- Email: [email protected]
Influence of spurious gratings on reprocessibility of dichromated gelatin reflection gratings
June 1994
~TDCAL ELSEVIER
Optical Matenals3 (1994) 151—155
Influence of spurious gratings on reprocessibility of dichromated gelatin reflection gratings Tuula Keinonen Physics Institut, Applied Optics, University ofErlangen-Nuremberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
Päivi Riihola Department ofPhysics, University of Joensuu,
P.O. Box 111, SF-80101 Joensuu,
Finland
Received 28 July 1993; revised manuscript received 20 November 1993
Abstract Reflection gratings were recorded in dichromated gelatin with different exposure energies. These gratings were reprocessed after storing them unprotected under laboratory conditions for three years. Reprocessibilityis observed to be dependent on the 2 than in the other exposure energies. It is suggested, exposure energy. It is higher in the exposure energy range (50—100) mJ/cm that this phenomenon is due to the presence ofthe spurious transmission gratings besides the primary reflection grating. These spurious gratings improve the reprocessibility ofthe dichromated gelatin reflection gratings.
1. Introduction Simultaneously when reflection gratings are recorded also multiple gratings are formed in the recording medium, due to internal reflections [1—5]. Matched boundary conditions are not satisfied at recording when no index matching is used. This is very often the case in practical applications of holographic optical elements when index-matching liquid cannot be used at recording. Sometimes these spurious gratings may be eliminated by using special recording conditions [6]. Spurious gratings are generally regarded only as a disadvantage, which cause unwanted noise. However, in our previous study concerning dichromated
sion gratings bind the reflective planes tighter together. These intersecting planes make the structure ofthe reflection gratings more rigid and stable during different steps of development processes. Dichromated gelatin, as well known, can be reprocessed. The reprocessibility or restoration of transmission gratings is presented by Chang [8] and the reprocessibility of methylene blue sensitized dichromated gelatin is studied by Changkakoti and Pappu [9]. We have studied the reprocessibility of dichromated gelatin reflection gratings in our previous work [101. After three years storage the reflection efficiency (RE, the ratio of the diffracted intensity and the incoming intensity) of the gratings was very low. By reprocessing reflection efficiency has been in-
gelatin reflection gratings, we have concluded that the
creased to the original reflection efficiency level. In
presence of the spurious gratings can improve the quality ofthe reflection gratings, due to the increased stability [7]. Because the transmission grating planes intersect the reflection grating planes the transmis-
this work we show that the reprocessibility ofdichromated gelatin reflection gratings is dependent on the exposure energy used at the recording.
0925-3467/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0925-3467(94)00003-9
152
T. Keinonen, P. Riihola /Optical Materials 3(1994)151—155
2. Experimentaldetails Reflection gratings were recorded in dichromated gelatin by using the wavelength of 488 nm of an Arlaser. The laser beams entered the gelatin plate from opposite sides at the angles of 250 and 300. The angles differed to prevent the overlapping ofthe surface reflections with the first order diffraction. Because of the recording geometry six different gratings are formed inside the gelatin due to the reference and signal beams as also due to internal reflections [7]. Four of these gratings are reflection gratings and two are transmission gratings relative to the replay beam. One of the reflection gratings is regarded as a primary grating and almost all of the incoming intensity is replayed from this grating. Also further spurious gratings are formed due to the mismatch of the refractive indices of the glass and the dichromated gelatin. However the diffractions from these gratings are weak, since the index modulations are low, Dichromated gelatin was prepared from Kodak 649F spectroscopic plates. Silver halides were removed by using fixer. The soaking time in fixer was 15 minutes. After washing the fixer away in running water for 10 minutes, the gelatin plate was dried in methanol. After being 10 minutes in this first methanol solution the plate was soaked in clean methanol for 10 minutes. Finally the plates were dried in open air in vertical position at least 12 hours [11—13]. Next day the gelatin was sensitized to blue light by using ammoniumdichromate (5%) solution. The soaking time in ammoniumdichromate was 5 mmutes. Photo Flow was used to lower the surface tension and thus increase the homogeneity ofthe gelatin plate and also the homogeneity of the sensitization process. After drying in horizontal position in air (under the humidity of 40%) over night the plates were exposed with two plane waves by using exposure energies from 10 mJ/cm2 to 220 mi/cm2. The beam ratio was ito 1.7 and the diameterofthe beams was about one centimeter. The exposed plates were developed in water and isopropanol baths, thus no posthardening was used. The soaking time in runfling water was 10 minutes. Dehydration was performed gradually in 50%, 90% and 100% isopropanol solutions the soaking times being 3, 3 and 10 minutes respectively. The processed plates were left to dry in air in horizontal position over night.
