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On light attenuation in inhomogeneous colour centre layers
October 1994
ELSEVIFR
Optical Materials 3 (1994) 265—267
~~T~CAL ~‘ ~
On light attenuation in inhomogeneous colour centre layers P. Silfsten a, P. Ketolainen b Department of Information Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenrante, Finland b Department ofPhysics, University ofJoensuu, P.O. Box ill, FIN-80101 Joensuu, Finland Received 20 March 1994; revised manuscript received 2 May 1994
Abstract A procedure is presented how to estimate light attenuation in an inhomogeneous photosensitive layer. As an example the behaviour ofradiation coloured NaCl crystals under light exposure is described.
1. Introduction When an inhomogeneous photosensitive layer is exposed to light making absorption changes in the matter the result is dependent on the direction of the incoming beam. As a typical example we mention hologram recording in radiation coloured alkali halide crystals. In these samples the colour centre concentration decreases more or less exponentially as a function of the crystal thickness. The hologram is formed due to absorption changes caused by the aggregation and recombination of the centres. This formation is ruled by the centre concentration and light intensity both of which have different values at different depths. In this paper we present a procedure how to estimate the attenuation of a light beam and consider its influence in an inhomogeneous colour centre layer. We already discussed the problem qualitatively in our previous papers on optical recordingin radiation coloured alkali halides [1,2]. Now, having found enhanced photosensitivityin coloureddoped crystals, a new interest has arisen. The experimental data used in this paper apply for NaC1 crystals coloured by 200 keY electron radiation and were obtained in connection with our previous studies. The radiation causes
the crystal to contain both electron-excess (F-type) and electron-deficit (V-type) centres. The F-type centres, being mostly F-centres (anion vacancy occupied by one electron) and small amounts of their aggregates (F2, F3, etc.), absorb in the visible and NIR regions, whereas the V-type units absorb in the near UV.
2. Local absorption coefficient in an inhomogeneous layer In order to calculate the light attenuation we have to know the behaviour of the absorption coefficient as a function of the layer depth. Let us suppose that the absorption coefficient can be expressed as —
—dI=I[p1+p~(z)]dz.
(2)
If instead, a very thin finite layer ~z is taken, the attenuation I~— Ii can be approximated by substituting
0925-3467/94/$07.O0 © 1994 Elsevier Science B.V. All rights reserved SSDI 0925-3467(94)00040-W
+
~ where j~ is constant relating to the absorption of the host material and j~( z) varies as a function of the layer depth z. In an infinitesimal layer dz the attenuation ofintensity I is
266
P. Silfsten, P. Ketolainen /Optical Materials 3(1994) 265—267
I=(I~+I~)/2where I~is the incoming and I~the transmitted intensity. Then Io—1
1=[ji1+jio(z)]
~z(I0+I1)/2.
40
(3)
Thus, for the beam transmitted by this Az layer we get
3~
—
E 20 10
1~=10 2—y1 Az—jio(z)Az
2+jt~Az+u0(z)Az~
(4)
If we divide the sample in successive equal Az layers we get analogously for the intensity outgoing from the nth layer the expression 2—/1~Az—u0(z)Az
I~=I~_~ 2+~1Az+~0(z)Az
0 0.00
0.05
0.10
0.15 0.20 Thickness (mm>
0.25
0.30
Fig. 1. ~i0(z) values as a function of layer depth. The NaCl crystals were coloured to ODF values 0.75 (solid curve) and 1.5 (dashed curve).
(5) 1000
can make a computer program to calculate the light intensity as a function of the coloured layer depth.
I
The thea~t0(z) function be obtained by measuring If weform now of know with the microdensitometer form of thecan function relative p0(z) optical we
500
densities as a function of the layer depth [3]. The values of~to(z)are directly proportional to these local optical density values. Further, the numerical value ofj~0at the surface can be obtained by such a fitting that the program calculates the same transmitted intensity as the measurement gives. The local Fcentre concentrations at different depths are directly proportional to the jto(z) values at the F-band wavelength. As an example we treated two NaC1 crystals which were coloured to total F-band optical densities ODF= 0.75 oured layer.and In ODF= both cases 1.5 measured the microdensitometric through the colexcept that for ODF= 1.5 the density was nearly conmeasurements showed an exponential decay of jt0(z) stant up to the depth of 0.05 mm. Fig.ODF= 1 presents the 75 and 1.5. The j~0(z)functions for ODF=O. equations of the functions were obtained to be ~~(0.75)
=
35 mm
25:
000
0.05
0~
)a
0.15
020
025
030
ThIckness (mm>
1000
25:
)b)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
ThIckness (mm>
Fig. 2. Light attenuation as a function of layer depth for ODF values 0.75 (a) and 1.5 (b). The arrow pointing to right: light is incident to the coloured surface.
e2~
and 3. Attenuation of the intensity u
2”~°-°5~ ,
0(l.5)=35 mm’ e where z is expressed as millimeters.
