Abstract

Bulk polymer composites have been investigated in a two-beam interference exposure system of titanocene (Irgacure 784, BASF) (TI) molecules dispersed in poly(methyl methacrylate) (PMMA) substrates, which are created through an optimized three-step thermo-polymerization method, at a wavelength of 532 nm. As a property of PMMA photopolymers, the dark enhancement of grating formation is observed, which mainly corresponds to the diffusion of TI molecules. We also examine the influences of dark enhancement on Bragg angular selectivity that shifts after a long-time dark reaction. Single grating under continuous exposure was recorded in TI/PMMA photopolymers with a diffraction efficiency of 74% and response time of 20 s. An enhanced multiplexed grating was also obtained after a completely dark reaction with the cumulative grating strength of 6.88. Compared to bulk PQ/PMMA photopolymers in millimeter magnitude, TI/PMMA photopolymers are more competitive for further research on volume holographic memory storage.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Photosensitive phenanthrenequinone (PQ) dispersed PMMA holographic materials have been widely investigated [1–6]. The PMMA host matrix materials with high transmittance can be used to record transmission and reflection gratings [1–3]. This kind of photopolymer is regarded as a suitable holographic memory medium due to its memory stability and density [4–6]. Holographic performances in PQ/PMMA photopolymers are demonstrated with high diffraction efficiency, high thickness, and temporal stability of gratings [7–9]. Meanwhile, this holographic medium can also record transient information under ultrafast nanosecond pulse exposure [10,11]. All these researches provide a feasible analysis of PQ/PMMA materials in holographic memories. However, solubility limitation of PQ molecules (up to 1 wt%) in MMA solution leads to a limited grating strength and long-time response time. Titanocene (Irgacure 784, BASF) (TI) molecules are a kind of excellent visible-light photo-initiators with high solubility in MMA monomers. High sensitivity and solubility of TI molecules dissolved in organic solvents have been investigated [12–15]. As for PMMA matrix, the thermo-polymerization method is available for preparing TI/PMMA materials with good optical properties [16–18]. In our previous work [19], we proposed an optimized three-step thermos-polymerization method to prepare TI/PMMA photopolymer. This cationic initiator dispersed photopolymer (TI/PMMA) is a potential material for further researches in volume holographic memories.

As a bulk holographic material with high thickness (>1 mm), the dark enhancement of transmission gratings in PMMA matrix photopolymers is one of the remarkable material properties. This phenomenon makes the grating strength continue to increase after termination of exposures. The main contribution of dark enhancement in materials is the diffusion of photo-initiators from dark zones to bright zones [20,21]. The dark enhancement effect after short-time exposure can significantly decrease the holographic scattering and the photo-initiator consumptions compared with long-time continuous exposure. A single grating dark enhancement is an available method to obtain a high and stable refractive index modulation, which has been demonstrated in [22]. In consideration of high density angular multiplexing capability in PMMA matrix photopolymers, the multiplexing gratings can also be improved by the effect of dark diffusional enhancement. These holographic properties can be studied in detail in the presence of cationic photo-initiator TI molecules doped PMMA materials.

TI/PMMA photopolymers can be synthesized by a modified three-step thermo-polymerization method [19]. In this paper, we examine two approaches to improve the transmission grating strength in materials after short-time exposure, a consecutive exposure and a dark diffusional enhancement, respectively. An optimized photo-initiator doping concentration of the material is chosen. Then, the dark enhancement in the single grating and the multiplexing gratings recording are investigated and analyzed. The diffusion of photo-initiator in the dark enhancement process is quantitatively calculated. This process contributes to an improvement of grating strength and response time. Finally, we study the shift of Bragg angular selectivity curve after exposure, which aims at exploring the shrinkage properties of the materials. All these investigations provide an improvement on holographic performances by doping a new-type cationic photo-initiator (TI molecules) into PMMA matrix compared to bulk PQ/PMMA photopolymers in millimeter magnitude.

2. Materials and experiments

In the experiments, there are three main processes, pre-polymerization, high temperature polymerization and low temperature polymerization. Firstly, TI molecules with an optimized concentration of 4.0 wt% were dissolved into an MMA solvent at room temperature. In order to prepare the bulk polymer, the thermo-initiator 2, 2-azobis (2-methlpropionitrile) (AIBN) was also dissolved in the solvent with the concentration of 2.0 wt%. The mixture was stirred for 24 hours at 40 °C to become homogeneous. Then, the solution was filtered and poured into glass molds to be initiated at 73 °C for 15min. Finally, the viscous solution was solidified at 45 °C for 48h. After polishing, the sample with 3 mm thick was prepared. The optimized doping concentrations and fabrication conditions were obtained in our previous work [19]. In PQ/PMMA fabricating process, PQ (0.1 wt %) and AIBN (0.05 wt %) powders were dissolved in MMA solvent. The mixture is pre-polymerized at 60°C for 2.5h to eliminate the nitrogen produced by thermal decomposition while heating the AIBN. By raising the temperature, approximately 1.0wt% PQ molecules were dissolved into the PMMA host matrix (the maximum solubility of PQ in MMA matrix). This solution was then initiated at 85 °C for 15 min and finally solidified at 60 °C for 72 h. After thermal polymerization, samples with the same size as TI/PMMA of 3 mm thick were prepared. Due to the solubility limitation of PQ molecules, we compared these two kind of materials with the same size and thickness, and also the same exposure intensity and time.