Reflection efficiency was measured one day, one year and three years after the development. The gelatm plates including the reflection gratings were stored unprotected in tiny envelopes in an archive box under laboratory conditions. After three years storage the plates were reprocessed by using the same process as in the original development. One day after the reprocessing reflection efficiency was measured again. Processing procedure described above was chosen for reprocessing because the reproducibility of the recordings is highest by using this process. Different processing procedures are studied detailed in our previous papers [13,14].
3. Results and discussion Maximum reflection efficiency of the recorded dichromated gelatin gratings was about 85% measured one day after the development. After one year storage the reflection efficiency has been measured again. In Fig. 1 the absolute decrease in reflection efficiency during a storage of one year, ~ ~2, where ~ is the original RE and ‘12 is the RE after one year storage), is displayed as a function ofexposure energy. The reflection efficiency of all the gratings decreased. The decrease is largest in the exposure energy range of (40—100) mi/cm2, the maximum decrease being near 40%. Several gratings are measured for each point, which is shown. In our previous studies we have noticed that there exists a slight reflection efficiency maximum in the exposure energy range (50—100) mJ/cm2 [7]. After reprocessing the same behaviour is to be obtained and it is shown in Fig. 2, where the reprocessed reflection —
50
-
20
-
[~ o F 0
50
100
150
200
Exposure energy (mJ/cm2) Fig. 1. Decrease in reflection efficiency (RE) during one year storage versus exposure energy.
T Keinonen. P. Riihola / Optical Materials 3 (1994) 151—155
slightly higher than in the above mentioned exposure
SO 60
/7
.
/ /
40
5’
20
.[
0
j’’’’
0
50
‘‘
I
100
150
200
250
2) Exposure energy (mi/cm Fig. 2. Restored reflection efficiency (RE) versus exposure energy. Restoration is done after three years storage. 04
\
0.3 0,2
153
__________________
where
ii~is the
original reflection efficiency and ~l3~S
in Fig. 4 (some additional measurements are also culated).Therestionisbetween8O%andl20°k reflection efficiency is nearly the onginal reflection
.
-0,2 0
—
the reprocessed reflection efficiency as in the previous chapter, too. The restoration of the reflection gratings calculated from the values of Fig. 3 is shown
________
-
-o,i
energyenergies. range. The relative the change is positive for these other However reflection efficiency is also for these energies relatively high after reprocessing. Thus reflection gratings can be reprocessed to the original reflection efficiency level with the good reproducibility. The restoration R [9] can be defined as R(%)=(l ‘1i ‘13)x 100%, (1)
50
100 150 200 Exposure energy (mJ/cm2)
250
Fig. 3. Relative change in reflection efficiency (RE) during restoration versus exposure energy.
