

P. E. Nordal and S. O. Kanstad, “New developments in photothermal radiometry,” Infrared Phys. 25, 295–304 (1985).
[CrossRef]

A. C. Tam, “Pulsed photothermal radiometry for noncontact spectroscopy, material testing and inspection measurements,” Infrared Phys. 25, 305–313 (1985).
[CrossRef]

J. Appl. Phys.

W. P. Leung and A. C. Tam, “Techniques of flash radiometry,” J. Appl. Phys. 56, 153–161 (1984).
[CrossRef]

R. D. Tom, E. P. O’Hara, and D. Benin, “A generalized model of photothermal radiometry,” J. Appl. Phys. 53, 5392–5400 (1982).
[CrossRef]

R. Santos and L. C. M. Miranda, “Theory of the photothermal radiometry with solids,” J. Appl. Phys. 52, 4194–4198 (1981).
[CrossRef]

A. Mandelis and J. Vanniasinkam, “Theory of nonradiative decay dynamics in solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
[CrossRef]

J. Vanniasinkam, A. Mandelis, S. Buddhudu, and M. Kokta, “Photopyroelectric deconvolution of bulk and surface optical absorption and nonradiative energy conversion efficiency spectra in Ti:sapphire crystals,” J. Appl. Phys. 75, 8090–8097 (1994).
[CrossRef]

J. Chem. Phys.

B. F. Gachter and J. A. Koningstein, “Zero phonon transitions and interacting Jahn-Teller phonon energies from the fluorescence spectrum of Ti:sapphire,” J. Chem. Phys. 60, 2003–2006 (1974).
[CrossRef]

Phys. Rev. B

A. Mandelis, J. Vanniasinkam, S. Buddhudu, A. Othonos, and M. Kokta, “Absolute nonradiative energy-conversion-efficiency spectra in Ti:sapphire crystals measured by noncontact quadrature photopyroelectric spectroscopy,” Phys. Rev. B 48, 6808–6821 (1993).
[CrossRef]

Rev. Sci. Instrum.

A. Mandelis, “Signal-to-noise ratio in lock-in amplifier synchronous detection: a generalized communications systems approach with applications to frequency, time, and hybrid (rate window) photothermal measurements,” Rev. Sci. Instrum. 65, 3309–3323 (1994).
[CrossRef]

Other

W. Koechner, Solid State Laser Engineering, 3rd ed. (Springer-Verlag, New York, 1992).

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Figures (8)

Fig. 1
Fig. 1

Experimental layout of a photothermal radiometric-detection system.

Fig. 2
Fig. 2

Three regions of thermal emission: The transient IR-radiation emission signal (normalized to its value at pulse cutoff) is shown in three distinct regions whose profiles are governed by direct IR emission (region I), surface-heat generation (region II), and bulk-heat generation (region III).

Fig. 3
Fig. 3

Comparison of the radiation-emission transient from a laser material in response to argon-ion laser excitation and Nd:YAG laser excitation. The early-time fast decay seen with argon-ion laser excitation in the 0–10-μs range is not present with the Nd:YAG excitation. Detector bandwidth is 2 to 14 μm. The y axis represents the IR emission, normalized to its value at pulse cutoff.

Fig. 4
Fig. 4

A plot of the predicted transient IR emission in the early-time range. Parameters used can be found in Table 1. The y axis represents the IR emission, normalized to its value at pulse cutoff.

Fig. 5
Fig. 5

Energy level diagram of a four-level laser system. Nj(t), population of level |j; τjk, total lifetime of level |j undergoing transition to level |k; ηR (ηNR), radiative (nonradiative) quantum yield of metastable level |2〉; Wp(t), ground-state pumping rate.

Fig. 6
Fig. 6

IR-radiation-emission boxcar transient (normalized to its value at pulse cutoff) from a high-FOM and a low-FOM crystal with the same surface polish, measured in the early-time microsecond range where bulk effects are not important. Detector bandwidth is 2 to 14 μm. τ21=3.01 μs for the FOM=40 crystal and 2.99 μs for the FOM=800 crystal, measured independently through luminescence experiments.

