Abstract

Equations that describe the photobleaching of photochromic layers illuminated by Gaussian laser beams are given. The photochromic samples are made of thionine, triethanolamine, and polyvinyl alcohol and follow simple kinetics law. Spatial absorbance and time-dependent power transmittance are well described by the developed equations. The model is used to calculate the Gaussian dimension of helium-neon laser beams from kinetics data.

© 2002 Optical Society of America

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References

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  1. S. Caron, R. A. Lessard, P. C. Roberge, “Photodarkening and partial photobleaching: application to dichromated gelatine,” Appl. Opt. 40, 707–713 (2001).
    [CrossRef]
  2. H. S. Loka, P. W. E. Smith, “A novel technique to measure laser beam spot sizes,” Appl. Opt. 38, 7159–7161 (1999).
    [CrossRef]
  3. L. Tarassov, Physique des Processus dans les Géenérateurs de Rayonnement Optique Cohérent (Mir, Moscow, 1985).
  4. R. J. Collier, C. B. Burckardt, L. H. Ling, Optical Holography (Academic, New York, 1971).
  5. J. M. Fleisher, C. B. Hitz, “Gaussian beam profiling: how and why,” Lasers & Opt. 6, 61–64 (1987).

2001 (1)

1999 (1)

1987 (1)

J. M. Fleisher, C. B. Hitz, “Gaussian beam profiling: how and why,” Lasers & Opt. 6, 61–64 (1987).

Burckardt, C. B.

R. J. Collier, C. B. Burckardt, L. H. Ling, Optical Holography (Academic, New York, 1971).

Caron, S.

Collier, R. J.

R. J. Collier, C. B. Burckardt, L. H. Ling, Optical Holography (Academic, New York, 1971).

Fleisher, J. M.

J. M. Fleisher, C. B. Hitz, “Gaussian beam profiling: how and why,” Lasers & Opt. 6, 61–64 (1987).

Hitz, C. B.

J. M. Fleisher, C. B. Hitz, “Gaussian beam profiling: how and why,” Lasers & Opt. 6, 61–64 (1987).

Lessard, R. A.

Ling, L. H.

R. J. Collier, C. B. Burckardt, L. H. Ling, Optical Holography (Academic, New York, 1971).

Loka, H. S.

Roberge, P. C.

Smith, P. W. E.

Tarassov, L.

L. Tarassov, Physique des Processus dans les Géenérateurs de Rayonnement Optique Cohérent (Mir, Moscow, 1985).

Appl. Opt. (2)

Lasers & Opt. (1)

J. M. Fleisher, C. B. Hitz, “Gaussian beam profiling: how and why,” Lasers & Opt. 6, 61–64 (1987).

Other (2)

L. Tarassov, Physique des Processus dans les Géenérateurs de Rayonnement Optique Cohérent (Mir, Moscow, 1985).

R. J. Collier, C. B. Burckardt, L. H. Ling, Optical Holography (Academic, New York, 1971).

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Figures (10)

Fig. 1
Fig. 1

Transmittance of a layer lit by a laser according to ρ/ρ0.

Fig. 2
Fig. 2

Concentration of dye according to ρ/ρ0 and thickness z.

Fig. 3
Fig. 3

Change of the power transmittance for homogeneous and Gaussian illumination.

Fig. 4
Fig. 4

Difference between the transmittance of a photobleachable layer illuminated by a uniform beam and by a Gaussian beam according to the fraction of the Gaussian radius.

Fig. 5
Fig. 5

Absorbance of a sample photobleached by a Gaussian beam: A, t = 10 s; B, t = 23 s; C, t = 56 s; D, t = 300 s. P inc = 4.95 mW and T 0 = 0.149.

Fig. 6
Fig. 6

k c t according to the exposure time; I c = 34 mW/cm2.

Fig. 7
Fig. 7

T P according to the exposure time; P inc = 3.95 mW, ρ0 = 0.077 cm, T 0 = 0.115, and k c = 1.2 s-1.

Fig. 8
Fig. 8

In(T c /1 - T c ) according to the exposure time.

Fig. 9
Fig. 9

Transmitted signal S tr according to the inverse of time.

Fig. 10
Fig. 10

Plot of k c according to incident intensity I c .

Tables (3)

Tables Icon

Table 1 Values of kct and the Calculated and Measured Gaussian Laser Beam Radii

Tables Icon

Table 2 Kinetic Parameters Obtained from Gaussian Photobleachinga

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Table 3 Determination of the Gaussian Radius of a Laser Beam from Photokinetics Parameters

Equations (22)

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Tx, y, t=Itrx, y, tIincx, y.
TPt=sItrtdssIincds=PtrtPinc.
Cx, y, z, tt=ϕ Ix, y, z, tz=-ϕκCx, y, z, tIx, y, z, t,
Tx, y, t=11+1/T0-1exp-k0Iincx, yt.
Iincθ, ρ=Iincρ=Ic exp-2ρ/ρ02,
Tρ, t=11+1/T0-1exp-kct exp-2ρ/ρ02,
kc=k0Ic.
Cρ, z, t=C01+expkct exp-2ρ/ρ02-1exp-κC0z,
Ptrt=θ=02πρ=0IincρTρ, tρdρdθ,
Ptrt=θ=02πρ=0×Ic exp-2ρ/ρ02ρdρdθ1+1/T0-1exp-kct exp-2ρ/ρ02,
Ptrt=π2 Icρ021+1kctlnT01+1T0-1×exp-kct.
Pinc=π2 Icρ02.
TPt=1+1kctlnT01+1T0-1exp-kct.
Iinc=Ic rectx/x0, y/y0.
TPρ, t=1+1kct1-exp-2ρ/ρ02ln1+1/T0-1exp-kctexp-2ρ/ρ021+1/T0-1exp-kct.
ΔSρρ0=t=0Tt-Tpρρ0, tdt.
ρ0=2πk0kc Pinc.
kct=lnTc1-Tc-lnT01-T0.
kct=ln T01+1/T0-1exp-kctTP-1=lnT0/TcTP-1.
TP1-TP=ln1-T0/1-TclnTc/T0.
TPt=PtrtPinc=StrtSinc1+ln T0kct,
Strt=Sinc+Sincln T0kct=a+bt.

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