efficiency is displayed as a function of the exposure energy. The maximum reflection efficiency (about 70% in the exposure energy 60 mJ/cm2) may be decreased due to the slant, which is present in the gratings due to the different recording angles. The differencebetween the beams was and therefore the slant was small. The well known static theory [15] does not explain the decrease in reflection efficiency when
efficiency or even higher. The restoration versus the exposure energy curve has a maximum at the exposure energies near 70 mJ/cm2. Thus near this exposure energy the reprocessing improves the reflection efficiency of dichromated gelatin reflection grating. According to the static theory it is expected that the reflection efficiency of dichromated gelatin gratings increases, when the exposure energy increases [15]. Reflection efficiency for a lossless dielectric grating is ‘1= 1/ [1 + (1 _.~2/v2)/sh2(v2—~2) 1/2] (2)
50
where urn 1d
the exposure energy and thus the index modulation increases. The relative change in reflection efficiency between the original and reprocessed reflection efficiencies is shown in Fig. 3. The relative change is defined as (‘11—’13)/’1I, where q~ is the reflection efficiency after the original development and ‘13 is the reprocessed reflection efficiency. The relative change in reflection efficiency has its minimum (negative value) in the exposurereflection energy range (40—120) mJ/ 2. The reprocessed efficiency is higher cm the original reflection efficiency, when these exthan posure energies are used. At higher and lower energies the relative change in reflection efficiency is
(3)
V= S
20 .
~ioo 5 80 60
0
I
I
50
100
I
150
200
250
Exposure energy (mJ/cm2) Fig. 4. Restoration of reflection gratings versus exposure energy.
154
~=z~0Kdsin(00—Ø)/2c5.
T Keinonen, P. Riihola / Optical Materials 3(1994) 151—155
(4)
In these equations n1 is the index modulation, dis the grating thickness, A is the wavelength, CR and cs are the slant factors, 0 is the slant angle, 0~is the Bragg angle, K is the grating period and .1~s0is the deviation from the Bragg angle. The equations are valid for an unslanted and a slanted grating. Reflection efficiency depends on the loss ofthe grating as also on the slant. The loss in the grating reduces reflection efficiency of a dielectric grating. Reflection efficiency of a lossy dielectric grating decreases when the slant increases. The increase in the loss has the same influence. Inwave the static theory only two waves, the reconstructing and the first order diffracted wave are assumed to be present in the replay. For Bragg incidence the Eq. (2) simplifies to = th~ v.
(5)
Reflection efficiency rapidly increases to 100% remaining then constant with a further increase of the index modulation. The spurious transmission gratings have the strongest influence on the properties of reflection gratings in the exposure energy range (50—100) mJ/ cm2 as presented previously [7]. It is shown that the interference planes due to these spurious transmission gratings make the structure of the primary reflection grating more stable during the development processes. In this exposure energy range the thickness of the grating and thus the Bragg angle ofthe grating has not been changed remarkably during the development processes. The structure ofthe reflection grating may be disturbed during the storage decreasing the reflection efficiency as seen in Fig. 1. The decrease in reflection efficiency is largest in the exposure energy range (50—100) mJ/cm2. This phenomenon can be explained by the presence of the spurious transmission gratings. During the storage the changes in the environmental conditions are very strong in our laboratory. The relative humidity changes between 20% and 80% during a year. The changes can be strong enough that the diffracting planes of the spurious gratings can be partly broken. Thus the regular structure of the grating is broken and the index modulation deteriorates causing the reflection efficiency to decrease. This effect, however, is not strong enough
to destroy the whole information included in the grating because the gratings can be reprocessed to the original reflection efficiency level. After three years storage the reflection efficiency of our dichromated gelatin gratings is decreased strongly. Because of the very low reflection efficiency we cannot notice anything about the variations in the reflection efficiency as a function of the exposure energy after three years storage. By reprocessing the original reflection efficiency level is reached very well and there exists a small maximum in the reprocessed reflection efficiency in the energy (50— 2 (Fig. 2). exposure We suggest that range this maximum due to the stable structure of the reflection 100) is mJ/cm grating, due to the presence ofthe spurious transmission gratings in this exposure energy range. It is noticeable that this effect exists still after several swelling and shrinking processes