Abstract

Photothermal lensing signal shapes are experimentally investigated and compared with those predicted theoretically in our earlier paper. The investigation included flowing and stationary media and pulsed and cw excitations. Good qualitative agreement between theory and experiment is found. Since the lensing signal is almost always accompanied by a deflection signal, the influence of the deflection signal on the detection of lensing signal is investigated. For a perfectly aligned detection geometry the influence of the deflection signal on the lensing signal is negligible, but in the presence of misalignments a significant amount of deflection signal could be superimposed on the lensing signal. The effect of lensing on the deflection signal is also been considered. The effect of the finite size of the probe beam on the lensing signals is also investigated.

© 1997 Optical Society of America

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References

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  1. See for example, Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, and other volumes in this series.
  2. See, for example, Proceedings of the Ninth International Confererence on Photoacoustic and Photothermal Phenomena, Progress in Natural Science, Supplement to Vol. 6 (Taylor & Francis, Washington, D.C., 1996).
  3. R. Vyas, R. Gupta, “Photothermal lensing spectroscopy in a flowing medium: theory,” Appl. Opt. 27, 4701–4711 (1988).
    [CrossRef] [PubMed]
  4. R. Gupta “The theory of photothermal effect in fluids” in Photothermal Investigations of Solids and Fluids, J. A. Sell, ed., (Academic, New York, 1989), pp. 81–126.
  5. A. Rose, R. Vyas, R. Gupta, “Pulsed Photothermal Deflection spectroscopy in a flowing medium: a quantitative investigation,” Appl. Opt. 25, 4626–4643 (1986).
    [CrossRef] [PubMed]
  6. Reeta Vyas, B. Monson, Y.-X. Nie, R. Gupta, “Continuous wave photothermal deflection spectroscopy in a flowing medium,” Appl. Opt. 27, 3914–3920 (1988).
    [CrossRef] [PubMed]
  7. J. M. Khosrofian, B. A. Garetz, “Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data,” Appl. Opt. 22, 3406–3410 (1983).
    [CrossRef] [PubMed]
  8. Q. He, “Photothermal spectroscopy of fluid and solid samples,” Ph.D. Dissertation (University of Arkansas, Fayetteville, Ark., 1995).

1988 (2)

1986 (1)

1983 (1)

Garetz, B. A.

Gupta, R.

He, Q.

Q. He, “Photothermal spectroscopy of fluid and solid samples,” Ph.D. Dissertation (University of Arkansas, Fayetteville, Ark., 1995).

Khosrofian, J. M.

Monson, B.

Nie, Y.-X.

Rose, A.

Vyas, R.

Vyas, Reeta

Appl. Opt. (4)

Other (4)

Q. He, “Photothermal spectroscopy of fluid and solid samples,” Ph.D. Dissertation (University of Arkansas, Fayetteville, Ark., 1995).

R. Gupta “The theory of photothermal effect in fluids” in Photothermal Investigations of Solids and Fluids, J. A. Sell, ed., (Academic, New York, 1989), pp. 81–126.

See for example, Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, and other volumes in this series.

See, for example, Proceedings of the Ninth International Confererence on Photoacoustic and Photothermal Phenomena, Progress in Natural Science, Supplement to Vol. 6 (Taylor & Francis, Washington, D.C., 1996).

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Figures (19)

Fig. 1
Fig. 1

Schematic illustration of the photothermal lensing effect.

Fig. 2
Fig. 2

Pump–probe beam configuration for (a) transverse, (b) collinear PTLS experiment.

Fig. 3
Fig. 3

Detection of the photothermal lens in collinear geometry. The thermal lens created by the pump beam is placed a distance z1 in front of the waist of the probe beam and is detected by measurement of the change in power of the probe beam passing through a pinhole in a screen.

Fig. 4
Fig. 4

Pinhole misaligned by a distance (ξ0, η0) with respect to the center of the probe beam.

Fig. 5
Fig. 5

(a) Predicted PTLS signals when the pinhole is misaligned by ξ0 with respect to the probe beam. w is the probe beam radius at the screen, and a is the pump beam radius. (b) Curves similar to those shown in (a) except that the sign of ξ0 is reversed.

