dark self-enhancement in dichromated poly(vinyl alcohol) gratings: a detailed study

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Dark self-enhancement in dichromated poly~vinylalcohol! gratings: a detailed study

Tuula Keinonen and Roma Grzymala

Experimental results concerning the real-time hologram recording process in dichromated poly~vinylalcohol! are presented. Self-enhancement, the increase in diffraction efficiency of the holographic grat-ings in the dark after recording, is also presented. The influence of the recording parameters ~pH,exposure energy, dichromate concentration! on the self-enhancement gain is shown. Maximum gainwas 6, and self-enhancement occurred during the 3 days following the exposure. The results and amodel for the reduction of chromium ions corresponding to the formation of the grating are discussed.© 1999 Optical Society of America

OCIS codes: 090.0090, 160.0160, 090.2900, 160.4670.

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1. Introduction

Dichromated poly~vinyl alcohol! ~DCPVA! as a real-time holographic recording material has been studiedduring the past decade by several researchers.1–5

Real-time holograms with high diffraction efficienciesas great as 20% were produced by Lelievre and Cou-ture.1 In their experiments diffraction efficiency as

function of the exposure energy during the exposureas measured, and the saturation of the diffractionfficiency was reported. Barikani et al.2 investi-

gated real-time hologram formation in the presenceof external electron donors and found them to bedetrimental to holographic characteristics. Highrelative humidity has been found to significantly im-prove the photospeed and the real-time diffractionefficiency.3 The influence of the pH of the coatingsolution and the concentration of the dichromate onthe photochemical evolution of the intermediateswere studied by Manivannan et al.4,5 The thermaland the photochemical evolution of Cr~V!, Cr~III!, and

polymer radical in DCPVA films have been moni-ored at room temperature.4 A high real-time dif-

fraction efficiency has been achieved.5 Holographic

T. Keinonen [email protected]! is with the Universityof Joensuu, P. O. Box 111, FIN-80101 Joensuu, Finland.R. Grzymala is with the Photonics Systems Laboratory, LouisPasteur University, Parc d9Innovation, Boulevard Sebastien

rant, 67 400 Illkirch-Graffenstaden, France.Received 25 March 1999; revised manuscript received 26 July

999.0003-6935y99y357214-08$15.00y0© 1999 Optical Society of America

7214 APPLIED OPTICS y Vol. 38, No. 35 y 10 December 1999

characterization and electron spin resonance spectro-scopic studies of DCPVA by Manivannan et al.showed the evolution of Cr~V! and Cr~III! and the roleof dyes in the formation of the hologram.6 Bolte et

l.7 also showed that the reduction of Cr~V! is a slowprocess. Real-time effects in dichromated gelatinwere studied by Newell et al.8 It was shown that,owing to the effect of a humid atmosphere, the grat-ing may self-develop into a phase grating of muchhigher efficiency.

The self-enhancement of a hologram is the increasein its diffraction efficiency after the recording overtime under light irradiation or in the dark. The self-enhancement was reported for the first time, to ourknowledge, in 1973 by Gaylord et al.9 for phase holo-grams in LiNbO3:Fe crystals. The phenomenon hasbeen observed in holograms recorded in alkali halidecrystals with F centers and in amorphous As2S3films,10–12 as well as in photopolymers.13,14 Accord-ing to the mechanism and the properties of the effect,different types of the self-enhancement can be distin-guished. Self-enhancement may be coherent self-enhancement that is due to the diffracted waves.When the grating recorded in its initial diffractionefficiency is read out either with one of the recordingbeams or at some other wavelength, the readoutbeam is diffracted from the grating and the readoutbeam and the diffracted beam interfere, causing fur-ther recording. Self-enhancement can also be inco-herent ~noncoherent! self-enhancement that is due tothe transmission increase of a hologram by incoher-ent light. The increase takes place when the holo-gram works and selects light at the Bragg angle.The procedure is similar to coherent self-