both in the developments and during the storage. The maximum at (50—100) mJ/cm2 and the following minimum (Fig. 2) are even slightly larger after the reprocessing than after the development and before the storage. The relative change in reflection efficiency has a minimum as shown in Fig. 3 in the same exposure energy range where the maximum ofthe reprocessed reflection efficiency exists (Fig. 2). The negative sign indicates here that the reflection efficiency after reprocessing is higher than the original reflection efficiency measured one day after exposure, [(~j~ ~) / ~ 1 <0 and thus ij~<173. In the same way the positive sign indicates that the original reflection efficiency is not reached by reprocessing. The relative changes are small but the differences between different exposure energies are clearly seen. We suggest that this behaviour is due to the spurious transmission gratings. In the exposure energy range (50—100) mJ/cm2 these spurious transmission gratings are most significant because these exposure energies correspond to the first diffraction efficiency maximum of the transmission gratings [12,161. The intersecting interference planes due to these transmission gratings make the structure of the reflection grating more flexible. The stored information of the gratings is not destroyed although the reflection efficiency decreases. The intersecting planes due to transmission gratings bind the reflecting planes tighter together and the maximum and the minimum distances ofthe reflecting planes are limited by the spurious gratings. Inside —
T Keinonen, P. Riihola / Optical Materials 3 (1994) 15 1—155
these boundaries the grating can change its thickness without losing the important information. The reflection gratings in this exposure energy range can be reprocessed better than the gratings recorded by using other exposure energies. This difference in reprocessing between different exposure energies explains also the larger maximum and minimum in Fig. 2 compared to the original reflection efficiency curve [7]. In the other energy ranges, where no transmission gratings exist or their influence is very small, the distance between reflecting planes can increase in swelling so large that the structure of the grating will be disturbed. The shrinkage of the gelatin can also be so strong that the distance between the reflecting planes decreases so much that it disturbs the grating structure. The spurious gratings cause also unwanted noise, but the noise is very low compared to the first order diffraction. The presence of the spurious gratings cannot be seen only as a disadvantage. They also improve the stability of the reflection gratingduring the development processes and against the environmental changes. As shown in the previous figures they also improve the reprocessing properties of reflection gratings.
4. Conclusions Reflection gratings recorded in dichromated gelatin with different exposure energies have been reprocessed after three years storage. It is noticed that the restoration is very high and that it depends on the exposure energy used at the recording. The relative change in reflection efficiency during the reprocessing has its minimum in the exposure energy range (50—100) mi/cm2 and so the restoration is the highest in this exposure energy range. Therefore it is verified that there are spurious transmission gratings
155
present at the primary reflection grating making the structure of the grating more stable to different changes in both environmental conditions as also during the developing processes. These spurious gratings improve the reprocessing properties of dichromated gelatin reflection gratings.
Acknowledgements The authors would like to thank the Academy of Finland and the Fund of Yliopistoseuran Naiset at the North-Karelian Fund of the Finnish Cultural Fund. Thanks to S. Haselbeck (University of Erlangen, Applied Optics) for helping in preparing the manuscript.
References [1] L.T. Blair, J. Takacs and L. Solymar, J. Mod. Optics 36
(1989) 83.
[2] M.P. Owen, A.A. Ward and L. Solymar, Appl. Optics 22 (1983) 159. [31J.W. Lewis and L. Solymar, Optics Comm. 47 (1983) 23. [4] T.Ya. Kalnitskaya and V.V. Smirnov, Opt. Spectrosc. 61 (1986) 250. [51yB. Konstantinov, Yu.F. Romanov, A.F. Rykhlov and A.Yu. Tropchenko, Soy. Phys. Tech. Phys. 27 (1982) 1134. [6] S. Sjolinder,OpticaActa3l (1984) 1013. [7] T. Keinonen and 0. Salminen, J. Mod. Optics 40 (1993) 1449.
[8] B.J. Chang, Optics Comm.
17 (1976) 270. [9] R. Changkakoti and S.V. Pappu, Appl. Optics 28 (1989) [10] T. Keinonen and P. Riihola, J. Mod. Optics 40 (1993) 2125. [11] D. Meyerhofer, RCA Review 23 (1972) 110. [12] B.J. Chang and CD. Leonard, Appl. Optics 18 (1979) 2407. [13] T. Keinonen and 0. Salminen, Appl. Optics 27 (1988) 2573. [14] 0. Salminen and T. Keinonen, J. Mod. Optics 36 (1989) [15] H. Kogelnik, Bell Syst. Tech. J. 48 (1969) 2909. [16] T. Keinonen and 0. Salminen, Publication of U. Joensuu, Series Bi, No.23 (1982).
