Abstract

Photodarkening or partial photobleaching of photochromic solid media is described by means of an approximated analytical equation. The equation shows that the effective rate of the photochemical reaction is proportional to the square root of the final transmittance of the illuminated layer. The model is applied to describe the photodarkening of dichromated gelatin at 488 nm.

© 2001 Optical Society of America

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References

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  1. K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).
  2. A. M. Braun, M. T. Maurette, E. Oliveros, Technologie Photochimique (Presses Polytechnique Romandes, Lausanne, Switzerland, 1987).
  3. J. C. Calverts, J. N. Pitts, Photochemistry (Wiley, New York, 1966).
  4. W. A. Noyes, P. A. Leighton, The Photochemistry of Gazes, (Reinhold, New York, 1941).
  5. J. C. Newell, L. Solymar, A. A. Ward, “Holograms in dichromated gelatin: real-time effects,” Appl. Opt. 24, 4460–4466 (1985).
    [CrossRef] [PubMed]
  6. R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
    [CrossRef]
  7. N. Capolla, R. A. Lessard, “Real time bleaching of methylene blue or thionine sensitized gelatin,” Appl. Opt. 30, 1196–1200 (1991).
    [CrossRef] [PubMed]
  8. A. Dubois, M. Canva, A. Brun, F. Chaput, J.-P. Boilot, “Photostability of dye molecules trapped in solid matrices,” Appl. Opt. 35, 3193–3199 (1996).
    [CrossRef] [PubMed]
  9. M. Sasaki, “Studies on photosensitive dichromated materials,” Rep. Inst. Ind. Sci. Univ. Tokyo 27, 1–58 (1978).

1996

1993

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

1991

1985

1978

M. Sasaki, “Studies on photosensitive dichromated materials,” Rep. Inst. Ind. Sci. Univ. Tokyo 27, 1–58 (1978).

Beeson, K. W.

K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).

Boilot, J.-P.

Braun, A. M.

A. M. Braun, M. T. Maurette, E. Oliveros, Technologie Photochimique (Presses Polytechnique Romandes, Lausanne, Switzerland, 1987).

Brun, A.

Calverts, J. C.

J. C. Calverts, J. N. Pitts, Photochemistry (Wiley, New York, 1966).

Canva, M.

Capolla, N.

Chaput, F.

Dubois, A.

Francis, C. V.

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

Horn, K. A.

K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).

Leighton, P. A.

W. A. Noyes, P. A. Leighton, The Photochemistry of Gazes, (Reinhold, New York, 1941).

Lessard, R. A.

Maurette, M. T.

A. M. Braun, M. T. Maurette, E. Oliveros, Technologie Photochimique (Presses Polytechnique Romandes, Lausanne, Switzerland, 1987).

McFarland, M.

K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).

Misemer, D. K.

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

Mohapatra, S. K.

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

Moshrefzadeh, R. S.

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

Newell, J. C.

Noyes, W. A.

W. A. Noyes, P. A. Leighton, The Photochemistry of Gazes, (Reinhold, New York, 1941).

Oliveros, E.

A. M. Braun, M. T. Maurette, E. Oliveros, Technologie Photochimique (Presses Polytechnique Romandes, Lausanne, Switzerland, 1987).

Pitts, J. N.

J. C. Calverts, J. N. Pitts, Photochemistry (Wiley, New York, 1966).

Radcliffe, M. D.

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

Sasaki, M.

M. Sasaki, “Studies on photosensitive dichromated materials,” Rep. Inst. Ind. Sci. Univ. Tokyo 27, 1–58 (1978).

Solymar, L.

Ward, A. A.

Wu, C.

K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).

Yardley, J. T.

K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).

Appl. Opt.

Appl. Phys. Lett.