The visible absorption spectra of TI/PMMA and PQ/PMMA photopolymers was examined and compared. From the absorption spectra as shown in Fig. 1(a), the absorption coefficient was 1.883 in TI/PMMA at the wavelength of 532nm, while the PQ/PMMA got only 0.192, which provides a basis for more photo-initiator polymerizing under the same exposure flux, eventually leads to an enhancement of grating strength and response time. Due to the high absorption of TI molecules at 532 nm, we set up a two-wave coupling interference system by green light recording and red light reconstructing, as shown in Fig. 1(b). The absorption coefficient of TI/PMMA was 0.128 (PQ/PMMA for 0.135), therefore, the 633nm light was used to reduce the light absorption while reconstructing. We use the 532 nm green-light CW laser beam to record volume holographic gratings, the beam is divided into two with equal intensity, the same optical path and polarization state when shutter 1 is open and shutter 2 is closed. The holographic grating is recorded in the exposure area by optical interference. Then, we turn off shutter 1 and turn on shutter 2 to let 633 nm red-light CW laser beam read the grating with the corresponding Bragg’s matched angle. The diffraction can be observed through the detector. This equipment is set up to avoid the absorption of photosensitive molecules under green-light exposure during the reconstruction process. In all of our experiments, we used 3 mm photopolymer materials of PQ/PMMA and TI/PMMA to investigate their holographic properties in order to avoiding the influences of sample thickness on holographic memory. Otherwise, the recording intersection angle was 20°. according to the Bragg condition and Interference formula as shown below:

2Λsinβ=kλ2,
Λ=λ1sinα1+sinα2,
where k = 1, λ1 = 532 nm (recording wavelength), α1=α2=10°(incident angle), λ2 = 633 nm (reconstructing wavelength). By these two equations, we could get β = 11.95°(reconstructing angle), which indicated the angle difference between the green light and red light was 1.95°. In the experiment, we first used the green light to record single grating in the sample, then we closed green light and open red light to expose the grating, the angle difference was achieved by adjusting the position of red light source and reflector(mirror) repeatedly. When we found the maximum diffraction read by red light, the red light source and reflector(mirror) was fixed.

 

Fig. 1 (a) Absorption spectra of TI/PMMA and PQ/PMMA photopolymers; (b) two-wave coupling interference system, PBS, polarization beam splitter.

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3. Results and discussion

3.1 Transmission gratings recorded by consecutive exposure

Holographic transmission gratings were recorded in 3 mm thick TI/PMMA photopolymers with consecutive exposure. The grating formation process can be described by the temporal evolution of diffraction efficiency. The TI molecules are a kind of cationic photo-initiator. The photo-initiation process of TI molecules is different from that of PQ molecules. A brief description of the complex photo-polymerization in TI/PMMA photopolymers can be expressed as [16,19,23]:

TI+hvRrRi[TI]*
PMMA/MMA+[TI]*TI-nMMA
[TI]*TI+By-products
TI+2PMMA/MMAnMMA-TI-nMMA

Firstly, TI molecule can absorb a photon to transfer into its excited state [TI]* with an initiation rate of Ri, no reacted [TI]* will return to the ground state TI with the rate of Rr, as shown in Eq. (3). In the photo-chemical process, there are two main reactions, one is a direct polymerization between [TI]* and monomers, the other is the indirect reactions between unstable diradicals and monomers. One part of the excited [TI]* can polymerize with monomers to form photoproducts as shown in Eq. (4). Then, another part [TI]* can photo-cleave into unstable diradicals and steady by-products (stable aryl compounds). The unstable diradicals can react with two PMMA or MMA monomers to form stable photoproducts. These two photo-chemical reactions lead to the formation of photoproducts. The grating strength becomes stable after the photo-initiators are depleted into bright zones during the exposure.

In this section, we examined the temporal evolution of diffraction efficiency in TI/PMMA samples with different exposure powers. In this article, we used τR to depict the response, which is not defined as the exposure time when the diffraction efficiency comes to its maximum. The response time is obtained by the exponential fitting of evolution curves of the diffraction efficiency with the exposure time, which can be described as, η(t)=ηmax[1exp(t/τR)], this fitting is a general method to describe response time in bulk photopolymer research [8–11]. The diffraction efficiency was defined as the ratio of diffracted light intensity to transmitted light intensity. These two factor was both considered after sample absorption. The experimental results are shown in Fig. 2. We obtained the maximum diffraction efficiency of 74% with the response time of 20 seconds. In comparison to the PQ/PMMA photopolymers with the same experimental condition, the diffraction efficiency is increased by 51%, while the response time is shortened by 35%, as shown in Fig. 2(a). It is implied that TI molecules is more photosensitive than PQ molecules.

 

Fig. 2 (a) Comparisons of diffraction efficiency between TI/PMMA and PQ/PMMA with the increment of exposure flux; (b) the temporal evolution of refractive index modulation in TI/PMMA samples.

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Then, Fig. 2(b) depicted the improvement of refractive index modulation with the increasing exposure energy. The amplitude of refractive index change is calculated from experimental results of diffraction efficiency according to Kogelnik theory [24].

η=sin2(Δnπdλcosθ)

The refractive index modulation of 7.61 × 10−5 with the exposure flux of 10 J/cm2 was obtained in TI molecules dispersed PMMA photopolymers with an optimized concentration, as shown in Fig. 2(b). The experimental results and analysis indicate the TI/PMMA materials are more available in volume holographic memory.

3.2 Dark enhancement of a single transmission grating after short-time exposure

In the TI/PMMA photopolymer, the consumption of photo-initiator TI molecules dominate the photo-polymerization reaction when the sample is under illumination. The primary consumption of TI molecules is related to the generation of excitons, expressed as

[TI](t)t=Ri

In photo-chemical process of illumination, the exposure energy is enough to excite the TI into [TI]* and make them keep the excited state. Therefore, the excitons generation of [TI]* is the main contribution of the photo-initiator consumption. According to [25], we obtain the initiation reaction formula, which can be expressed as Ri = fkd[TI], where kd is the [TI]* generation rate constant and f presents the fraction of [TI]* reactions [25]. The solution of Eq. (6) can be given by

[TI](t)=[TI]0exp(fkdt)=[TI]0exp(E/Eτ),

where E is the exposure flux, which is defined as the product of exposure intensity and exposure time,Eτ is the exposure constant related to the polymerization rate [20]. The residual TI molecules in the substrate after exposure can be depicted as

[Residual](t)=[TI]0[TI](t)=[TI]0[1exp(E/Eτ)]

With the consumption of TI molecules, there is also a growth on photoproduct content, which contributes to the formation of gratings. Meanwhile, we use the following formula to describe the temporal dark enhancement of diffraction efficiency after exposure.

