Abstract

Picosecond pump-probe absorption spectroscopy is a spatially resolved technique that is capable of measuring species concentrations in an absolute sense without the need for calibrations. When laser pulses are used that are shorter than the collision time in a sample, this pump-probe technique exhibits reduced sensitivity to collisional effects such as electronic quenching. We describe modeling and experimental characterization of this technique. The model is developed from rate equations that describe the interactions of the pump and probe pulses with the sample. Calculations based on the density-matrix equations are used to identify limits of applicability for the model. Excellent agreement between the model and the experimental data is observed when both 1.3- and 65-ps pulses are used to detect potassium in a flame and in an atomic vapor cell.

© 2002 Optical Society of America

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References

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  1. G. J. Fiechtner, M. A. Linne, “Absolute concentrations of potassium by picosecond pump/probe absorption in fluctuating, atmospheric pressure flame,” Combust. Sci. Technol. 100, 11–27 (1994).
  2. T. B. Settersten, M. A. Linne, “Modeling pulsed excitation for gas-phase laser diagnostics,” J. Opt. Soc. Am. B (to be published).
  3. T. B. Settersten, “Picosecond pump/probe diagnostics for combustion,” Ph.D. dissertation (Colorado School of Mines, Golden, Colo., 1999).
  4. T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
    [CrossRef]
  5. G. J. Fiechtner, G. B. King, N. M. Laurendeau, “Rate-equation model for quantitative concentration measurements in flames with picosecond pump-probe absorption spectroscopy,” Appl. Opt. 34, 1108–1116 (1995).
    [CrossRef] [PubMed]
  6. W. J. Jones, “Concentration-modulated absorption spectroscopy. Part 3. The effect of finite spectral linewidths,” J. Chem. Soc. Faraday Trans. II 83, 693–705 (1987).
    [CrossRef]
  7. W. P. Partridge, N. M. Laurendeau, “Formulation of a dimensionless overlap fraction to account for spectrally distributed interactions in fluorescence studies,” Appl. Opt. 34, 2645–2647 (1995).
    [CrossRef] [PubMed]
  8. G. J. Blanchard, M. J. Wirth, “Transform-limited behavior from a synchronously pumped cw dye laser,” Opt. Commun. 53, 394–400 (1985).
    [CrossRef]
  9. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 665–666.
  10. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Krieger, Malabar, Fa.1992), pp. 89–90, 122–129.
  11. G. J. Blanchard, M. J. Wirth, “Measurement of small absorbances by picosecond pump-probe spectroscopy,” Anal. Chem. 58, 532–535 (1986).
    [CrossRef]
  12. M. A. Linne, D. C. Morse, J. L. Skilowitz, G. J. Fiechtner, J. R. Gord, “Two-dimensional pump-probe imaging in reacting flows,” Opt. Lett. 20, 2414–2416 (1995).
    [CrossRef] [PubMed]
  13. J. W. Daily, “Saturation of fluorescence with a Gaussian laser beam,” Appl. Opt. 17, 225–229 (1978).
    [CrossRef] [PubMed]
  14. M. Mailander, “Determination of absolute transition probabilities and particle densities by saturated fluorescence excitation,” J. Appl. Phys. 49, 1256–1259 (1978).
    [CrossRef]
  15. B. T. Ahn, G. J. Bastiaans, F. Albahadily, “Practical determination of flame species via laser saturation fluorescence spectroscopy,” Appl. Spectrosc. 36, 106–116 (1982).
    [CrossRef]
  16. J. T. Salmon, N. M. Laurendeau, “Analysis of probe volume effects associated with laser-saturated fluorescence measurements,” Appl. Opt. 24, 1313–1321 (1985).
    [CrossRef] [PubMed]

1999

T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
[CrossRef]

1995

1994

G. J. Fiechtner, M. A. Linne, “Absolute concentrations of potassium by picosecond pump/probe absorption in fluctuating, atmospheric pressure flame,” Combust. Sci. Technol. 100, 11–27 (1994).

1987

W. J. Jones, “Concentration-modulated absorption spectroscopy. Part 3. The effect of finite spectral linewidths,” J. Chem. Soc. Faraday Trans. II 83, 693–705 (1987).
[CrossRef]

1986

G. J. Blanchard, M. J. Wirth, “Measurement of small absorbances by picosecond pump-probe spectroscopy,” Anal. Chem. 58, 532–535 (1986).
[CrossRef]

1985

G. J. Blanchard, M. J. Wirth, “Transform-limited behavior from a synchronously pumped cw dye laser,” Opt. Commun. 53, 394–400 (1985).
[CrossRef]

J. T. Salmon, N. M. Laurendeau, “Analysis of probe volume effects associated with laser-saturated fluorescence measurements,” Appl. Opt. 24, 1313–1321 (1985).
[CrossRef] [PubMed]

1982

1978

J. W. Daily, “Saturation of fluorescence with a Gaussian laser beam,” Appl. Opt. 17, 225–229 (1978).
[CrossRef] [PubMed]

M. Mailander, “Determination of absolute transition probabilities and particle densities by saturated fluorescence excitation,” J. Appl. Phys. 49, 1256–1259 (1978).
[CrossRef]

Ahn, B. T.