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enhancement, but it is less effective. Relaxational~or dark! self-enhancement is due to the transmissionncrease of a hologram by thermostimulated relax-tion processes. Light-induced self-enhancementakes place in all real-time recording media, but darkelf-enhancement is a special property of only someaterials. Self-enhancement both during and after

he recording can together be regarded as a two-stageolographic recording method, which is profitablehen the recording energy or the exposure time is

imited at the first stage. Such a recording methodas the advantage of a large vibration stability at theecond stage. This is especially important in thease of those materials, such as dichromated poly-ers, that are insensitive and need long exposure

imes.A strong enhancement effect, reinforcement has

been demonstrated in thionine–poly~vinyl alcohol!~PVA! layers by Caron et al.15 They suggest that theeffect, observed after the object beam was blocked offand with the recording wavelength, is due to theBorrmann effect or to the effect caused by excitedmolecules. A transient grating made of metastablemolecules interferes destructively with a permanentgrating made of final photochemical products.Salminen et al.11,12 explained the effect observed inholographic gratings in As2S3 crystals by the diffu-sion that is also known in photorefractive crystals.Lougnot et al.16 modeled the hologram formation onphotopolymers, also taking into account the diffusion;their model explains hologram formation in the poly-mers during the exposure. Lougnot and Turck13 ob-erved that, after the holographic irradiation of thehotopolymer is interrupted at an early stage of theonversion, the thermal postpolymerization en-ances the spatial modulation of segment densityetween bright and dark areas that goes along withn increase of the modulation of the refractive indexnd an improvement of the diffraction efficiency.he key phenomenon is the balance between thehemical initiation of the polymerization and the dif-usion of unreacted species from non-light-struckreas to bright regions of the record. A slight self-nhancement at low energy has also been observed.alcera et al.17 studied acrylic acid—Cr~VI! solution.

When kept in the dark, the mixture was observed toundergo a slow reaction, leading to the formation ofCr~III!.

In this paper we show a detailed holographictudy of the self-enhancement effect in DCPVAlms. In these films the hologram formation isifferent from that in the self-enhancement mate-ials discussed in the literature and mentionedbove. We show the influence of exposure energy,H, and dichromate concentration on the self-nhancement, and we discuss the process and theodel for the chromium-ion reduction in DCPVA

uring and after the exposure.

2. Experiment and Results

Real-time hologram formation in DCPVA was stud-ied. We prepared DCPVA films for the experiments

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by dissolving 7 g of PVA powder ~Aldrich! in 100 ml ofdistilled water. The solution was heated to 60 °C,and ammonium dichromate ~0.8–1.4 g! was added tothe solution. Pouring this solution on a clean lev-eled glass substrate resulted in a transparent orangefilm of thickness 20 mm.

After ;20 h, DCPVA films were exposed with twocoherent beams. The basic real-time setup is shownin Fig. 1. This is a simple two-beam arrangement.The two blue ~488-nm! recording beams came from anargon-ion Spectra-Physics laser or an argon-ion Co-herent laser. The reading beam, aligned to theBragg angle, was at 632.8 nm, supplied by a He–Nelaser. The interbeam angle was 30°, correspondingto 1060 cyclesymm in the DCPVA grating. Theroom humidity was 40%, and the room temperaturewas 20 °C. The beam ratio in the experiments was1 to 1.5. The recording beams were expanded andcollimated, but the reading He–Ne beam was unex-panded. The real-time diffraction efficiency of therecorded holograms is defined as h 5 I1yIi, where I1 isthe intensity of the first-order diffracted beam and Iiis the intensity of the incident beam.

The diffracted beam was measured in real time asa function of the exposure time. The saturation ofthe diffraction in the DCPVA grating similar to thatof the earlier studies1–3,5 was observed. The maxi-mum diffraction efficiency was found to be 0.15% forthe DCPVA grating during the blue light exposure.The total intensity of the recording beams was 1.3mWycm2 for the 488-nm wavelength. Absorptionand reflections on the surfaces were not taken intoaccount when the diffraction efficiency was calcu-lated. Figure 2~a! presents a typical holographicrowth curve during the exposure for the film withH 5 4.83 and Fig. 2~b! with pH 5 8.13. When thexposure was continued, the diffracted intensitytarted to decrease. The saturation was reachedith lower energy, when pH was lower. With use of

ower pH the saturation level could also be main-ained longer.

In the second experiment the recording beamsere shut off near the saturating exposure energy.he detection of the diffracted beam with the He–Ne

aser beam was continued after that. Self-nhancement of the diffracted beam after the record-ng was then observed. The dependencies of theelf-enhancement on the dichromate concentration,xposure energy, and pH of the solution were mea-

Fig. 1. Experimental setup for the real-time hologram measure-ments. BS, beam splitter; LPSF, lens pinhole spatial filter.