(6) By using the program described above it is very easy to calculate the attenuation of the light beam going
P. Silfsten, P. Ketolainen / Optical Materials 3 (1994) 265—267
267
,~~K1III~~I
through an inhomogeneously coloured crystal. Figs. 2a and 2b describe the cases ODF= 0.75 and ODF=
2.625
3.000 2250
dent on the coloured or uncoloured surface, is marked in the figure. As a nominal value of the maximum intensity we used 1000. 1.5, Torespectively. describe the exposure direction behaviour of the ofbeams, photosensimcitive materials oneThe often uses the Hurter-Driffield curve which expresses the change of optical density
1.875
1.500 0.00
0.05
0.10
)b)
0.15
0.20
025
0.30
ThIckness (mm>
as our in a function case the of logarithmic log I valuesexposure. as a function If we of present layer thickness we get pairs of mirror image curves. 75 This is shown in Figs. 3a and 3b for the cases ODF=O. and ODF= 1.5, respectively.
3.00
2.75
4. Conclusions
2.50
tosensitive layer must depend strongly on which side Basing on what we considered above we can state that the exposure result of an inhomogeneous pho-
0 —
2.25
2.00 0.00
0.05
0.10
(a)
0.15
0.20
0.25
0.30
of the sample is exposed. As an example we show Fig. 4 where the optical density of an NaCI crystal has been measured at 488 nm as a function ofexposure energy at that particular wavelength ofargon laser. The crys-
Thickness (mm>
Fig. 3. Logarithmic intensityas a function of layer depth forODF values 0.75 (a) and 1.5 (b). The arrow pointing to right: light is incident to the coloured surface.
:
tal was colouredto a high density ODF=4.8 and contamed also a remarkable amount of aggregate centres. Surprisingly, both curves in the figure show increase in the beginning of the exposure which is due to the fact that new isolated F centres are formed due to the dissociation of aggregates, induced by the 488 nm line lyingjust under the F band. Thus, when making light induced changes in inhomogenous layers, the light direction, intensity and attenuation mustbe carefully taken into account. The procedure described in this paper shows that local intensity values can be estimated before starting the exposure experiments.
01
References 0 0
20
40
60
80
100
120
Energy (.~>
Fig. 4. Optical density as a function of exposure energy for a heavily coloured crystal having ODF= 4.8. Both the exposure and the density measurement was carried out at 488 nm. The arrow pointing to right: light is incident to the coloured surface.
[1] 0. Salminen, P. Ketolainen and P. Silfsten, Appi. Optics 25 (1986) 4598. [2] 0. Salminen, P. Silfsten and P. Ketolainen, Cryst. Latt. Def. and Amorph. Mat. 17 (1987) 99. [3] P. Silfsten and P. Ketolainen, Meas. Sci. Technol. 1 (1990) 834.
ELSEVIFR
Optical Materials 3 (1994) 265—267
~~T~CAL ~‘ ~
On light attenuation in inhomogeneous colour centre layers P. Silfsten a, P. Ketolainen b Department of Information Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenrante, Finland b Department ofPhysics, University ofJoensuu, P.O. Box ill, FIN-80101 Joensuu, Finland Received 20 March 1994; revised manuscript received 2 May 1994
Abstract A procedure is presented how to estimate light attenuation in an inhomogeneous photosensitive layer. As an example the behaviour ofradiation coloured NaCl crystals under light exposure is described.
1. Introduction When an inhomogeneous photosensitive layer is exposed to light making absorption changes in the matter the result is dependent on the direction of the incoming beam. As a typical example we mention hologram recording in radiation coloured alkali halide crystals. In these samples the colour centre concentration decreases more or less exponentially as a function of the crystal thickness. The hologram is formed due to absorption changes caused by the aggregation and recombination of the centres. This formation is ruled by the centre concentration and light intensity both of which have different values at different depths. In this paper we present a procedure how to estimate the attenuation of a light beam and consider its influence in an inhomogeneous colour centre layer. We already discussed the problem qualitatively in our previous papers on optical recordingin radiation coloured alkali halides [1,2]. Now, having found enhanced photosensitivityin coloureddoped crystals, a new interest has arisen. The experimental data used in this paper apply for NaC1 crystals coloured by 200 keY electron radiation and were obtained in connection with our previous studies. The radiation causes
the crystal to contain both electron-excess (F-type) and electron-deficit (V-type) centres. The F-type centres, being mostly F-centres (anion vacancy occupied by one electron) and small amounts of their aggregates (F2, F3, etc.), absorb in the visible and NIR regions, whereas the V-type units absorb in the near UV.
2. Local absorption coefficient in an inhomogeneous layer In order to calculate the light attenuation we have to know the behaviour of the absorption coefficient as a function of the layer depth. Let us suppose that the absorption coefficient can be expressed as —
—dI=I[p1+p~(z)]dz.
(2)
If instead, a very thin finite layer ~z is taken, the attenuation I~— Ii can be approximated by substituting
0925-3467/94/$07.O0 © 1994 Elsevier Science B.V. All rights reserved SSDI 0925-3467(94)00040-W
+
~ where j~ is constant relating to the absorption of the host material and j~( z) varies as a function of the layer depth z. In an infinitesimal layer dz the attenuation ofintensity I is
266
P. Silfsten, P. Ketolainen /Optical Materials 3(1994) 265—267
I=(I~+I~)/2where I~is the incoming and I~the transmitted intensity. Then Io—1
1=[ji1+jio(z)]
~z(I0+I1)/2.
