The dark enhancements of diffraction efficiency in single and multiple gratings are investigated theoretically and experimentally in phenanthrenequinone doped poly-(methyl methacrylate) materials. It is demonstrated a possibility to improve holographic characteristics of the material via the enhancement. Nearly 17-fold increment of diffraction efficiency is observed after exposure. The dependences of PQ’s concentration on the rate and increment of dark enhancement are achieved quantitatively. And the enhancement in multiplexing is presented as a simple and efficient method to improve response of the material and homogeneity of diffraction efficiency. PQ’s diffusion and enhancement process of refractive index modulation are simulated by a diffusion model for describing enhancement dynamics qualitatively and quantitatively. This study provides a significant foundation for the application of dark enhancement in holographic storage.
©2010 Optical Society of America
In recent years the interest in photopolymer material as one of promising candidates for holographic memory has increased [1–3]. Among these materials, phenanthrenequinone (PQ) doped poly-(methyl methacrylate) (PMMA) photopolymers have attracted much attention due to their neglectable shrinkage and good stability [4–8]. The main disadvantage of this material is low response [9–13]. To enhance the response and obtain high diffraction efficiency, the general methods are increasing the photosensitizer concentration and incident irradiance. However there are some drawbacks as follows. In preparation of material, the PQ’s concentration, whatever, is limited by its saturated dissolvability, which only is 0.7wt% at room temperature [5,6]. The investigation for increasing the PQ’s concentration is difficult and scarce. In experiments, the high consecutive irradiance would bring an amplification of holographic scattering noise  and evident dropping in diffraction efficiency due to overmodulation .
Dark enhancement of holographic gratings is one of alternative way to overcome these limitations. After short recording exposure, enhancement of diffraction efficiency is observed in the photopolymer . It is attributed to the diffusion of primary PQ molecules from dark regions into bright regions, which results in the enhancement of modulation depth. However the applicability of dark enhancement for improving holographic characteristics of materials not attracted much attention. So far, the quantitative analysis aimed at the dark diffusional enhancement has seldom been studied, especially the influence of dark enhancement on multiplexing. In this paper the dark enhancement of holographic gratings in PQ-PMMA photopolymer was investigated theoretically and experimentally in single and multiple gratings. The quantitative dependence of PQ’s concentration on the enhancement brings about a probability for improving the diffraction efficiency and response of materials. Finally the dark enhancement dynamics are simulated using the diffusion model for qualitative and quantitative description.
2. Photochemical mechanism and diffusion model
Firstly we briefly analyze the physical mechanism of photochemical reaction in the materials. After the preparation of materials there are several components, such as PQ molecules and MMA residual molecules and polymer matrix . Under illumination the PQ molecules attachment to free MMA molecules cannot be avoided. The bimolecular termination of MMA is neglected, because structure change of PQ molecules induced the strong change of refractive index. The complex photochemical processes can be simply described as [6,7],15]. f presents only a fraction of radicals reacted due to the cage effect. ‘’ presents the concentration of components. The temporal evolution of primary PQ molecules and corresponding photoproduct can be given by , respectively14,16]
To get the details of dark enhancement in PQ-PMMA material, a diffusion model is used to describe the enhancement dynamics of gratings. So far, several models have been presented to describe the diffusion of monomer in photopolymers [17,18]. Nonlocal polymerization driven diffusion model is an effective approach in analyzing the photochemical dynamics of photopolymers, because the monomer and photoproducts are introduced into non-local area [19–22]. However when the illumination is turned off, the polymerization term is vanished in this model. Diffusion of free PQ and MMA molecules from the dark region to the bright region cannot be avoided due to the concentration gradients after exposure . The spatial modulation of PQ molecules concentration was larger than that of MMA molecules, because most of PQ molecules bond with MMA molecules and polymer matrix during exposure [5,6]. Therefore the diffusion process can be described by diffusion model
In our experiments, the samples were consisted of poly (methyl methacrylate) (PMMA) host matrix and phenanthrenequinone (PQ) photosensitizer. However only up to 0.7wt% of PQ could be dissolved in a solvent methyl methacrylate (MMA) at room temperature [6–11]. To increase the PQ’s concentration, a simple and efficient strategy is introduced. The thermal initiator 2, 2-azobis (2-methlpropionitrile) (AIBN) and PQ molecules were dissolved in a solvent MMA. If the mixture was purified at room temperature, the corresponding upper limit of PQ’ concentration could not be changed. In this step the mixture was purified at 60°C not room temperature about 2 hours until it turned to a uniform solution and poured into a glass mold. By using the process, approximately 1.0wt% PQ molecules were solved into the materials. The solution was then initiated at 80°C for 20min and solidified at 60°C for 120h. After the thermal polymerization, the sample with PQ’s concentration 0.1M and the thickness of 2mm was prepared.
4. Dark enhancement of diffraction efficiency in single gratings
Dark enhancement may be provided a simple and efficient method to obtain high and steady diffraction efficiency in single grating. Comparing with consecutive exposure, short exposure can prevent the amplification of holographic scattering and reduce the consumption of photosensitizer components in the exposure spot. Moreover, the dark enhancement takes place inside the materials and can achieve automatically. The rate and increment of dark enhancement are significant parameters for describing the diffusion kinetics quantitatively. Consequently building the quantitative relationship between PQ’s concentration and both parameters is necessary for investigating the dark enhancement.