0 December 1999 y Vol. 38, No. 35 y APPLIED OPTICS 7215

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sured. Figure 3~a! presents the self-enhancement ofhe grating in the film with pH 5 4.83 and Fig. 3~b! in

the film with pH 5 8.13. Diffracted intensity duringxposure and immediately after that is shown in Fig.for different dichromate concentrations from 0.8%

o 1.4% ~pH 5 5!. Diffraction efficiency continues toincrease, after the exposure is stopped, more quicklywhen the dichromate concentration is higher. Thechange in diffracted intensity in the 3 days followingthe exposure is shown in Fig. 5 for the different di-chromate concentrations. The relative self-enhancement was strongest with the dichromateconcentration 1.2%. The dependence of the self-enhancement on the exposure energy is shown inFigs. 6~a! and 6~b! for pH values 4.82 and 8.13, re-pectively. Diffraction efficiency is presented onlyfter the recording is shut off. Maximum self-nhancement is achieved clearly during the first dayfter the exposure with pH 5 4.82. After that theiffraction efficiency starts to decrease. With pH 5.13 the maximum diffraction efficiency is alsochieved during the first day, but it is maintainedonger. In our experiments maximum self-nhancement was reached within 1–3 days.

Fig. 2. Diffraction efficiency as a function of exposure time; ~a!pH 5 4.83,12 ~b! pH 5 8.13.


3. Discussion

The slight increase in the diffracted intensity is notthe only observed self-enhancement in our experi-ments; a remarkable change in diffraction efficiencywas observed as well. After the recording was

Fig. 3. Diffraction efficiency during and after the exposure; ~a!pH 5 4.83,12 ~b! pH 5 8.13.

Fig. 4. Diffraction efficiency during and after the exposure fordifferent dichromate concentrations.

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stopped the diffraction efficiency started to increasewith an even higher rate than that with which itincreased at the end of the blue line exposure, andeven in that case, when the exposure was stoppedafter the saturation. The diffraction efficiency wasdetected until the saturation in the self-enhancement

Fig. 5. Difference in diffracted intensity during 3 days for differ-ent concentrations.

Fig. 6. Diffraction efficiency some days after the recording; ~a!pH 5 4.83, ~b! pH 5 8.13.

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was reached, generally within 3 days in the DCPVAfilm.

The basic recording mechanism in DCPVA, whichbelongs to the synthetic polymers, is attributed to aphoto-cross-linking process of polymer when mixedwith ammonium dichromate. Hexavalent chro-mium Cr~VI! is reduced, and polymer becomes oxi-dized. Light-activated Cr~VI! in the polymer matrixgenerates Cr~V! and a polymer radical involving anelectron-transfer process. Light induces further re-actions to generate the final products, Cr~III! andross-linked PVA. Final product is a complex be-ween Cr~III! and probably the hydroxy groups of the

PVA. So polymer chains become photo cross linkedin agreement with the interference pattern producedby the writing–recording beams.

Cr~VI! is consumed slowly during the photochemi-cal reaction. The rate of the photoreduction of Cr~VI!depends on pH, the intensity of the incident light, andthe nature and concentration of reducing agents.Datta and Soller18 reported that, in PVA, the Cr~V!concentration increases during exposure and pla-teaus after an exposure time of 1 h. Shelf aging ofdichromated photoresist during the storage could berelated to the dark stability of the Cr~V! complex.However, approximately 8–10% of the dichromatedions must be converted to Cr~V! in the dark to obtaina good negative image. Manivannan et al.4 showedthat the other pathway in the reduction of chromiumions, the thermal oxidation reaction, has a minor rolecompared with the photochemical pathway. Thisthermal reaction in the dark during the storage wasseen to be a disadvantage, because it reduced themaximum index modulation ability. Manivannan etal. also presented the photoprocess during the expo-sure in DCPVA–xanthene dye systems.6 Both ther-mal and photochemical processes are included intheir model. Bolte et al.7 showed that the reductionof Cr~V! is a slow process and that the complete trans-ormation into Cr~III! is achieved after several days

both in DCPVA and in dichromated gelatin. Ralli-son19 found that, when he let the film sit for 5 or 6days before development, the cross linking also ap-peared to occur in the dark reaction after exposureover time. The same cross-linking effect is causedby the fixer; so after the storage the fixer could beomitted from the development process.