40
(3)
Thus, for the beam transmitted by this Az layer we get
3~
—
E 20 10
1~=10 2—y1 Az—jio(z)Az
2+jt~Az+u0(z)Az~
(4)
If we divide the sample in successive equal Az layers we get analogously for the intensity outgoing from the nth layer the expression 2—/1~Az—u0(z)Az
I~=I~_~ 2+~1Az+~0(z)Az
0 0.00
0.05
0.10
0.15 0.20 Thickness (mm>
0.25
0.30
Fig. 1. ~i0(z) values as a function of layer depth. The NaCl crystals were coloured to ODF values 0.75 (solid curve) and 1.5 (dashed curve).
(5) 1000
can make a computer program to calculate the light intensity as a function of the coloured layer depth.
I
The thea~t0(z) function be obtained by measuring If weform now of know with the microdensitometer form of thecan function relative p0(z) optical we
500
densities as a function of the layer depth [3]. The values of~to(z)are directly proportional to these local optical density values. Further, the numerical value ofj~0at the surface can be obtained by such a fitting that the program calculates the same transmitted intensity as the measurement gives. The local Fcentre concentrations at different depths are directly proportional to the jto(z) values at the F-band wavelength. As an example we treated two NaC1 crystals which were coloured to total F-band optical densities ODF= 0.75 oured layer.and In ODF= both cases 1.5 measured the microdensitometric through the colexcept that for ODF= 1.5 the density was nearly conmeasurements showed an exponential decay of jt0(z) stant up to the depth of 0.05 mm. Fig.ODF= 1 presents the 75 and 1.5. The j~0(z)functions for ODF=O. equations of the functions were obtained to be ~~(0.75)
=
35 mm
25:
000
0.05
0~
)a
0.15
020
025
030
ThIckness (mm>
1000
25:
)b)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
ThIckness (mm>
Fig. 2. Light attenuation as a function of layer depth for ODF values 0.75 (a) and 1.5 (b). The arrow pointing to right: light is incident to the coloured surface.
e2~
and 3. Attenuation of the intensity u
2”~°-°5~ ,
0(l.5)=35 mm’ e where z is expressed as millimeters.
(6) By using the program described above it is very easy to calculate the attenuation of the light beam going
P. Silfsten, P. Ketolainen / Optical Materials 3 (1994) 265—267
267
,~~K1III~~I
through an inhomogeneously coloured crystal. Figs. 2a and 2b describe the cases ODF= 0.75 and ODF=
2.625
3.000 2250
dent on the coloured or uncoloured surface, is marked in the figure. As a nominal value of the maximum intensity we used 1000. 1.5, Torespectively. describe the exposure direction behaviour of the ofbeams, photosensimcitive materials oneThe often uses the Hurter-Driffield curve which expresses the change of optical density
1.875
1.500 0.00
0.05
0.10
)b)
0.15
0.20
025
0.30
ThIckness (mm>
as our in a function case the of logarithmic log I valuesexposure. as a function If we of present layer thickness we get pairs of mirror image curves. 75 This is shown in Figs. 3a and 3b for the cases ODF=O. and ODF= 1.5, respectively.
3.00
2.75
4. Conclusions
2.50
tosensitive layer must depend strongly on which side Basing on what we considered above we can state that the exposure result of an inhomogeneous pho-
0 —
2.25
2.00 0.00
0.05
0.10
(a)
0.15
0.20
0.25
0.30
of the sample is exposed. As an example we show Fig. 4 where the optical density of an NaCI crystal has been measured at 488 nm as a function ofexposure energy at that particular wavelength ofargon laser. The crys-
Thickness (mm>
Fig. 3. Logarithmic intensityas a function of layer depth forODF values 0.75 (a) and 1.5 (b). The arrow pointing to right: light is incident to the coloured surface.
:
tal was colouredto a high density ODF=4.8 and contamed also a remarkable amount of aggregate centres. Surprisingly, both curves in the figure show increase in the beginning of the exposure which is due to the fact that new isolated F centres are formed due to the dissociation of aggregates, induced by the 488 nm line lyingjust under the F band. Thus, when making light induced changes in inhomogenous layers, the light direction, intensity and attenuation mustbe carefully taken into account. The procedure described in this paper shows that local intensity values can be estimated before starting the exposure experiments.
01
References 0 0
20
40
60
80
100
120
Energy (.~>
Fig. 4. Optical density as a function of exposure energy for a heavily coloured crystal having ODF= 4.8. Both the exposure and the density measurement was carried out at 488 nm. The arrow pointing to right: light is incident to the coloured surface.
[1] 0. Salminen, P. Ketolainen and P. Silfsten, Appi. Optics 25 (1986) 4598. [2] 0. Salminen, P. Silfsten and P. Ketolainen, Cryst. Latt. Def. and Amorph. Mat. 17 (1987) 99. [3] P. Silfsten and P. Ketolainen, Meas. Sci. Technol. 1 (1990) 834.