η(t)=ηsat[1exp(t/τ)]+C1,

where ηsat is the saturation diffraction efficiency of the dark diffusional enhancement of the grating strength. τ presents the dark diffusion time constant, which exhibits the photo-sensitivity of TI/PMMA photopolymers. And C1 represents the initial grating diffraction efficiency. The exponential term in Eqs. (9) and (10) is a kind of fitting method to describe the trends in dark enhancement process of sensitivity and strength. Eτ is presented to compare the polymerization rate. Also, τ is presented to depict the response time in the dark diffusion process. These two parameter are both obtained by fitting the experimental results, which is aimed at making a quantitative comparison of polymerization rate and response time.

In the experiment, a single grating was recorded under 20 seconds exposure with different intensities and then we examined the dark enhancement evolution of diffraction efficiency for 1000 seconds after exposure in the darkness, as shown in Fig. 3. The exponential function in Eq. (11) was used to fit the temporal evolution of the dark enhancement process. The fittings in Fig. 3 quantitatively described the diffusion rate and duration of photosensitive molecules.

 

Fig. 3 (a) The dark enhancement of single transmission grating with different exposure flux, (b) comparisons of dark enhancement between TI/PMMA and PQ/PMMA polymers.

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The time constant in dark enhancement process reached to 164, 139 and 130 seconds corresponding to the exposure intensity of 115 mW/cm2, 96 mW/cm2 and 64 mW/cm2. Meanwhile, the saturation diffraction efficiency closed to 68%, 63% and 59%, as shown in Fig. 3(a). As the exposure energy was being increased, the saturated diffraction efficiency was increasing while the sensitivity was declining. It was indicated that more photo-initiators were initiated with higher exposure density. The experimental results demonstrated that the TI molecules diffusion after exposure was the main contribution to the enhancement of grating strength, due to the short lifetime of free radicals, which could not lead a further reaction with monomers without illumination for hundreds of seconds. Also, we examined the dark diffusion process between TI/PMMA and PQ/PMMA polymers with the same exposure flux, as shown in Fig. 3(b). Compared to PQ/PMMA polymers, the increment of dark diffusion had an improvement of 52% in TI/PMMA polymers. According to the free-volume theory [25], the diffusion coefficient of TI molecules is related to their consumptions in exposure process. An approximate formula with an exponential increment of residual TI molecules’ concentration can be expressed as

D([TI](t))=D0exp(C1[Residual](t))+C2,

where C1 and C2 are the constants, and D0 is the diffusional constant. The diffusional time constants in the dark enhancement process were obtained with different exposure energy, as shown in Fig. 4(a). We neglected the diffusion of TI molecules in the short-time exposure due to the diffusions mainly occurred in the dark enhancement process. The curve in Fig. 4(b) was fitted by Eq. (12) which was aimed at calculating the diffusion coefficient of photosensitive molecules. According to the expression D0=Km·Λ2/4π2τ, where Λ is the grating fringe spacing, KM is the molecular constant in order to compare the diffusion under the same number of photosensitive molecules. The diffusion coefficient of TI molecules can mainly be described by the diffusional time constant τ. The fitting curves were in good agreement with experimental results, which demonstrated that the diffusion coefficient was related to the TI consumption concentration. The diffusion coefficient of TI molecules D=5.5×1015m2/s was higher than that of PQ molecules with the value of 3.5×1015m2/s, while the solubility of TI molecules was 2.3 times than that of PQ molecules. It is indicated TI molecules are more photo-sensitive than PQ molecules with a higher diffusion rate and photosensitive molecules quantity.

 

Fig. 4 (a) Time constants in dark diffusional process; (b) diffusion coefficient and fitting curves of TI molecules.

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TI and PQ molecules are two kinds of photo-initiators. Though the excitation process of them while exposing is different, the general grating formation mechanism is the same, that is, the photo-initiators (TI/PQ molecules) are consumed to form photo-product in the bright region of exposure position, which leads to a concentration gradient difference between photo-initiator molecules in the bright and dark region. The generation of photo-product causes the change of refractive index modulation. During the post exposure, the exposure position is in the dark and there is no photo-initiator excitation happen, i.e. the polymerization term is vanished. However, we still observed the increment of diffraction efficiency in TI/PMMAs, which is mainly due to the diffusion of free TI molecules from the dark region to bright region caused by the concentration gradients after exposure according to the diffusion model in PMMA host photopolymers [21], finally, it results in the enhancement of modulation depth. The diffusion of photo-initiator in photopolymer has been observed in some researches by atomic force microscopy (AFM) and electron-probe microanalyzer (EPMA) [26,27]. Meanwhile, the diffusion coefficient is related to the reciprocal of photosensitive molecules concentration based on the free volume theory according to [21]. An approximate expression of TI molecules consumption concentrations with an exponential increase can be depicted in Eq. (12). The residual TI molecules concentration can be obtained from Eq. (10), where Eτ is a constant determined by the material itself. Therefore, we can calculate the TI consumption by substituting different exposure flux. Also, D0=Km·Λ2/4π2τ, where D0 is a diffusion coefficient related to the diffusional time constant described in Eq. (11). The τ is also a constant determined by the material itself. Therefore, the diffusion coefficient D can be depicted by substituting the parameters above.

After a detail investigation of photo-initiator diffusion in TI/PMMA photopolymers after exposure, we also examined the shift of Bragg angular selectivity in the darkness. In Fig. 5, a shift of the Bragg angular selectivity curve is shown. TI/PMMA and PQ/PMMA materials were both examined with the same thickness (3mm). Single grating was recorded for 100 seconds with the exposure energy of 115 mW/cm2. The experimental results indicate that the shift distance of Bragg angular selectivity increases with time, up to the 100 minutes when a termination occurs in the darkness. Eventually, the shift reached 0.05° and became stable after 100 minutes, as shown in Fig. 5(a). The shift of Bragg angular selectivity was an important parameter to describe the volume holographic shrinkage. Compared to the growing shrinkage in PQ/PMMA photopolymers after exposure, we could see the TI/PMMA polymers had an increment on saturation Bragg angle shifting, which got 20% higher than PQ/PMMA polymers, as shown in Fig. 5(b). This is mainly because the photo-initiator (TI molecules) concentration in TI/PMMA is much more than that (PQ molecules) of PQ/PMMA, which leads more monomers and photo-initiators polymerize. It causes a larger concentration gradient of photo-initiator between the bright and the dark region. After exposure, TI molecules diffuse from dark region to bright region with a faster rate, which eventually contributes to the changing of fringe spacing [28,29]. Higher diffusion rate of photo-initiator makes more shrinkage in the exposure area of sample.