One can observe modification of the pH values ofexposed films containing dichromate compounds. Itis also known that, at low original pH, the rate ofCr~VI! photoreduction is higher than at higher pHvalues. This can also be seen when one comparesFigs. 2~a! and 2~b!. In Fig. 2~a! the pH of the solu-tion for preparing the film is 4.82, and the saturationis achieved with lower exposure energy than in thefilms of Fig. 2~b!, where the dichromate solution with

pH of 8.13 is used. At pH , 5 the major species isCrO4

2 ~in solution!, and at pH . 8, mostly CrO422

is present. It is generally accepted that, at pH . 8,a photochemical reaction does not occur easily, evenin the dry film. However, we have recorded gratingsin the films made of solutions with pH . 8. In these


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films, as well, the self-enhancement effect is presentas seen in Fig. 3~b!. In both cases ~pH 5 4.82 and

H 5 8.13! the diffracted intensity increased after thexposure was completed. For reasons not yet knownhe diffracted intensity had a small decrease before ittarted to increase for higher pH. This is probablyue to some error in the experiment. The curve istherwise a typical self-enhancement curve forCPVA seen in our experiments.Figure 4 presents diffraction efficiency during and

fter the recording for different dichromate concen-rations of the film. The exposure is not stopped athe same time, because the saturation is achieved byifferent exposure energies. The exposure is shutff ~arrows in the figure! just before the saturationevel of each film with different dichromate concen-ration. After that the diffraction efficiency in-reases more with higher dichromate concentration,ut it must be noted that in that case the originaliffraction efficiency was higher as well. In Fig. 4he diffraction efficiency is presented more than 100 sfter the exposure has been shut off. In Fig. 5 thehange in the diffraction efficiency within 3 days afterhe exposure is presented for the gratings in the filmsith different dichromate concentrations. The rela-

ive increase in diffraction efficiency was highest withhe dichromate concentration 1.2%. But the initialiffraction efficiency before the self-enhancementas increased with the increasing dichromated con-

entration’s being highest with the concentration.4%. With lower pH the saturation in the self-nhancement is achieved in 1 day, after which thefficiency starts to decrease @shown in Fig. 6~a!#.ith higher pH @Fig. 6~b!# the saturation is also

achieved in 1 day, but the diffraction efficiency startsto decrease more slowly, achieving approximately thesame level after 3 days.

The self-enhancement process can be characterizedby the self-enhancement coefficient,

j 5 h1yh0,

and by the self-enhancement rate,

b 5 djydt,

where h0 is the initial diffraction efficiency imme-diately after the recording. The self-enhancementcoefficient for the grating with pH 5 8.13 was 2.8,

nd for a lower pH it was 2.1 for the same concen-ration ~1.4%!. The highest self-enhancement co-fficient observed in our experiments with DCPVAas 6. The self-enhancement coefficient for differ-nt ammonium dichromate concentrations is shownn Fig. 7 as a function of the time after the exposure.he self-enhancement coefficient increases for alloncentrations, being highest for the highest con-entration measured until 2000 s. Although it wasbserved that the change in the diffracted intensityas highest for the concentration 1.2%, it seems

hat the dependence is not so straightforward. Ateast the self-enhancement depends on the initial dif-raction efficiency. Maximum self-enhancement,


hich was generally achieved after 1 day, is shown inig. 8 for different dichromate concentrations. Self-nhancement is highest when the lowest dichromateoncentration is used, because the self-enhancementate is then the highest as well, as seen in Fig. 9.

The influence of the exposure energy on the self-nhancement coefficient is shown in Fig. 10 for pH 5.83 and pH 5 8.13. For lower pH the self-

enhancement is strongly dependent on the exposureenergy, but for higher pH only a slight change in theself-enhancement coefficient is found when the expo-sure energy is increased. For the pH near 5 that isnormally used with DCPVA the self-enhancement ishighest, when the exposure energy is lowest ~the firstpoint in the figure!. This energy corresponds to theexposure energy long before the saturation in thediffraction efficiency is reached during the exposure.When the exposure energy is near the saturationenergy, the self-enhancement coefficient is lower.

