Ciara E. Close

Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model

The nonlocal polymerization-driven diffusion model (NPDD) has been shown to predict high spatial frequency cut-off in photopolymers and to accurately predict higher order grating components. We propose an extension to the NPDD model to account for the temporal response associated with polymer chain growth. An exponential response function is proposed to describe transient effects during the polymerization process. The extended model is then solved using a finite element technique and the nature of grating evolution examined in the case when illumination is stopped prior to the saturation of the grating recording process. Based on independently determined refractive index measurements we determine the temporal evolution of the refractive index modulation and the resulting diffraction efficiency using rigorous coupled wave theory. Material parameters are then extracted based on fits to experimental data for nonlinear and both ideal and non-ideal kinetic models.

Improvement of the spatial frequency response of photopolymer materials by modifying polymer chain length

One of the key predictions of the nonlocal photopolymerization driven diffusion (NPDD) model is that a reduction in the extent of the nonlocal effects within a material will improve the high spatial frequency response. The NPDD model is generalized to more accurately model material absorbtivity. By eliminating the necessity for the steady-state approximation to describe the rate of change of monomer radical concentration, a more accurate physical representation of the initial transient behavior, at the start of grating growth, is achieved, which includes the effects of oxygen-based inhibition. The spatial frequency response of an acrylamide/polyvinylalcohol-based photopolymer is then improved through the addition of a chain transfer agent (CTA), sodium formate. Using the NPDD model demonstrates that the CTA has the effect of decreasing the average length of the polyacrylamide (PA) chains formed, thus reducing the nonlocal response parameter, σ. Further independent confirmation of the resulting reduction in the PA average molecular weight is provided using a diffusion-based holographic technique.

Monomer diffusion rates in photopolymer material. Part I. Low spatial frequency holographic gratings

For photopolymers, knowing the rate of diffusion of the active monomer is important when modeling the material evolution during recording in order to understand and optimize their performance. Unfortunately, a confusingly wide range of values have been reported in the literature. Re-examining these results, experiments are carried out for both coverplated (sealed) and uncoverplated material layers and the measurements are analyzed using appropriate models. In this way, a more detailed analysis of the diffraction processes taking place for large-period gratings is provided. These results, combined with those in Part II, provide unambiguous evidence that the monomer diffusion rate in a commonly used acrylamide polyvinyl alcohol-based material is of the order of 10 �10 cm 2 =s. This value closely agrees with the predictions of the nonlocal polymerization-driven diffusion model.

Modeling the photochemical effects present during holographic grating formation in photopolymer materials

The development of a theoretical model of the processes present during the formation of a holographic grating in photopolymer materials is crucial in enabling further development of holographic applications. To achieve this, it is necessary to understand the photochemical and photophysical processes involved and to isolate their effects, enabling each to be modeled accurately. While photopolymer materials are practical materials for use as holographic recording media, understanding the recording mechanisms will allow their limitations for certain processes to be overcome. In this paper we report generalizations of the nonlocal polymer driven diffusion (NPDD) model to include the effects of photosensitive dye absorption and the inhibition effects.

Temporal response and first order volume changes during grating formation in photopolymers

We examine the evolution of the refractive index modulation when recording gratings in an acrylamide based photopolymer. A nonlocal diffusion model is used to predict theoretically the grating evolution. The model has been developed to account for both nonlocal spatial and temporal effects in the medium, which can be attributed to polymer chain growth. Previously it was assumed that the temporal effect of chain growth could be neglected. However, temporal effects due to chain growth and monomer diffusion are shown to be significant, particularly over short recording periods where dark field amplification is observed. The diffusion model is solved using a finite-difference technique to predict the evolution of the monomer and polymer concentrations throughout grating recording. Using independently measured refractive index values for each component of the recording medium, the Lorentz-Lorenz relation is used to determine the corresponding refractive index modulation. The corresponding diffraction efficiency is then determined using rigorous coupled wave analysis. The diffraction efficiency curves are presented for gratings recorded using short exposure times, monitored in real time, both during and after recording. The effect of volume shrinkage of polymer on grating evolution is also examined. Both the nonlocal temporal response of the material and monomer diffusion are shown to influence refractive index modulation postexposure.