 

Fig. 5 (a) Bragg angular selectivity shifting of TI/PMMA polymers after exposure; (b) comparisons of Bragg angle maximum shifting between PQ/PMMA and TI/PMMA polymers.

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Consequently, the dark enhancement of single transmission grating after short-time exposure was investigated. The diffraction efficiency increased by 230% in the dark enhancement process with the diffusional time constant of 164 s at a diffusion rate in 10−15 m2/s. The maximum diffraction efficiency under dark enhancement was 68%. It is indicated TI/PMMA photopolymer is a kind of photo-sensitive bulk materials with slight shrinkage and rapid diffusion.

3.3 Cumulative grating strengths enhanced by the dark enhancement

The storage density of TI/PMMA photopolymers was studied in this section. 20 gratings were recorded at one certain position in the TI/PMMA photopolymer by rotating the sample. The diffraction efficiency of each grating was examined under equal exposure energy of 1.25 J/cm2. We also investigated the dark enhancement of multiplexed gratings, as shown in Fig. 6. The saturation diffraction efficiency was obtained at 600s after the illumination. It was also indicated that TI molecules diffusion had a main contribution to the multiplexed gratings enhancement. Compared with the consecutive exposure process, the dark enhancement caused by TI molecules diffusion was a slow process. However, this was a very effective way to enhance the grating strength without additional illumination. In the experiment, TI/PMMA polymers have a direct improvement compared with PQ/PMMA in multiplexing storage capacity.

 

Fig. 6 Diffraction efficiencies of multiplexed gratings with time intervals of (a) 0 s, (b) 300 s, (c) 600 s, and (d) 900 s.

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We used the dynamic range M# to describe the holographic multiplexing capacity, which could be defined as the summation of all the grating strengths recorded at the same spot in the sample, expressed as [22]

M#=i=1Nηi,

where N represents the maximum number of gratings stored in the TI/PMMA material. Figure 7(a) and 7(b) depicted the increment of cumulative grating strength during the consecutive exposure process and the temporal evolution in the dark enhancement of M#. As a result, M# of TI/PMMA polymers reached 4.85 after consecutive exposure and increased to 6.88 with 600 seconds dark diffusion. At the same exposure condition, M# of PQ/PMMA photopolymers came to 3.15 after continuous exposure and improved to 3.51 with 100 seconds dark diffusion. Compared with bulk PQ/PMMA photopolymers, the M# of TI/PMMA increased by 1.54 times after exposure and approximately 2-fold with the complete dark diffusion, as shown in Fig. 7(b). In the experiment, we found the cumulative grating strength started to decay after 600 seconds in the dark enhancement process, which was mainly caused by the generation of macromolecular photoproducts. In the long time dark diffusion process, the grating strength grow up firstly, then decrease. This is mainly due to the two diffusion in the exposure area of photosensitive molecules and macromolecular photoproducts, respectively. This two process can be described in Eq. (14). By fitting the temporal evolution of dark enhancement process, we can get the diffusion coefficients. A corresponding expression of the cumulative grating strength (Cgs) was obtained as

 

Fig. 7 (a) The dynamic range increased by consecutive exposure; (b) the temporal evolution of the dynamic range.

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Cgs=Aexp(4π2DTIt/Λ2)Bexp(4π2Dprot/Λ2),

where A and B are the constants of component content, DTI and Dpro represent the diffusion coefficients of TI molecules and photoproducts. From the temporal evolution of the dynamic range fitted by Eq. (14) we could see, the corresponding values of DTI=8.0×1016m2/s and Dpro=6.7×1016m2/s were obtained. It was indicated that the attenuation of cumulative grating strength was mainly caused by the diffusion of macromolecular photoproducts after the molecules diffusion reached a dynamic equilibrium.

We used the scattering ratio to describe the generation of holographic noise because the noise in the grating recording process was mainly derived from the scattering of our materials. The scattering ratio can be expressed as [30]:

S(t)=(1I(t)/I0)×100%,

where I(t) is the transmitted intensity at t time, while I0 is the initial transmitted intensity. The scattering ratio is defined as the ratio of the light, which scatters outside the exposure area to the initial transmitted intensity of incident light. Scattering ratio can directly describe the scattering loss of materials, which is regarded as the biggest source of noise in this kind polymer. Generally, with the accumulation of incident light, the intensity of transmitted light detected in the exposure area decreases gradually until it reaches the minimum value, accompanied by the maximum scattering of incident light. The experimental results were shown in Fig. 8. The maximum scattering ratio of TI/PMMA was 58% while PQ/PMMA was 76%, which indicated that TI/PMMA had better anti-scattering ability compared to PQ/PMMA, which could be more available in holographic memory applications. The first possible reason is that the solubility in MMA matrix is different between TI and PQ molecules. TI molecules (up to 10 wt%) exhibit better solubility in MMA matrix than that of PQ molecules (up to 1.0wt%). This leads to a more uniform distribution of TI molecules in prepared samples, which may avoid excessive scattering. Also, with the increment of photo-initiator concentration, more monomers will polymerize with photo-initiators, which indicated that the chain polymerization reaction between monomers will decrease. By this mean, the chain length of photo-product can be reduced, eventually leads to the attenuation of scattering. The second may due to the differences of excitation process between TI and PQ molecules. TI molecules can be cleaved while exposure, but not for PQ molecules. This process can effectively reduce the size of scattering centers in TI/PMMAs to avoid scattering loss. In our previous work [10,11], we demonstrated the sensitivity of our materials under nanoseconds pulsed exposure. The response time could reach 0.8 μs, which exhibited our materials, had the ability to record ultrafast transient information in our life and applications. Meanwhile, the storage capacity of our materials could attain 1 GB/cm3 according to the dynamic range of 6.88 and exposure area size of 6.3 cm2. Also, the static and dynamic sensitivity of TI/PMMA can reach 8 × 10−6cm2/J and 3 × 10−5cm2/J [19]. All these indicators make the material fully competitive in holographic memory applications.