Fig. 6
Fig. 6

Detection of the lensing signal by a slit rather than a pinhole. The pinhole in the screen (see Fig. 3) is replaced with a slit aligned in the ξ direction. η0 is the misalignment of the slit with respect to the center of the probe beam.

Fig. 7
Fig. 7

Experimental arrangement for the pulsed photothermal lensing experiment in the transverse configuration.

Fig. 8
Fig. 8

(a) Collinear PTLS signals in a stationary medium. The change in the potential difference at the photodetector ΔV has been plotted as a function of time. Each curve is identified by a trace number at the left of the diagram, the bottom trace being number 1 and the top being trace 3. The scale for each curve is also given at the left of the diagram; for example, the horizontal scale for trace 1 is 500 µs/division and the vertical scale is 50 mV/division. The pump energy for a single pulse was E = 0.8 mJ, and the dc output was V0 = 1.1 V. The position of the probe beam was x/a ≃ 0, 0.5, 1 for traces 1, 2, and 3, respectively. (b) Transverse PTLS signals in a stationary medium. The pump energy for a single pulse was E = 1.4 mJ and the dc output was V0 = 4 V. The position of the probe beam was x/a ≃ 0, 0.25, 0.75 for traces 1, 2, and 3, respectively.

Fig. 9
Fig. 9

Predicted PTLS signals in a stationary medium for (a) collinear and (b) transverse configurations corresponding to the experimental conditions.

Fig. 10
Fig. 10

(a) Transverse PTLS signals in a flowing medium. As in Fig. 8, the potential difference at the photodetector ΔV has been plotted against the time, and the horizontal and the vertical scales are given to the left of each trace. The flow velocity was vx = 4.8 m/s, the pump energy for a single pulse was E = 1.8 mJ, and the dc output was V0 = 4 V. The position of the probe beam was x/a ≃ 0, 0.5, 1, 2 for traces 1, 2, 3, and 4, respectively. (b) Collinear PTLS signals in a flowing medium. The flow velocity was vx = 3.85 m/s, the pump energy for a single pulse was E = 1.1 mJ, and the dc output was V0 = 2.1 V. The position of the probe beam was x/a ≃ 0, 0.5, 1, 2 for traces 1, 2, 3, and 4, respectively.

Fig. 11
Fig. 11

Predicted PTLS signals in a flowing medium for a (a) transverse and (b) collinear configuration corresponding to the experimental conditions.

Fig. 12
Fig. 12

PTLS signals when the pinhole was misaligned by a distance ξ0 with respect to the probe beam. The potential difference at the photodetector ΔV is plotted against time, as before for E ∼ 1 mJ; V0 ∼ 2 V. The probe beam size at the aperture was w ≃ 2 mm. (a) Traces 1–4 (bottom to top) correspond to ξ0 ≃ 0, 0.25, 0.5, 1 mm, respectively. (b) Signals for negative values of the misalignments. Traces 1–4 correspond to ξ0 ≃ -1, -0.5, -0.25, 0 mm, respectively.

Fig. 13
Fig. 13

Effect of noninfinitesimal probe beam size. The pump beam radius is a = 0.3 mm and the probe beam radii are w1 = 0.1, 0.3, 0.6 mm, respectively.

Fig. 14
Fig. 14

Experimental arrangement for the cw photothermal lensing experiment in the transverse configuration.

Fig. 15
Fig. 15

Experimental PTLS signals in the transverse configuration for (a) vx ∼ 1.5 cm/s and (b) vx = 10 cm/s. The dc output was V0 = 3.6 V. The solid curves were drawn to guide the eye and are not the results of fits to the theory.

Fig. 16
Fig. 16

Theoretical PTLS signals in the transverse configuration as a function of x/a for several flow velocities (from Ref. 3).

Fig. 17
Fig. 17

Experimental lensing signal for cw excitation and collinear case; dc output V0 = 2.25 V. The solid curve was drawn to guide the eye and is not the result of a fit to the theory.