The rate of the self-enhancement calculated for thesame films as in Fig. 10 is shown in Fig. 11. Thevalues respond to the change in the diffraction effi-

Fig. 7. Self-enhancement coefficient as a function of the timeafter recording for different dichromate concentrations.

Fig. 8. Self-enhancement coefficient as a function of dichromateconcentration.

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ciency during the first day after the recording. Forlower pH the rate of the increase in the diffractionefficiency is highest for the lowest exposure energy.For higher pH value the rate was almost independentof the exposure energy used. But the rate is clearly

Fig. 9. Self-enhancement rate as a function of dichromate con-centration.

Fig. 10. Self-enhancement coefficient as a function of exposureenergy; ~a! pH 5 4.83, ~b! pH 5 8.13.

Fig. 11. Self-enhancement rate as a function of exposure energy.

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higher for higher pH, as is the self-enhancement co-efficient. The self-enhancement rate versus. thetime immediately after the recording is shown in Fig.12. The rate of change in the diffraction efficiency isfastest during the first 200 s after the exposure andafter that decreases more slowly. The amount ofCr~V! ions will reduce strongly at first, thus decreas-ng the self-enhancement rate later. The maximumn the self-enhancement is achieved in 1 day as seenbove.In our experiments the initial diffraction efficiency,

he efficiency just after the exposure, has been chang-ng, as is normal. Figure 13 shows the dependencef the self-enhancement coefficient on the initial dif-raction efficiency. The curve is the second-orderolynomial fit to the measurement points. Whenhere have also been less reductions from Cr~V! tor~III! during the exposure, there is an evident ten-ency for the gain to be higher if the initial diffractionfficiency has been lower. The measurements of theependence between the exposure energy and theelf-enhancement together with the dependence ofhe self-enhancement on the initial diffraction effi-

Fig. 12. Self-enhancement coefficient as a function of time.

Fig. 13. Self-enhancement coefficient as a function of initial dif-fraction efficiency.


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ciency show the usefulness of the self-enhancementeffect. By using lower exposure energies or wheninitial diffraction efficiencies are low, higher final dif-fraction efficiencies can be achieved because of theself-enhancement effect.

By using holographic characterization and electronspin resonance spectroscopic studies, Manivannan et

l.4,6 showed the evolution of chromium ions in dif-ferent stages of the irradiation and verified that thedark reaction plays a minor role in the formation ofthe Cr~V! ions. Further, Bolte et al.7 showed thatCr~V! changes to Cr~III! slowly and that the light onlyslightly accelerates the process. Lelievre and Cou-ture1 also detected a low increase in diffraction effi-ciency for DCPVA after the exposure was stopped.They deduced that this temporal grating growth wasdue to the incomplete photo-cross-linking process.Newell et al.8 believed that phase modulation ob-tained in dichromated-gelatin holograms after stor-age is produced by a mechanism similar to that foundin dichromated-gelatin holograms washed in waterafter exposure but not fully developed by means ofdrying in isopropanol. In the exposed regions thegelatin is hardened by Cr~III! ions formed during pho-tochemical reactions. When an exposed gelatinlayer is placed in an atmosphere of increased relativehumidity, it will absorb water and swell. Because ofthe hardening process, it will swell less in exposedregions than in unexposed regions. This differentialswelling is seen to be the reason for the phase mod-ulation. The phase modulation is in phase with theabsorption modulation. However, in our experi-ments with DCPVA there has not been differentialswelling during the storage after the exposure, andthis does not, therefore, explain the observed self-enhancement effect.

Our experiments show that there is a strong darkself-enhancement effect in DCPVA gratings after theirradiation has been stopped. This self-enhancementmay be due to

1. Dark reaction: Cr~VI! continues to reduce toCr~V! after the irradiation. It is known that Cr~VI! isonsumed slowly during the photochemical reactionnduced during the exposure. This oxidation reac-ion takes place in the whole sensitized film indepen-ent of the irradiation level. But all Cr~V! formed

during the exposure is also not reduced to Cr~III! dur-ing this exposure, and this reduction continues in thedark. This reduction is larger in the more-exposedregions than in the less-exposed regions and thenumber of cross-linkages between Cr~III! and the

olymer, and thus the index modulation increases,nducing an increase in the diffraction efficiency.