Albahadily, F.

Bastiaans, G. J.

Blanchard, G. J.

G. J. Blanchard, M. J. Wirth, “Measurement of small absorbances by picosecond pump-probe spectroscopy,” Anal. Chem. 58, 532–535 (1986).
[CrossRef]

G. J. Blanchard, M. J. Wirth, “Transform-limited behavior from a synchronously pumped cw dye laser,” Opt. Commun. 53, 394–400 (1985).
[CrossRef]

Daily, J. W.

Fiechtner, G.

T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
[CrossRef]

Fiechtner, G. J.

Gord, J.

T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
[CrossRef]

Gord, J. R.

Jones, W. J.

W. J. Jones, “Concentration-modulated absorption spectroscopy. Part 3. The effect of finite spectral linewidths,” J. Chem. Soc. Faraday Trans. II 83, 693–705 (1987).
[CrossRef]

King, G. B.

Laurendeau, N. M.

Linne, M. A.

T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
[CrossRef]

M. A. Linne, D. C. Morse, J. L. Skilowitz, G. J. Fiechtner, J. R. Gord, “Two-dimensional pump-probe imaging in reacting flows,” Opt. Lett. 20, 2414–2416 (1995).
[CrossRef] [PubMed]

G. J. Fiechtner, M. A. Linne, “Absolute concentrations of potassium by picosecond pump/probe absorption in fluctuating, atmospheric pressure flame,” Combust. Sci. Technol. 100, 11–27 (1994).

T. B. Settersten, M. A. Linne, “Modeling pulsed excitation for gas-phase laser diagnostics,” J. Opt. Soc. Am. B (to be published).

Mailander, M.

M. Mailander, “Determination of absolute transition probabilities and particle densities by saturated fluorescence excitation,” J. Appl. Phys. 49, 1256–1259 (1978).
[CrossRef]

Measures, R. M.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Krieger, Malabar, Fa.1992), pp. 89–90, 122–129.

Morse, D. C.

Partridge, W. P.

Salmon, J. T.

Settersten, T.

T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
[CrossRef]

Settersten, T. B.

T. B. Settersten, “Picosecond pump/probe diagnostics for combustion,” Ph.D. dissertation (Colorado School of Mines, Golden, Colo., 1999).

T. B. Settersten, M. A. Linne, “Modeling pulsed excitation for gas-phase laser diagnostics,” J. Opt. Soc. Am. B (to be published).

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 665–666.

Skilowitz, J. L.

Wirth, M. J.

G. J. Blanchard, M. J. Wirth, “Measurement of small absorbances by picosecond pump-probe spectroscopy,” Anal. Chem. 58, 532–535 (1986).
[CrossRef]

G. J. Blanchard, M. J. Wirth, “Transform-limited behavior from a synchronously pumped cw dye laser,” Opt. Commun. 53, 394–400 (1985).
[CrossRef]

AIAA J.

T. Settersten, M. A. Linne, J. Gord, G. Fiechtner, “Density matrix and rate equation analyses for picosecond pump/probe combustion diagnostics,” AIAA J. 37, 723–731 (1999).
[CrossRef]

Anal. Chem.

G. J. Blanchard, M. J. Wirth, “Measurement of small absorbances by picosecond pump-probe spectroscopy,” Anal. Chem. 58, 532–535 (1986).
[CrossRef]

Appl. Opt.

Appl. Spectrosc.

Combust. Sci. Technol.

G. J. Fiechtner, M. A. Linne, “Absolute concentrations of potassium by picosecond pump/probe absorption in fluctuating, atmospheric pressure flame,” Combust. Sci. Technol. 100, 11–27 (1994).

J. Appl. Phys.

M. Mailander, “Determination of absolute transition probabilities and particle densities by saturated fluorescence excitation,” J. Appl. Phys. 49, 1256–1259 (1978).
[CrossRef]

J. Chem. Soc. Faraday Trans. II

W. J. Jones, “Concentration-modulated absorption spectroscopy. Part 3. The effect of finite spectral linewidths,” J. Chem. Soc. Faraday Trans. II 83, 693–705 (1987).
[CrossRef]

Opt. Commun.

G. J. Blanchard, M. J. Wirth, “Transform-limited behavior from a synchronously pumped cw dye laser,” Opt. Commun. 53, 394–400 (1985).
[CrossRef]

Opt. Lett.