Fig. 18
Fig. 18

Theoretical PTLS signals in the collinear configuration as a function of x/a for several flow velocities (from Ref. 3).

Fig. 19
Fig. 19

Detection of PTDS signal by a bicell detector.

Equations (29)

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I0=I00exp-2ξ2+η2/w20,
It=I0texp-2ξ-z2ϕx,Lt2wx2t-2η2wy2t,
--Itdξdη=--I0dξdη.
I0tI00=w02wxtwyt.
SL=Pt-P0=ξ0-bξ0+bη0-bη0+bItdηdξ-ξ0-bξ0+bη0-bη0+bI0dηdξ.
SL=I0tAexp-2ξ0-z2ϕx,Lt2wx2t-2η02wy2t-I00A exp-2ξ02+η02w20,
SL=I00Aexp-2ξ02+η02/w20×I0tI00exp-2ξ0-z2ϕx,Lt2wx2t-ξ02w20-2η02wy2t-η02w20-1.
SL=P0, ξ0, η0w20-wxtwytwxtwyt-2ξ02wx2tw20-wx2twxtwyt-2η02wy2tw20-wy2twxtwyt+w20wxtwyt4ξ0wxtz2ϕx,Ltwxt-2w20wxtwytz2ϕx,Ltwxt2,
P0, ξ0, η0=I00A exp-2ξ02+η02/w20.
SL=P0, ξ0, η0z11fx,Lt+1fy,Lt-ξ0w02×4z1fx,Lt-η0w024z1fy,Lt+4ξ0w0z2ϕx,Ltw0-2z2ϕx,Ltw02,
SL=P0, η0z1fy,Lt-η0w024z1fy,Lt,
P0,η0=π/21/2w0bI00exp-2η02/w20.
ST=I0tA exp-2ξ0-y2ϕx,Tt2wx2t-2ζ02w20-I00A exp-2ξ02+ζ02w20,
ST=P0, ξ0, ζ0w0-wxtwxt-2ξ02wx2tw20-wx2twxtw0+w0wxt4ξ0wxty2ϕx,Ttwxt-2w0wxty2ϕx,Ttwxt2.
ST=P0, ξ0, ζ0y1fx,Tt-ξ0w024y1fx,Tt+4ξ0w0y2ϕx,Ttw0-2y2ϕx,Ttw02,
gx=2π1/21w1exp-2x2w12.
SLx, t=8αE0lz1πρCpnT1a2+8Dt22-4x-vxt2a2+8Dt×exp-2x-vxt2a2+8Dt.
SLx, tgx=-SLu, tgx-udu=8αE0lz1πνCpnT1C3w12+C2×1+C2C2+w12-4C2xvxt2C2+w122×exp-2x-vxt2C2+w12,
wxt=w0z2z01-z1fx,Lt,
1fx,Lx, t=-nT2Tx, y, tx2y=0,
1fy,Lx, t=-nT2Tx, y, ty2y=0,
1fx,Tx, t=-nT2T(x, y, tx2dy.
ϕx,Lx, y, t=n0nTTx, y, tx,
ϕx,Tx, t=1n0nTTx, y, txldy.
Tx, y, t=2αE0πt0ρCpot018Dt-τ+a2×exp-2x-vxt-τ2+y28Dt-τ+a2dτ for t>t0
Tx, y, t=2αPavπρCp0t1+cosωτ8Dt-τ+a2×exp-2x-vxt-τ2+y28Dt-τ+a2dτ
S0=-ξ0-I0dηdξ-ξ0-I0dηdξI002πw0ξ0,
St=-ξ0+z2ϕx,Lt-I0texp-2ξ2wx2t+η2wy2tdηdξ-ξ0+z2ϕx,Lt-I0texp-2ξ2wx2t+η2wy2t×dηdξ2πI0twytξ0+z2ϕx,Lt,
St-S0=2πI00w20z2ϕx,Ltw0+ξ0w0zz1fx,Lt,

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