2. Diffusion: Cr~III!, unreacted Cr~VI!, or Cr~V!may diffundate from the less-exposed regions to themore-exposed regions. Diffusion of Cr~III! ions ispossible only if all Cr~III! ions are not bounded in thecross linkages. Diffusive processes are known to ex-ercise an influence on both the long-range migrationof reactive species from dark to bright areas and onthe short-range diffusion of the same species to the


initiating centers or to the reactive sites of the mac-roradicals.

3. Polymerization: The polymerization was notcompleted during the drying period. During the ex-posure there exist the polymerizations of vinyl mono-mers initiated by coordination complexes such asCr~VI! or Cr~III!. Polymerization continues after ex-posure, bringing, together with Cr~III! ions, new cross-inkages, which are responsible of the gratingormation.

4. Stress: The internal stress of the coating in-reases with decreasing relative humidity duringrying and exposure periods. If the coating expandsy absorbing moisture at room temperature, the in-ernal strain is relaxed. Also, when a cross-linkingeaction is interrupted, the internal stress of the coat-ng decreases. When stresses are relaxed, they maynduce cracks such as those in dichromated gelatinuring the isopropanol treatment. The addition ofigments increases Young’s modulus as well as thenternal stress of the coating. Thus the internaltress increases in proportion to the concentration.

ecause films with low dichromate concentration hadigher self-enhancement in our experiments, the in-ernal stress or its relaxation cannot be the primaryeason for the self-enhancement effect. Self-nhancement was also observed in dichromated gel-tin where it was even stronger, and therefore theolymerization does not seem to be the reason for theffect. All the observations presented in this paperherefore go together to suggest that the dark reac-ion of the chromium ion is mainly responsible for theelf-enhancement of the holographic grating inCPVA.It is generally accepted that the dark reaction be-

ore exposure is less effective in high-pH conditions.n our experiments the self-enhancement, the in-rease in diffraction efficiency after the exposure,as, however, been higher when the pH was higher.herefore the light, and not the dark reaction, is

mportant in initiating the reduction from Cr~VI! toCr~V!. But after the recording Cr~V! also changes toCr~III! in the dark, thus increasing the diffractionfficiency after the exposure over time. This is ingreement with the studies of Manivannan et al.4,6 on

the role of different chromium ions during the expo-sure and with the observations of Bolte et al.7 on thehromium-ion evolution after the exposure. Aodel of the processes is shown in Fig. 14. In thisodel the dark reaction at the second stage in theajor pathway is seen as being essential when we

onsider the self-enhancement effect. It must beoted that this dark reaction takes place after thexposure is stopped. The pathway from Cr~VI! to

Cr~III! by means of a light-induced reduction fromr~VI! to Cr~V! and then a dark reaction from Cr~V! to

Cr~III! is quite effective, causing the dark self-enhancement effect. Even with the presence of theslight diffusion of unreacted species or of the furtherpolymerization initiated by Cr~III! the reduction reac-ion in the dark at the second stage is essential.

4. G. Manivannan, R. Changkakoti, and R. A. Lessard, “Primary

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4. Summary and Conclusions

In this paper we have presented the self-enhancement of the holographic gratings in DCPVAfilms during storage in the dark. The maximumself-enhancement gain was 6. The dark reactionduring the limited time after the recording did notdistort the diffraction efficiency of the grating butincreased it. This effect offers the possibility of us-ing DCPVA films in real-time measurements forlonger periods. It also offers the possibility of usinglower exposure energies as holograms are recordedand thus allows for vibration-free recordings.

Tuula Keinonen thanks the French Government,the Magnus Ehrnrooth Foundation of the FinnishScience Society, and the North Carelian Foundationof the Finnish Cultural Foundation for financial sup-port. Thanks are also due to Lisa Leonard. Herpresence helped in many situations during the study,especially with the linguistic and the practical prob-lems.

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3. M. Barikani, E. Simova, and M. Kavehrad, “Dichromated poly-vinyl alcohol for the real-time hologram recording: effect ofhumidity,” Opt. Mater. 4, 477–485 ~1995!.

Fig. 14. Reductions of dichromate ions during and after the ex-posure.

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photoprocesses of Cr~VI! in real-time holographic recording ma-terial: dichromated poly~vinyl alcohol!,” J. Phys. Chem. 97,7228–7233 ~1993!.

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dark self-enhancement in dichromated poly(vinyl alcohol) gratings: a detailed study

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