To get an evident dark enhancement of diffraction efficiency, a series of transmission gratings were recorded at 532nm using 100 mW/cm2, which were repeated for several exposures flux, namely 3.7 × 103, 7.3 × 103, 1.1 × 104, 1.5 × 104, and 2.4 × 104 mJ/cm2, respectively. The experimental results are shown in Fig. 1 . The maximum increment is at the 2.4 × 104 mJ/cm2, and nearly 17-fold increment of diffraction efficiency is observed. The experimental results are in good agreement with the predicted values using exponential function. It is implied that the diffusion of PQ molecules is a key parameter to determine the dark enhancement dynamics. It is obvious that the polymerization does not stop instantly when illumination is turned off [16,23]. However comparing with the time of 6000s for dark enhancement, the lifetime of active radicals generally is short, which leads to the diffusion of radicals can be neglected after exposure. Therefore, the PQ’s diffusion dominates the all dark enhancement of volume grating.
The photoreaction of PQ molecules to the polymer chains and other components could be considered as photo-induced polymerization in an incompletely polymerized PMMA material like our sample . The diffusion coefficient is related to reciprocal of the PQ’s concentration based on the “free volume” theory [16,23]. An approximate expression considering an exponential decrease of PQ’s concentration appears as followsEq. (6). We measure the evolution of diffraction efficiency under the continuous recording process, as shown in inset of Fig. 2(a) . In this process the diffusion of PQ molecules is neglected due to the short exposure time. The exposure constant Eτ = 1.7 × 104mJ/cm2 is determined by fitting the exponential function. The dependence of diffusion coefficients versus reciprocal of residual PQ’s concentrations is illuminated in Fig. 2(a). The definite enhancement rate can be obtained by selecting appropriated PQ’s concentration. The constants D 0 = 3.8 × 10−18m2/s is higher than the value 10−19~10−20 m2/s in ref . It can be ascribed to the differences between bulk thermal polymerization and drying polymer-dye mixture in preparation of materials [6,8]. The former results in broad molar mass distribution and high diffusion rate. Moreover the neglected initial dark reaction of active radicals, which is determined by the lifetime of radicals, maybe also enhance the rate of dark enhancement. When the dark enhancement reaches a steady state, the increment of refractive index modulation can be approximately described asFig. 2(b). Consequently this curve provides a quantitative description between the increment and exposures. The value of R2 represented in this figure shows the agreement between the experiments and the theoretical behavior assumed.
5. Dark enhancement of multiplexing gratings
Figure 3(a) shows dark enhancement in multiplexing gratings. Cumulative grating strengths are calculated for analyzing the response region of the materials, as shown in Fig. 3(b). After recording several gratings with constant exposure 1.1 × 104 mJ/cm2, the response of material reaches the saturation. However, the dependence of cumulative grating strength on the cumulative exposure returns to linear region when the enhancement reaches a steady state. It is implied that the response region of materials is far from the saturation because of the dark enhancement. The further holographic recording from taking place in the exposure spot can be achieved.
Figure 4 shows that the homogeneity improvement of diffraction efficiency by dark enhancement. Because the increment of weak gratings is larger than the strong gratings during dark enhancement in multiplexing, we record the gratings in the linear response region of materials with constant exposure 1.1 × 104 mJ/cm2. The larger enhancements of weak gratings reduce the difference of diffraction efficiency between several gratings. Therefore the more uniform diffraction efficiency can be obtained only by using constant exposure method. It is implied that in linear region of materials, we can utilize this simple method to achieve uniform diffraction efficiency in multiplexing and avoid using complex calculated technique  and experimental procedures  of schedule exposure in the photopolymers.
6. Numerical simulation
To illustrate the dynamics of dark enhancement, we solved the Eq. (9) by taking into account the initial conditions (t = te) and the given boundary. When the sample was illuminated by the modulated light for t = te, the distribution of PQ molecules and polymers could approximately be described as
Figure 5 shows the spatial-temporal dynamics of PQ’s concentration and refractive index modulation after recording exposure. In order to illustrate the boundary of the grating, only a fraction of fringe periods was described. In Fig. 5(a) and (b), at initial time the spatial profile of PQ’s concentration is clear-cut. At steady state the distribution of concentration will be an uniform constant. It is interesting that the change of PQ’s concentration at the boundary of grating is larger than other position, because the molecules concentration approximately keep up a constant around the exposure spot, and a lot of PQ molecules are supplied into the grating. In Fig. 5(c) and (d) the change of refractive index modulation is remarkable in this process. The distribution of refractive index modulation profile in depth is approximately equivalent due to high transmittance 80% at 532nm and 2mm thickness . Therefore the efficient thickness of sample approximately is closed to the physical thickness.
A detailed study of diffusional enhancements in holographic gratings in PQ-PMMA photopolymer is presented. The enhancement provided an efficient method to obtain high and steady diffraction efficiency and prevent the amplification of holographic scattering under consecutive exposure. The quantitative rate and increment bring a significant probability for applicability of enhancement. Dark enhancement in multiplexed gratings is introduced to optimize the response of the photopolymer and enhance its applicability. This process brings an alternative way to improve the homogeneity of diffraction efficiency and simplify the complex exposure schedule. The detailed PQ’s diffusion process and growth of refractive index modulation are indicated by solving the diffusion model. It is provided a significant strategy for qualitative and quantitative description about enhancement dynamics for the first time. This study can contribute to understanding of the photochemical process in the photopolymer and provide a significant foundation for applicability of dark enhancement in holographic data storage. The study for reducing the diffusion time and fixed the enhanced diffraction efficiency is still under way.
The research has been financially supported by the Fundamental Research Foundation of Commission of Science Technology and Industry for National Defense of China (Grant No. 2320060089).
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