Other

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), pp. 665–666.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Krieger, Malabar, Fa.1992), pp. 89–90, 122–129.

T. B. Settersten, M. A. Linne, “Modeling pulsed excitation for gas-phase laser diagnostics,” J. Opt. Soc. Am. B (to be published).

T. B. Settersten, “Picosecond pump/probe diagnostics for combustion,” Ph.D. dissertation (Colorado School of Mines, Golden, Colo., 1999).

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Figures (6)

Fig. 1
Fig. 1

Pump-probe beams cross to form the interaction volume centered at position z = z 0 on the probe-beam propagation axis. Cylindrical coordinate systems for the pump and probe beams are shown. The perturbation due to the pump pulse is localized along the z′ axis and affects only the probe pulse in the z 1zz 2 region.

Fig. 2
Fig. 2

Predicted modulation depth versus N 0 l (upper set of curves) and the fractional difference between the linearized RE and the DME results (lower set of curves) for 2-ps sech2 pulses. Results for various relaxation times (1/γ21, 1/Γ21) are indicated: (a) 52.4 ns,26.2 ns, (b) 1 ns,10 ns, (c) 500 ps, 5 ns, and (d) 100 ps, 1 ns.

Fig. 3
Fig. 3

Lasers and optical setup for picosecond PPAS measurements. Either Pu1 or Pu2 was used as the pump beam for a PPAS measurement, and a beam block was placed in the unused beam.

Fig. 4
Fig. 4

PPAS modulation depth for 1.3-ps pulses interacting with potassium in the vapor cell plotted as a function of pump-pulse energy. Data set 1 (open circles), N 0 ≈ 2 × 1012 cm-3; data set 2 (solid triangles), N 0 ≈ 1011 cm-3. Data set 2 was scaled to match data set 1 in the linear power regime. The dashed line represents a linear relationship between αmod and the pump-pulse energy.

Fig. 5
Fig. 5

PPAS modulation depth for 1.3-ps pulses interacting with potassium in the vapor cell plotted as a function of the number density calculated from diode-laser absorption measurements. The shaded region corresponds to prediction of the spectrally resolved RE model, with the ±2σ uncertainty in the calculation setting the upper and the lower bounds. The model uncertainty is a result of the uncertainties of the experimental parameters listed in Table 2.

Fig. 6
Fig. 6

PPAS modulation depth for 65-ps pulses interacting with potassium in the methane/air flame plotted as a function of the number density calculated from diode-laser absorption measurements: dashed line, linearized RE model, Eq. (18); shaded region, prediction of the spectrally resolved RE model, with the ±2σ uncertainty in the calculation setting the upper and the lower bounds. The model uncertainty is a result of the uncertainties of the experimental parameters listed in Table 2.

Tables (2)

Tables Icon

Table 1 Comparison of PPAS Modulation Depth for Pu1-Pr and Pu2-Pr

Tables Icon

Table 2 Parameter Values and Uncertainties for the Data in Figs. 5 and 6

Equations (18)

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αmod=pron-proffproff,
Iνν, t, r, z=zATtLνRrΔt0Δν0,
Tt=ln2+1sech22 ln2+1t-t0Δt0,
Lν=ln2+1sech22 ln2+1ν-ν0Δν0.
Δt0Δν0=4π2ln2+12.
Rr=exp-2r2/w2,
Iνν, t, r, z=Iνν, t, r, 0exp-0zkν, r, zdz,
kν, r, z=hνcTjN1,jr, zB12,j-N2,jr, zB21,jgjν.
ΔNjr, z=N1,jeqB12,jΔt0c- Iν,puν, r, zgjνdν,
ΔNjr, zN1,jeq-N1,jr, z=N2,jr, z.
ΔNjr, z=N1,jeqpu0RrApuB12,jΔt0c-LνΔνo gjν×exp-hνcjN1,jeqB12,jgjνzdν.
prL=pr002πrRrA×-LνΔν0exp-0Lκν, r, zdzdνdr.
proffL=pr0-LνΔν0×exp-hνcj N1,jeqB12,j gjνLdν.
pronL=pr002πrRrA-+LνΔν1/2×expj- hνcgjνN1,jeqB12,jL+z1z2hνc×gjνΔNjr, zB12,j+B21,jdνdr.
αmod=jhν21,jcLν21,jΔν0B12,j+B21,j×0z1z22πrRrA ΔNjr, zdzdr,
l=2wpusin θπ21+wprwpu21/2.
αmod=puΔt0Apujhν21,jc2Lν21, jΔν02×B12,jB12,j+B21,jN1,jeqz0l.
αmod=N0l puApuln2+1Δν02×c464π2hA212ν215g2g11+g2g1.

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