~TDCAL ELSEVIER
Optical Matenals3 (1994) 151—155
Influence of spurious gratings on reprocessibility of dichromated gelatin reflection gratings Tuula Keinonen Physics Institut, Applied Optics, University ofErlangen-Nuremberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
Päivi Riihola Department ofPhysics, University of Joensuu,
P.O. Box 111, SF-80101 Joensuu,
Finland
Received 28 July 1993; revised manuscript received 20 November 1993
Abstract Reflection gratings were recorded in dichromated gelatin with different exposure energies. These gratings were reprocessed after storing them unprotected under laboratory conditions for three years. Reprocessibilityis observed to be dependent on the 2 than in the other exposure energies. It is suggested, exposure energy. It is higher in the exposure energy range (50—100) mJ/cm that this phenomenon is due to the presence ofthe spurious transmission gratings besides the primary reflection grating. These spurious gratings improve the reprocessibility ofthe dichromated gelatin reflection gratings.
1. Introduction Simultaneously when reflection gratings are recorded also multiple gratings are formed in the recording medium, due to internal reflections [1—5]. Matched boundary conditions are not satisfied at recording when no index matching is used. This is very often the case in practical applications of holographic optical elements when index-matching liquid cannot be used at recording. Sometimes these spurious gratings may be eliminated by using special recording conditions [6]. Spurious gratings are generally regarded only as a disadvantage, which cause unwanted noise. However, in our previous study concerning dichromated
sion gratings bind the reflective planes tighter together. These intersecting planes make the structure ofthe reflection gratings more rigid and stable during different steps of development processes. Dichromated gelatin, as well known, can be reprocessed. The reprocessibility or restoration of transmission gratings is presented by Chang [8] and the reprocessibility of methylene blue sensitized dichromated gelatin is studied by Changkakoti and Pappu [9]. We have studied the reprocessibility of dichromated gelatin reflection gratings in our previous work [101. After three years storage the reflection efficiency (RE, the ratio of the diffracted intensity and the incoming intensity) of the gratings was very low. By reprocessing reflection efficiency has been in-
gelatin reflection gratings, we have concluded that the
creased to the original reflection efficiency level. In
presence of the spurious gratings can improve the quality ofthe reflection gratings, due to the increased stability [7]. Because the transmission grating planes intersect the reflection grating planes the transmis-
this work we show that the reprocessibility ofdichromated gelatin reflection gratings is dependent on the exposure energy used at the recording.
0925-3467/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0925-3467(94)00003-9
152
T. Keinonen, P. Riihola /Optical Materials 3(1994)151—155
2. Experimentaldetails Reflection gratings were recorded in dichromated gelatin by using the wavelength of 488 nm of an Arlaser. The laser beams entered the gelatin plate from opposite sides at the angles of 250 and 300. The angles differed to prevent the overlapping ofthe surface reflections with the first order diffraction. Because of the recording geometry six different gratings are formed inside the gelatin due to the reference and signal beams as also due to internal reflections [7]. Four of these gratings are reflection gratings and two are transmission gratings relative to the replay beam. One of the reflection gratings is regarded as a primary grating and almost all of the incoming intensity is replayed from this grating. Also further spurious gratings are formed due to the mismatch of the refractive indices of the glass and the dichromated gelatin. However the diffractions from these gratings are weak, since the index modulations are low, Dichromated gelatin was prepared from Kodak 649F spectroscopic plates. Silver halides were removed by using fixer. The soaking time in fixer was 15 minutes. After washing the fixer away in running water for 10 minutes, the gelatin plate was dried in methanol. After being 10 minutes in this first methanol solution the plate was soaked in clean methanol for 10 minutes. Finally the plates were dried in open air in vertical position at least 12 hours [11—13]. Next day the gelatin was sensitized to blue light by using ammoniumdichromate (5%) solution. The soaking time in ammoniumdichromate was 5 mmutes. Photo Flow was used to lower the surface tension and thus increase the homogeneity ofthe gelatin plate and also the homogeneity of the sensitization process. After drying in horizontal position in air (under the humidity of 40%) over night the plates were exposed with two plane waves by using exposure energies from 10 mJ/cm2 to 220 mi/cm2. The beam ratio was ito 1.7 and the diameterofthe beams was about one centimeter. The exposed plates were developed in water and isopropanol baths, thus no posthardening was used. The soaking time in runfling water was 10 minutes. Dehydration was performed gradually in 50%, 90% and 100% isopropanol solutions the soaking times being 3, 3 and 10 minutes respectively. The processed plates were left to dry in air in horizontal position over night.