 

Fig. 8 The scattering ratio of TI/PMMA and PQ/PMMA.

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In this article, we mainly want to explore a new kind of glass-like bulk photopolymer due to its stability and storage capacity [8,21], PQ/PMMA as a kind of bulk photopolymer with high transmittance exhibits better holographic properties among the photopolymer. Therefore, we have enumerated a series of parameters of bulk photopolymers in the last few years’ researches, as shown in Table 1.

Tables Icon

Table 1. Comparisons of Holographic Parameters on Different Kind of Bulk Photopolymers

It can be seen that TI/PMMA a better holographic performance on diffraction efficiency (η), response time (τR) and cumulative grating strength (M#), which indicates this kind of photopolymer can be valuable to make further investigations on bulk holographic materials preparation and memory.

4. Summary

In this paper, the holographic memory performances in an optimized TI molecules concentration dispersed PMMA photopolymers were experimentally investigated. The transmission grating recorded in consecutive exposure and short-time exposure were examined, respectively. Under consecutive illumination, we obtained the maximum diffraction efficiency of 74% with the response time of 20 seconds, and the refractive index modulation reached 7.61 × 10−5 with the exposure flux of 10 J/cm2. Under short-time exposure, we examined the dark enhancement mainly caused by TI molecules diffusion. We obtained the maximum diffraction efficiency of 68%, which was increased by 230% in the dark enhancement process with the diffusional time constant of 164 s at a diffusion rate in 10−15 m2/s. This material still had a slight shrinkage with 0.05° shift of Bragg angular selectivity after 100 minutes without exposure. Moreover, multiplexing gratings strength were improved by the dark enhancement process for 600 seconds. 20 transmission gratings were recorded at the same spot of TI/PMMA material. The corresponding dynamic range was 6.88 with the TI molecules diffusion rate of DTI=8.0×1016m2/s. Compared to the bulk PQ/PMMA photopolymers, the solubility of TI molecules (up to 10wt%, while PQ only up to 1.0wt%) in MMA solutions is higher, which leads to more adequate photosensitizers polymerize during exposure and diffuse after exposure. Also, higher photosensitizers contribute to more generation of photo-products. These will eventually bring an improvement on its holographic performances.

Funding

National Basic Research Program of China (2013CB328702); the National Natural Science Foundation of China (11374074).

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18. Y. Liu, F. Fan, Y. Hong, J. Zang, G. Kang, and X. Tan, “Volume holographic recording in Irgacure 784-doped PMMA photopolymer,” Opt. Express 25(17), 20654–20662 (2017). [CrossRef]   [PubMed]  

19. P. Liu, L. Wang, Y. Zhao, Z. Li, and X. Sun, “Holographic memory performances of titanocene dispersed poly (methyl methacrylate) photopolymer with different preparation conditions,” Opt. Mater. Express 8(6), 1441–1453 (2018). [CrossRef]  

20. V. Moreau, Y. Renotte, and Y. Lion, “Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model,” Appl. Opt. 41(17), 3427–3435 (2002). [CrossRef]   [PubMed]  

21. H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010). [CrossRef]   [PubMed]  

22. D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011). [CrossRef]  

23. D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010). [CrossRef]  

24. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Labs Tech. J. 48(9), 2909–2947 (1969). [CrossRef]  

25. J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” J. Opt. Soc. Am. B 22(2), 407–416 (2005). [CrossRef]  

26. Y. Tomita, K. Chikama, Y. Nohara, N. Suzuki, K. Furushima, and Y. Endoh, “Two-dimensional imaging of atomic distribution morphology created by holographically induced mass transfer of monomer molecules and nanoparticles in a silica-nanoparticle-dispersed photopolymer film,” Opt. Lett. 31(10), 1402–1404 (2006). [CrossRef]   [PubMed]  

27. C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011). [CrossRef]   [PubMed]  

28. J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009). [CrossRef]  

29. M. Moothanchery, I. Naydenova, and V. Toal, “Study of the shrinkage caused by holographic grating formation in acrylamide based photopolymer film,” Opt. Express 19(14), 13395–13404 (2011). [CrossRef]   [PubMed]  

30. H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009). [CrossRef]  

31. H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018). [CrossRef]  

32. Y. F. Chen, J. H. Lin, S. H. Lin, K. Y. Hsu, and W. T. Whang, “PQ:DMNA/PMMA photopolymer having amazing volume holographic recording at wavelength of insignificant absorption,” Opt. Lett. 38(12), 2056–2058 (2013). [CrossRef]   [PubMed]  