Fig. 7
Fig. 7

IR-radiation-emission boxcar transient (normalized to its value at pulse cutoff) from a 5-μm polished surface and a 0.25-μm polished surface of two Ti:sapphire crystals of the same bulk FOM, measured in the early-time microsecond range where bulk effects are absent and surface effects dominate. Detector bandwidth is 2 to 14 μm. τ21=2.61 μs for the crystal with the 0.25-μm polished surface and 2.56 μs for the crystal with the 5-μm polished surface, measured independently through luminescence experiments.

Fig. 8
Fig. 8

Comparison of IR-radiation-emission profiles (normalized to their values at pulse cutoff) of the two laser-quality polished samples of Fig. 7 with an unpolished crystal. Detector bandwidth is 2 to 14 μm.

Tables (1)

Tables Icon

Table 1 Explanation of Variables Used in the Early-Time Eq. (19)

Equations (29)

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βIR(z, t; λ)=βIR(o)(z; λ)+ΔβIR(z, t; λ),
WP(λ, θT; z)=2πhc2Aλ5exphcλkBθT(z, t)-1,
ΔWP[λ, θT=T+θ(z, t)]WPθTθT=Tθ(z, t).
ΔWP(λ, T; z, t)
=hcλkBTWP(λ, T) exp(hc/λkBT)exp(hc/λkBT)-1 θ(z, t)T.
WP[λ, θT(z, t)]WP(λ, T)+ΔWP(λ, T; z, t).
P(λ, t)=0LβIR(z, t; λ)exp-0zβIR(z, t; λ)dz×ΔWP[λ, θT(z, t)]dz.
P(λ, t)=0L[βIR(o)(z; λ)+ΔβIR(z, t; λ)][WP(λ, T)+ΔWP(λ, T; z, t)]×exp-0z[βIR(o)(z; λ)+ΔβIR(z, t; λ)]dzdz.
0zβIR(o)(z; λ)dz=βIR(o)(λ)z,
0LΔβIR(z, t; λ)dz1.
exp-0L[βIR(o)(z; λ)+ΔβIR(z, t; λ)]dz
exp[-βIR(o)z].
P(λ, t)=0LβIR(o)(z; λ)WP(λ, T)×exp[-βIR(o)z]dz+0LβIR(o)(z; λ)ΔWP(λ, T; z, t)×exp[-βIR(o)z]dz+0LΔβIR(z, t; λ)WP(λ, T)×exp[-βIR(o)z]dz+0LΔβIR(z, t; λ)ΔWP(λ, T; z, t)×exp[-βIR(o)z]dz,
P(λ, t)0LβIR(o)(z; λ)ΔWP(λ, T; z, t)×exp[-βIR(o)z]dz+0LΔβIR(z, t; λ)WP(λ, T)×exp[-βIR(o)z]dz.
ΔβIR(z, t; λ)=(1-Γs)σIRN2(t)exp(-βvisz),
P(λ, t)=WP(λ, T)×hcβIR(o)exp(hc/λkBT)λkT2exphcλkBT-1 ×0Lθ(z, t)exp[-βIR(o)z]dz+σIR0LN2(t)exp(-βTz)dz,
P(λ, t)=WP(λ, T)a(λ)0θ(z, t)exp[-βIR(o)z]dz+b(λ)N2(t),
a(λ)hcβIR(o) exp(hc/λkBT)λkBTexphcλkBT-1,
b(λ)σIRβT(λvis).
S(t; λvis)=[1-R(λvis)]λ1λ2[1-R(λ)]P(λ, t)dλ.
S(t; λvis)=A(λvis)0θ(z, t)×exp[-βIR(o)z]dz+B(λvis)(1-ΓS)N2(t),
I(t)
=2I0ΓSαπk×2τIRπ t-τIR1-YττIRift<τp0τpY[βIR(o)α(t-tO)]dt0ift>τp,
S(t>τp; λvis)=(1-Γs)B(T, λvis)WpoNTτ×[exp(τp/τ21)-exp(-Wpoτp)]×exp(-t/τ21)+2A(T, λvis)I0ΓSατIRπk×YtτIR-Yt-τpτIR+2πτIR (t-t-τp),
1τ1τ21+Wpo,
S(t; λvis)=ϕ1τ[exp(τp/τ21)-e(-Wpoτp)]exp(-t/τ21)+ϕ2YtτIR-Yt-τpτIR+2πτIR (t-t-τp),
ϕ1=(1-Γs)B(T, λvis)WpoNT,
ϕ2=2A(T, λvis)IoΓSατIRπk,
Qs=IoΓs(W/m2),

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