Reflection efficiency was measured one day, one year and three years after the development. The gelatm plates including the reflection gratings were stored unprotected in tiny envelopes in an archive box under laboratory conditions. After three years storage the plates were reprocessed by using the same process as in the original development. One day after the reprocessing reflection efficiency was measured again. Processing procedure described above was chosen for reprocessing because the reproducibility of the recordings is highest by using this process. Different processing procedures are studied detailed in our previous papers [13,14].
3. Results and discussion Maximum reflection efficiency of the recorded dichromated gelatin gratings was about 85% measured one day after the development. After one year storage the reflection efficiency has been measured again. In Fig. 1 the absolute decrease in reflection efficiency during a storage of one year, ~ ~2, where ~ is the original RE and ‘12 is the RE after one year storage), is displayed as a function ofexposure energy. The reflection efficiency of all the gratings decreased. The decrease is largest in the exposure energy range of (40—100) mi/cm2, the maximum decrease being near 40%. Several gratings are measured for each point, which is shown. In our previous studies we have noticed that there exists a slight reflection efficiency maximum in the exposure energy range (50—100) mJ/cm2 [7]. After reprocessing the same behaviour is to be obtained and it is shown in Fig. 2, where the reprocessed reflection —
50
-
20
-
[~ o F 0
50
100
150
200
Exposure energy (mJ/cm2) Fig. 1. Decrease in reflection efficiency (RE) during one year storage versus exposure energy.
T Keinonen. P. Riihola / Optical Materials 3 (1994) 151—155
slightly higher than in the above mentioned exposure
SO 60
/7
.
/ /
40
5’
20
.[
0
j’’’’
0
50
‘‘
I
100
150
200
250
2) Exposure energy (mi/cm Fig. 2. Restored reflection efficiency (RE) versus exposure energy. Restoration is done after three years storage. 04
\
0.3 0,2
153
__________________
where
ii~is the
original reflection efficiency and ~l3~S
in Fig. 4 (some additional measurements are also culated).Therestionisbetween8O%andl20°k reflection efficiency is nearly the onginal reflection
.
-0,2 0
—
the reprocessed reflection efficiency as in the previous chapter, too. The restoration of the reflection gratings calculated from the values of Fig. 3 is shown
________
-
-o,i
energyenergies. range. The relative the change is positive for these other However reflection efficiency is also for these energies relatively high after reprocessing. Thus reflection gratings can be reprocessed to the original reflection efficiency level with the good reproducibility. The restoration R [9] can be defined as R(%)=(l ‘1i ‘13)x 100%, (1)
50
100 150 200 Exposure energy (mJ/cm2)
250
Fig. 3. Relative change in reflection efficiency (RE) during restoration versus exposure energy.
efficiency is displayed as a function of the exposure energy. The maximum reflection efficiency (about 70% in the exposure energy 60 mJ/cm2) may be decreased due to the slant, which is present in the gratings due to the different recording angles. The differencebetween the beams was and therefore the slant was small. The well known static theory [15] does not explain the decrease in reflection efficiency when
efficiency or even higher. The restoration versus the exposure energy curve has a maximum at the exposure energies near 70 mJ/cm2. Thus near this exposure energy the reprocessing improves the reflection efficiency of dichromated gelatin reflection grating. According to the static theory it is expected that the reflection efficiency of dichromated gelatin gratings increases, when the exposure energy increases [15]. Reflection efficiency for a lossless dielectric grating is ‘1= 1/ [1 + (1 _.~2/v2)/sh2(v2—~2) 1/2] (2)
50
where urn 1d
the exposure energy and thus the index modulation increases. The relative change in reflection efficiency between the original and reprocessed reflection efficiencies is shown in Fig. 3. The relative change is defined as (‘11—’13)/’1I, where q~ is the reflection efficiency after the original development and ‘13 is the reprocessed reflection efficiency. The relative change in reflection efficiency has its minimum (negative value) in the exposurereflection energy range (40—120) mJ/ 2. The reprocessed efficiency is higher cm the original reflection efficiency, when these exthan posure energies are used. At higher and lower energies the relative change in reflection efficiency is
(3)
V= S
20 .