33. C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014). [CrossRef]   [PubMed]  

References

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  1. U. Mahilny, A. Trofimova, S. Nazarov, A. Tolstik, R. Heintzmann, and E. Tolstik, “Highly concentrated phenanthrenequinone–polymethylmethacrylate composite for thick reflection holograms recording at 532 nm,” Opt. Mater. Express 6(11), 3427–3437 (2016).
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  2. A. Trofimova, S. Nazarov, A. Tolstik, U. Mahilniy, E. Tolstik, and R. Heintzmann, “Multiplexed holograms in phenanthrenequinone–polymethylmethacrylate composite for microscopic applications,” Opt. Mater. Express 7(5), 1446–1452 (2017).
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  3. S. Vyas, P. H. Wang, and Y. Luo, “Spatial mode multiplexing using volume holographic gratings,” Opt. Express 25(20), 23726–23737 (2017).
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  4. P. H. Wang, V. R. Singh, J. M. Wong, K. B. Sung, and Y. Luo, “Non-axial-scanning multifocal confocal microscopy with multiplexed volume holographic gratings,” Opt. Lett. 42(2), 346–349 (2017).
    [Crossref] [PubMed]
  5. S. H. Lin, S. L. Cho, S. F. Chou, J. H. Lin, C. M. Lin, S. Chi, and K. Y. Hsu, “Volume polarization holographic recording in thick photopolymer for optical memory,” Opt. Express 22(12), 14944–14957 (2014).
    [Crossref] [PubMed]
  6. Y. W. Yu, C. H. Yang, T. H. Yang, S. H. Lin, and C. C. Sun, “Analysis of a lens-array modulated coaxial holographic data storage system with considering recording dynamics of material,” Opt. Express 25(19), 22947–22958 (2017).
    [Crossref] [PubMed]
  7. D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
    [Crossref] [PubMed]
  8. D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
    [Crossref]
  9. D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
    [Crossref]
  10. P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
    [Crossref] [PubMed]
  11. P. Liu, Y. Zhao, Z. Li, and X. Sun, “Improvement of ultrafast holographic performance in silver nanoprisms dispersed photopolymer,” Opt. Express 26(6), 6993–7004 (2018).
    [Crossref] [PubMed]
  12. W. S. Kim, Y. C. Jeong, and J. K. Park, “Nanoparticle-induced refractive index modulation of organic-inorganic hybrid photopolymer,” Opt. Express 14(20), 8967–8973 (2006).
    [Crossref] [PubMed]
  13. Y. N. Hsiao, K. Y. Hsu, and S. H. Lin, “An irgacure 784 doped photopolymers for display holograms recording at 532 nm,” Opt. Mem. Neural. Networks 18(4), 253–259 (2009).
    [Crossref]
  14. S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
    [Crossref]
  15. N. Suzuki and Y. Tomita, “Real-time phase-shift measurement during formation of a volume holographic grating in nanoparticle-dispersed photopolymers,” Appl. Phys. Lett. 88(1), 011105 (2006).
    [Crossref]
  16. S. H. Lin, Y. N. Hsiao, and K. Y. Hsu, “Preparation and characterization of Irgacure 784 doped photopolymers for holographic data storage at 532 nm,” J. Opt. A, Pure Appl. Opt. 11(2), 024012 (2009).
    [Crossref]
  17. D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
    [Crossref]
  18. Y. Liu, F. Fan, Y. Hong, J. Zang, G. Kang, and X. Tan, “Volume holographic recording in Irgacure 784-doped PMMA photopolymer,” Opt. Express 25(17), 20654–20662 (2017).
    [Crossref] [PubMed]
  19. P. Liu, L. Wang, Y. Zhao, Z. Li, and X. Sun, “Holographic memory performances of titanocene dispersed poly (methyl methacrylate) photopolymer with different preparation conditions,” Opt. Mater. Express 8(6), 1441–1453 (2018).
    [Crossref]
  20. V. Moreau, Y. Renotte, and Y. Lion, “Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model,” Appl. Opt. 41(17), 3427–3435 (2002).
    [Crossref] [PubMed]
  21. H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
    [Crossref] [PubMed]
  22. D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
    [Crossref]
  23. D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
    [Crossref]
  24. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Labs Tech. J. 48(9), 2909–2947 (1969).
    [Crossref]
  25. J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” J. Opt. Soc. Am. B 22(2), 407–416 (2005).
    [Crossref]
  26. Y. Tomita, K. Chikama, Y. Nohara, N. Suzuki, K. Furushima, and Y. Endoh, “Two-dimensional imaging of atomic distribution morphology created by holographically induced mass transfer of monomer molecules and nanoparticles in a silica-nanoparticle-dispersed photopolymer film,” Opt. Lett. 31(10), 1402–1404 (2006).
    [Crossref] [PubMed]
  27. C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
    [Crossref] [PubMed]
  28. J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
    [Crossref]
  29. M. Moothanchery, I. Naydenova, and V. Toal, “Study of the shrinkage caused by holographic grating formation in acrylamide based photopolymer film,” Opt. Express 19(14), 13395–13404 (2011).
    [Crossref] [PubMed]
  30. H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
    [Crossref]
  31. H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
    [Crossref]
  32. Y. F. Chen, J. H. Lin, S. H. Lin, K. Y. Hsu, and W. T. Whang, “PQ:DMNA/PMMA photopolymer having amazing volume holographic recording at wavelength of insignificant absorption,” Opt. Lett. 38(12), 2056–2058 (2013).
    [Crossref] [PubMed]
  33. C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
    [Crossref] [PubMed]

2018 (4)

2017 (5)

2016 (1)

2014 (2)

2013 (1)

2011 (5)

M. Moothanchery, I. Naydenova, and V. Toal, “Study of the shrinkage caused by holographic grating formation in acrylamide based photopolymer film,” Opt. Express 19(14), 13395–13404 (2011).
[Crossref] [PubMed]

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

2010 (4)

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

2009 (5)

J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
[Crossref]

H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
[Crossref]

S. H. Lin, Y. N. Hsiao, and K. Y. Hsu, “Preparation and characterization of Irgacure 784 doped photopolymers for holographic data storage at 532 nm,” J. Opt. A, Pure Appl. Opt. 11(2), 024012 (2009).
[Crossref]

Y. N. Hsiao, K. Y. Hsu, and S. H. Lin, “An irgacure 784 doped photopolymers for display holograms recording at 532 nm,” Opt. Mem. Neural. Networks 18(4), 253–259 (2009).
[Crossref]

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

2006 (3)

2005 (1)

2002 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Labs Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Bachelot, R.

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

Bouhelier, A.

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

Cao, L.

Chang, F.

Chen, Y. F.

Chi, S.

Chikama, K.

Cho, S. L.

Choi, Y.-S.

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

Chou, S. F.

Deeb, C.

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

Ecoffet, C.

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

Endoh, Y.

Fan, F.

Furushima, K.

Gallego, S.

Gleeson, M. R.

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

He, Q.

Heintzmann, R.

Heo, Y.

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

Hong, Y.

Hsiao, Y. N.

Y. N. Hsiao, K. Y. Hsu, and S. H. Lin, “An irgacure 784 doped photopolymers for display holograms recording at 532 nm,” Opt. Mem. Neural. Networks 18(4), 253–259 (2009).
[Crossref]

S. H. Lin, Y. N. Hsiao, and K. Y. Hsu, “Preparation and characterization of Irgacure 784 doped photopolymers for holographic data storage at 532 nm,” J. Opt. A, Pure Appl. Opt. 11(2), 024012 (2009).
[Crossref]

Hsu, K. Y.