R. S. Moshrefzadeh, D. K. Misemer, M. D. Radcliffe, C. V. Francis, S. K. Mohapatra, “Nonuniform photobleaching of dyed polymers for optical waveguides,” Appl. Phys. Lett. 62, 16–18 (1993).
[CrossRef]

Rep. Inst. Ind. Sci. Univ. Tokyo

M. Sasaki, “Studies on photosensitive dichromated materials,” Rep. Inst. Ind. Sci. Univ. Tokyo 27, 1–58 (1978).

Other

K. W. Beeson, K. A. Horn, M. McFarland, C. Wu, J. T. Yardley, “Photochemical formation of polymeric waveguides and devices for optical interconnection applications,” in ICALEO ’89: Optical Sensing and Measurement, K. G. Harding, ed., Proc. SPIE1374, 176–185 (1990).

A. M. Braun, M. T. Maurette, E. Oliveros, Technologie Photochimique (Presses Polytechnique Romandes, Lausanne, Switzerland, 1987).

J. C. Calverts, J. N. Pitts, Photochemistry (Wiley, New York, 1966).

W. A. Noyes, P. A. Leighton, The Photochemistry of Gazes, (Reinhold, New York, 1941).

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Figures (7)

Fig. 1
Fig. 1

Dye concentration C(z, t) and light intensity I(z, t) in a photobleachable medium after exposure.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Photodarkening of DCG at 488 nm for an incident intensity of 161 mW/cm2.

Fig. 4
Fig. 4

Example of a plot of ln(T/ T - T F ) versus exposure time.

Fig. 5
Fig. 5

Slope k TF versus TF for I 0 = 161 mW/cm2.

Fig. 6
Fig. 6

Final absorbance versus initial absorbance of DCG layers at a dichromate concentration of 0.65 mol/L.

Fig. 7
Fig. 7

Determination of the photodarkening constant k 0.

Tables (1)

Tables Icon

Table 1 Physical and Kinetics Constants of DCG

Equations (25)

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N1+hνϕ1 P1,
N2+hν  P2.
C1z, tt=-k1C1z, tTz, t,
C2z, tt=-|v2|,
Tz, tz=-Tz, tκ1C1z, t+κ2C2z, t.
Tz, t=Iz, t/I0,
k1=k0I0.
ϕ=k0κhcλ NA×109,
T1z, t=exp-κ10z C1z, tdz,T2z, t=exp-κ20z C2z, tdz.
Tz, t=exp-κ10z C1z, tdzexp-κ20z C2z, tdz=T1z, tT2z, t.
 ln T1z, tt=-k10z-κ1C1z, tdz×exp-κ10z C1z, tdz×exp-κ20z C2z, tdz,
 ln T1z, tt=-k1T10, tT1z, t T2dT1=-k11T1z, t T2dT1.
 ln T1z, ttk1T2z, t1-T1z, t.
T1z, t11+expκ1C01z-1exp-k10tT2z, tdt.
Tz, tT2z, t1+T02T0-1exp-k10tT2z, tdt,
T01=exp-κ1C01z,T02=exp-κ2C02z,T0=T01T02=exp-κ1C01z-κ2C02z.
Tz, t=11+1T0z-1exp-kt.
R+hνϕk P.
Pz, t=C0-Rz, t.
A=-ln Tz, t=κR0z Rz, tdz+κP0z Pz, tdz,
Tz, t=exp-κPC0zexp-κR-κP0z Rz, tdz=T2z, tT1z, t.
κ2=κP=κF,C2z, t=C0,κ1=κR-κP,C1=Rz, t,TF=T2z, t=T02=exp-κPC0z=exp-κFC0z,T1z, 0=T01=exp-κR-κPRz, 0z,
Tz, tTFz1+TFzT0z-1exp-ktTFz.
κ2=κ,C2z, t=1-xC0,κ1=κ,C1z, t=xC0-P1z, t,TF=T2z, t=T02=exp-κ1-xC0z,T1z, 0=T01=exp-κxC0z.
lnTtTt-TF=kTFt+lnT0T0-TF.

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