~ioo 5 80 60
0
I
I
50
100
I
150
200
250
Exposure energy (mJ/cm2) Fig. 4. Restoration of reflection gratings versus exposure energy.
154
~=z~0Kdsin(00—Ø)/2c5.
T Keinonen, P. Riihola / Optical Materials 3(1994) 151—155
(4)
In these equations n1 is the index modulation, dis the grating thickness, A is the wavelength, CR and cs are the slant factors, 0 is the slant angle, 0~is the Bragg angle, K is the grating period and .1~s0is the deviation from the Bragg angle. The equations are valid for an unslanted and a slanted grating. Reflection efficiency depends on the loss ofthe grating as also on the slant. The loss in the grating reduces reflection efficiency of a dielectric grating. Reflection efficiency of a lossy dielectric grating decreases when the slant increases. The increase in the loss has the same influence. Inwave the static theory only two waves, the reconstructing and the first order diffracted wave are assumed to be present in the replay. For Bragg incidence the Eq. (2) simplifies to = th~ v.
(5)
Reflection efficiency rapidly increases to 100% remaining then constant with a further increase of the index modulation. The spurious transmission gratings have the strongest influence on the properties of reflection gratings in the exposure energy range (50—100) mJ/ cm2 as presented previously [7]. It is shown that the interference planes due to these spurious transmission gratings make the structure of the primary reflection grating more stable during the development processes. In this exposure energy range the thickness of the grating and thus the Bragg angle ofthe grating has not been changed remarkably during the development processes. The structure ofthe reflection grating may be disturbed during the storage decreasing the reflection efficiency as seen in Fig. 1. The decrease in reflection efficiency is largest in the exposure energy range (50—100) mJ/cm2. This phenomenon can be explained by the presence of the spurious transmission gratings. During the storage the changes in the environmental conditions are very strong in our laboratory. The relative humidity changes between 20% and 80% during a year. The changes can be strong enough that the diffracting planes of the spurious gratings can be partly broken. Thus the regular structure of the grating is broken and the index modulation deteriorates causing the reflection efficiency to decrease. This effect, however, is not strong enough
to destroy the whole information included in the grating because the gratings can be reprocessed to the original reflection efficiency level. After three years storage the reflection efficiency of our dichromated gelatin gratings is decreased strongly. Because of the very low reflection efficiency we cannot notice anything about the variations in the reflection efficiency as a function of the exposure energy after three years storage. By reprocessing the original reflection efficiency level is reached very well and there exists a small maximum in the reprocessed reflection efficiency in the energy (50— 2 (Fig. 2). exposure We suggest that range this maximum due to the stable structure of the reflection 100) is mJ/cm grating, due to the presence ofthe spurious transmission gratings in this exposure energy range. It is noticeable that this effect exists still after several swelling and shrinking processes both in the developments and during the storage. The maximum at (50—100) mJ/cm2 and the following minimum (Fig. 2) are even slightly larger after the reprocessing than after the development and before the storage. The relative change in reflection efficiency has a minimum as shown in Fig. 3 in the same exposure energy range where the maximum ofthe reprocessed reflection efficiency exists (Fig. 2). The negative sign indicates here that the reflection efficiency after reprocessing is higher than the original reflection efficiency measured one day after exposure, [(~j~ ~) / ~ 1 <0 and thus ij~<173. In the same way the positive sign indicates that the original reflection efficiency is not reached by reprocessing. The relative changes are small but the differences between different exposure energies are clearly