S. H. Lin, S. L. Cho, S. F. Chou, J. H. Lin, C. M. Lin, S. Chi, and K. Y. Hsu, “Volume polarization holographic recording in thick photopolymer for optical memory,” Opt. Express 22(12), 14944–14957 (2014).
[Crossref] [PubMed]

Y. F. Chen, J. H. Lin, S. H. Lin, K. Y. Hsu, and W. T. Whang, “PQ:DMNA/PMMA photopolymer having amazing volume holographic recording at wavelength of insignificant absorption,” Opt. Lett. 38(12), 2056–2058 (2013).
[Crossref] [PubMed]

S. H. Lin, Y. N. Hsiao, and K. Y. Hsu, “Preparation and characterization of Irgacure 784 doped photopolymers for holographic data storage at 532 nm,” J. Opt. A, Pure Appl. Opt. 11(2), 024012 (2009).
[Crossref]

Y. N. Hsiao, K. Y. Hsu, and S. H. Lin, “An irgacure 784 doped photopolymers for display holograms recording at 532 nm,” Opt. Mem. Neural. Networks 18(4), 253–259 (2009).
[Crossref]

Jeong, Y. C.

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

W. S. Kim, Y. C. Jeong, and J. K. Park, “Nanoparticle-induced refractive index modulation of organic-inorganic hybrid photopolymer,” Opt. Express 14(20), 8967–8973 (2006).
[Crossref] [PubMed]

Jiang, Y.

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
[Crossref]

J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
[Crossref]

Jiang, Y.-Y.

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

Jin, G.

Kang, G.

Kelly, J. V.

Kim, S. I.

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

Kim, W. S.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Labs Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Lee, S.

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

Li, C.

Li, L.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Li, X.

Li, Z.

Lin, C. M.

Lin, J. H.

Lin, S. H.

Lion, Y.

Liu, H.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
[Crossref]

Liu, P.

Liu, S.

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

Liu, Y.

Luo, S.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
[Crossref]

Luo, Y.

Mahilniy, U.

Mahilny, U.

Moothanchery, M.

Moreau, V.

Naydenova, I.

Nazarov, S.

Neipp, C.

Nohara, Y.

O’Neill, F. T.

Ortuno, M.

Park, J. K.

Park, J.-K.

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

Plain, J.

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

Renotte, Y.

Sabol, D.

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

Sheridan, J. T.

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

J. V. Kelly, F. T. O’Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,” J. Opt. Soc. Am. B 22(2), 407–416 (2005).
[Crossref]

Singh, V. R.

Song, Q.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Soppera, O.

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

Sun, C. C.

Sun, X.

P. Liu, Y. Zhao, Z. Li, and X. Sun, “Improvement of ultrafast holographic performance in silver nanoprisms dispersed photopolymer,” Opt. Express 26(6), 6993–7004 (2018).
[Crossref] [PubMed]

P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
[Crossref] [PubMed]

P. Liu, L. Wang, Y. Zhao, Z. Li, and X. Sun, “Holographic memory performances of titanocene dispersed poly (methyl methacrylate) photopolymer with different preparation conditions,” Opt. Mater. Express 8(6), 1441–1453 (2018).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
[Crossref]

H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
[Crossref]

Sun, X.-D.

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

Sung, K. B.

Suzuki, N.

Tan, X.

Toal, V.

Tolstik, A.

Tolstik, E.

Tomita, Y.

Trofimova, A.

Vyas, S.

Wang, H.

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

Wang, J.

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
[Crossref]

Wang, L.

Wang, P. H.

Wang, S.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Wang, W.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Whang, W. T.

Wong, J. M.

Yang, C. H.

Yang, T. H.

Yu, D.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
[Crossref]

Yu, Y. W.

Zang, J.

Zhao, Y.

Zhou, K.

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

H. Liu, D. Yu, Y. Jiang, and X. Sun, “Characteristics of holographic scattering and its application in determining kinetic parameters in PQ-PMMA photopolymer,” Appl. Phys. B 95(3), 513–518 (2009).
[Crossref]

Appl. Phys. Lett. (1)

N. Suzuki and Y. Tomita, “Real-time phase-shift measurement during formation of a volume holographic grating in nanoparticle-dispersed photopolymers,” Appl. Phys. Lett. 88(1), 011105 (2006).
[Crossref]

Bell Labs Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Labs Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Chin. Phys. B (1)

D. Yu, H. Wang, H. Liu, J. Wang, Y.-Y. Jiang, and X.-D. Sun, “Dark diffusional enhancement of holographic multiplexed gratings in phenanthrenequinone doped poly (methyl methacrylate) photopolymer,” Chin. Phys. B 20(11), 114217 (2011).
[Crossref]

J. Am. Chem. Soc. (1)

C. Deeb, C. Ecoffet, R. Bachelot, J. Plain, A. Bouhelier, and O. Soppera, “Plasmon-based free-radical photopolymerization: effect of diffusion on nanolithography processes,” J. Am. Chem. Soc. 133(27), 10535–10542 (2011).
[Crossref] [PubMed]

J. Appl. Phys. (2)

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resinphotopolymer,” J. Appl. Phys. 107(5), 053113 (2010).
[Crossref]

J. Mater. Chem. (1)

S. Lee, Y. C. Jeong, Y. Heo, S. I. Kim, Y.-S. Choi, and J.-K. Park, “Holographic photopolymers of organic/inorganic hybrid interpenetrating networks for reduced volume shrinkage,” J. Mater. Chem. 19(8), 1105–1114 (2009).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

S. H. Lin, Y. N. Hsiao, and K. Y. Hsu, “Preparation and characterization of Irgacure 784 doped photopolymers for holographic data storage at 532 nm,” J. Opt. A, Pure Appl. Opt. 11(2), 024012 (2009).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Holographic storage stability in PQ-PMMA bulk photopolymer,” Opt. Commun. 283(21), 4219–4223 (2010).
[Crossref]

D. Yu, H. Liu, J. Wang, Y. Jiang, and X. Sun, “Study on holographic characteristics in ZnMA doped PQ-PMMA photopolymer,” Opt. Commun. 284(12), 2784–2788 (2011).
[Crossref]

Opt. Express (11)

P. Liu, F. Chang, Y. Zhao, Z. Li, and X. Sun, “Ultrafast volume holographic storage on PQ/PMMA photopolymers with nanosecond pulsed exposures,” Opt. Express 26(2), 1072–1082 (2018).
[Crossref] [PubMed]