seen. We suggest that this behaviour is due to the spurious transmission gratings. In the exposure energy range (50—100) mJ/cm2 these spurious transmission gratings are most significant because these exposure energies correspond to the first diffraction efficiency maximum of the transmission gratings [12,161. The intersecting interference planes due to these transmission gratings make the structure of the reflection grating more flexible. The stored information of the gratings is not destroyed although the reflection efficiency decreases. The intersecting planes due to transmission gratings bind the reflecting planes tighter together and the maximum and the minimum distances ofthe reflecting planes are limited by the spurious gratings. Inside —
T Keinonen, P. Riihola / Optical Materials 3 (1994) 15 1—155
these boundaries the grating can change its thickness without losing the important information. The reflection gratings in this exposure energy range can be reprocessed better than the gratings recorded by using other exposure energies. This difference in reprocessing between different exposure energies explains also the larger maximum and minimum in Fig. 2 compared to the original reflection efficiency curve [7]. In the other energy ranges, where no transmission gratings exist or their influence is very small, the distance between reflecting planes can increase in swelling so large that the structure of the grating will be disturbed. The shrinkage of the gelatin can also be so strong that the distance between the reflecting planes decreases so much that it disturbs the grating structure. The spurious gratings cause also unwanted noise, but the noise is very low compared to the first order diffraction. The presence of the spurious gratings cannot be seen only as a disadvantage. They also improve the stability of the reflection gratingduring the development processes and against the environmental changes. As shown in the previous figures they also improve the reprocessing properties of reflection gratings.
4. Conclusions Reflection gratings recorded in dichromated gelatin with different exposure energies have been reprocessed after three years storage. It is noticed that the restoration is very high and that it depends on the exposure energy used at the recording. The relative change in reflection efficiency during the reprocessing has its minimum in the exposure energy range (50—100) mi/cm2 and so the restoration is the highest in this exposure energy range. Therefore it is verified that there are spurious transmission gratings
155
present at the primary reflection grating making the structure of the grating more stable to different changes in both environmental conditions as also during the developing processes. These spurious gratings improve the reprocessing properties of dichromated gelatin reflection gratings.
Acknowledgements The authors would like to thank the Academy of Finland and the Fund of Yliopistoseuran Naiset at the North-Karelian Fund of the Finnish Cultural Fund. Thanks to S. Haselbeck (University of Erlangen, Applied Optics) for helping in preparing the manuscript.
References [1] L.T. Blair, J. Takacs and L. Solymar, J. Mod. Optics 36
(1989) 83.
[2] M.P. Owen, A.A. Ward and L. Solymar, Appl. Optics 22 (1983) 159. [31J.W. Lewis and L. Solymar, Optics Comm. 47 (1983) 23. [4] T.Ya. Kalnitskaya and V.V. Smirnov, Opt. Spectrosc. 61 (1986) 250. [51yB. Konstantinov, Yu.F. Romanov, A.F. Rykhlov and A.Yu. Tropchenko, Soy. Phys. Tech. Phys. 27 (1982) 1134. [6] S. Sjolinder,OpticaActa3l (1984) 1013. [7] T. Keinonen and 0. Salminen, J. Mod. Optics 40 (1993) 1449.
[8] B.J. Chang, Optics Comm.
17 (1976) 270. [9] R. Changkakoti and S.V. Pappu, Appl. Optics 28 (1989) [10] T. Keinonen and P. Riihola, J. Mod. Optics 40 (1993) 2125. [11] D. Meyerhofer, RCA Review 23 (1972) 110. [12] B.J. Chang and CD. Leonard, Appl. Optics 18 (1979) 2407. [13] T. Keinonen and 0. Salminen, Appl. Optics 27 (1988) 2573. [14] 0. Salminen and T. Keinonen, J. Mod. Optics 36 (1989) [15] H. Kogelnik, Bell Syst. Tech. J. 48 (1969) 2909. [16] T. Keinonen and 0. Salminen, Publication of U. Joensuu, Series Bi, No.23 (1982).