P. Liu, Y. Zhao, Z. Li, and X. Sun, “Improvement of ultrafast holographic performance in silver nanoprisms dispersed photopolymer,” Opt. Express 26(6), 6993–7004 (2018).
[Crossref] [PubMed]

W. S. Kim, Y. C. Jeong, and J. K. Park, “Nanoparticle-induced refractive index modulation of organic-inorganic hybrid photopolymer,” Opt. Express 14(20), 8967–8973 (2006).
[Crossref] [PubMed]

S. Vyas, P. H. Wang, and Y. Luo, “Spatial mode multiplexing using volume holographic gratings,” Opt. Express 25(20), 23726–23737 (2017).
[Crossref] [PubMed]

S. H. Lin, S. L. Cho, S. F. Chou, J. H. Lin, C. M. Lin, S. Chi, and K. Y. Hsu, “Volume polarization holographic recording in thick photopolymer for optical memory,” Opt. Express 22(12), 14944–14957 (2014).
[Crossref] [PubMed]

Y. W. Yu, C. H. Yang, T. H. Yang, S. H. Lin, and C. C. Sun, “Analysis of a lens-array modulated coaxial holographic data storage system with considering recording dynamics of material,” Opt. Express 25(19), 22947–22958 (2017).
[Crossref] [PubMed]

D. Yu, H. Liu, Y. Jiang, and X. Sun, “Mutual diffusion dynamics with nonlocal response in SiO2 nanoparticles dispersed PQ-PMMA bulk photopolymer,” Opt. Express 19(15), 13787–13792 (2011).
[Crossref] [PubMed]

Y. Liu, F. Fan, Y. Hong, J. Zang, G. Kang, and X. Tan, “Volume holographic recording in Irgacure 784-doped PMMA photopolymer,” Opt. Express 25(17), 20654–20662 (2017).
[Crossref] [PubMed]

H. Liu, D. Yu, X. Li, S. Luo, Y. Jiang, and X. Sun, “Diffusional enhancement of volume gratings as an optimized strategy for holographic memory in PQ-PMMA photopolymer,” Opt. Express 18(7), 6447–6454 (2010).
[Crossref] [PubMed]

M. Moothanchery, I. Naydenova, and V. Toal, “Study of the shrinkage caused by holographic grating formation in acrylamide based photopolymer film,” Opt. Express 19(14), 13395–13404 (2011).
[Crossref] [PubMed]

C. Li, L. Cao, Q. He, and G. Jin, “Holographic kinetics for mixed volume gratings in gold nanoparticles doped photopolymer,” Opt. Express 22(5), 5017–5028 (2014).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

H. Liu, D. Yu, K. Zhou, S. Wang, S. Luo, L. Li, W. Wang, and Q. Song, “Novel pH-sensitive photopolymer hydrogel and its holographic sensing response for solution characterization,” Opt. Laser Technol. 101, 257–267 (2018).
[Crossref]

Opt. Lett. (3)

Opt. Mater. (1)

J. Wang, X. Sun, S. Luo, and Y. Jiang, “The shift of Bragg angular selectivity curve in darkness in glass-like photopolymer for holographic recording,” Opt. Mater. 32(1), 261–265 (2009).
[Crossref]

Opt. Mater. Express (3)

Opt. Mem. Neural. Networks (1)

Y. N. Hsiao, K. Y. Hsu, and S. H. Lin, “An irgacure 784 doped photopolymers for display holograms recording at 532 nm,” Opt. Mem. Neural. Networks 18(4), 253–259 (2009).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) Absorption spectra of TI/PMMA and PQ/PMMA photopolymers; (b) two-wave coupling interference system, PBS, polarization beam splitter.
Fig. 2
Fig. 2 (a) Comparisons of diffraction efficiency between TI/PMMA and PQ/PMMA with the increment of exposure flux; (b) the temporal evolution of refractive index modulation in TI/PMMA samples.
Fig. 3
Fig. 3 (a) The dark enhancement of single transmission grating with different exposure flux, (b) comparisons of dark enhancement between TI/PMMA and PQ/PMMA polymers.
Fig. 4
Fig. 4 (a) Time constants in dark diffusional process; (b) diffusion coefficient and fitting curves of TI molecules.
Fig. 5
Fig. 5 (a) Bragg angular selectivity shifting of TI/PMMA polymers after exposure; (b) comparisons of Bragg angle maximum shifting between PQ/PMMA and TI/PMMA polymers.
Fig. 6
Fig. 6 Diffraction efficiencies of multiplexed gratings with time intervals of (a) 0 s, (b) 300 s, (c) 600 s, and (d) 900 s.
Fig. 7
Fig. 7 (a) The dynamic range increased by consecutive exposure; (b) the temporal evolution of the dynamic range.
Fig. 8
Fig. 8 The scattering ratio of TI/PMMA and PQ/PMMA.

Tables (1)

Tables Icon

Table 1 Comparisons of Holographic Parameters on Different Kind of Bulk Photopolymers

Equations (15)

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2 Λ sin β = k λ 2 ,
Λ = λ 1 sin α 1 + sin α 2 ,
TI+ h v R r R i [TI] *
PMMA/MMA + [ T I ] * TI- n MMA
[ T I ] * TI + By-products
TI + 2 PMMA/MMA n MMA-TI- n MMA
η = sin 2 ( Δ n π d λ cos θ )
[ T I ] ( t ) t = R i
[ T I ] ( t ) = [ T I ] 0 exp ( f k d t ) = [ T I ] 0 exp ( E / E τ ) ,
[ R e s i d u a l ] ( t ) = [ T I ] 0 [ T I ] ( t ) = [ T I ] 0 [ 1 exp ( E / E τ ) ]
η ( t ) = η s a t [ 1 e x p ( t / τ ) ] + C 1 ,
D ([TI]( t ))= D 0 e x p ( C 1 [ R e s i d u a l ] ( t ) ) + C 2 ,
M # = i = 1 N η i ,
C g s = A exp ( 4 π 2 D TI t / Λ 2 ) B exp ( 4 π 2 D pro t / Λ 2 ) ,
S ( t ) = ( 1 I ( t ) / I 0 ) × 100 % ,

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