Optimized scheduling for holographic data storage

An algorithm, based on the non-local photopolymerization-driven diffusion (NPDD) model, which determines an appropriate recording schedule based on the physical properties of the recording mediums properties, is examined. While the algorithm was originally developed using a two-harmonic approximation to the NPDD spatially non-local model, here we examine the algorithms validity using a more rigorous NPDD formulation, solved using a finite difference method. Then the predictions of the algorithm and the inverse-square scaling law of holographic diffraction are examined experimentally, for a peristrophic multiplexing scheme. The scaling law is shown to significantly break down for low numbers of high diffraction efficiency gratings. A recently proposed modified form of the scaling law is then validated experimentally.

Optimized holographic data storage: diffusion and randomization

The control of the exposure patterns, which maximizes the capacity of a holographic recording medium, is of critical importance in any holographic data storage system. In this paper, we develop a method to theoretically explore linear photopolymer storage media in which a polymerization driven monomer diffusion process takes place. Using this method we examine a technique, involving randomly shifting the exposure pattern between exposures, to increase material capacity. The randomization acts to reduce the effects of past exposures by reducing the monomer concentration spatial distribution which arises due to those exposures. Following a detailed description of a series of assumptions and approximations, we derive an analytic formula, which allows us to explore the results of applying the technique. It is shown that, in the particular situation discussed, randomization can provide a useful tool in reducing constraints on the relaxation times necessary between exposures.

The impact of inhibition processes during grating formation in photopolymer materials

Photopolymer materials are good materials for the recording of holographic optical elements (H.O.Es), as they are inexpensive and self-processing. Understanding the mechanisms present during the fabrication of gratings in these materials is crucial in enabling further developments. One such mechanism is the presence of an inhibition period at the start of grating growth during which the formation of polymer chains is suppressed. Some previous studies have indicated possible explanations for this effect and mathematical models have been proposed to approximate the observed behaviour. We have carried out a set of experiments with the specific aim of developing an improved understanding of this process. In this paper we discuss these experimental results and provide a theoretical model, which describes the inhibition process in our Acrylamide based photopolymer and predicts this behaviour under certain conditions.

Fabrication and testing of holographic gratings

Holographic and diffractive optical elements (D.O.E.’s) have a variety of engineering applications. However, the availability of an inexpensive, self-processing, environmentally stable material with good spatial frequency response is crucial for further development in successful applications of holography. A number of different materials are currently being examined. In this paper we examine an Acrylamide-based photopolymer recording material, as it is one of the promising materials currently available. The material is self-processing and can be sensitised to different recording wavelengths using a dye. The self-processing capability simplifies the recording and testing processes and enables holographic interferometry to be carried out without the need for complex realignment procedures. The material requires further improvement as it has a number of limitations, e.g. it has a poor spatial frequency response range (500-2500 l/mm). The improvement of this material will require bulk testing of the material. Therefore a LabView controlled automated fabrication and testing system was developed. Arrays of D.O.E.’s were recorded in the Acrylamide based photopolymer material using the automated system and the refractive index modulation and the thickness of the grating were extracted.

Control and Measurement of the Physical Properties in Acrylamide Based Photopolymer Materials

Recent improvements in holographic materials have led to advances in a variety of applications, including data storage and interferometry. To further increase the possibility of commercial applications in these areas it is necessary to have available an inexpensive, self-processing, environmentally stable material that has a good spatial frequency response. One promising type of material is Acrylamide-based photopolymer recording materials. The material can be made self-processing and can be sensitised to different recording wavelengths using different photosensitive dyes. The self-processing capability of this material simplifies the recording and testing processes and enables holographic interferometry to be carried out without the need for complex realignment procedures. Although this material has a lot of advantages over others it has significant disadvantages such as its spatial frequency response range (500-2500 lines/mm). Therefore, it is of ever-increasing importance to resolve uncertainties regarding optical and material properties, i.e. the refractive index and the diffusion constants. Using experimental diffraction efficiency measurements, a value for the refractive index modulation can be obtained. Then carrying out analysis using the Polymerisation Driven Diffusion model (PDD) values for the diffusion coefficients of various materials in the grating layer can be found. Applying the Lorentz-Lorenz relation, refractive index variations within the material can be more fully understood. With the resulting improved understanding it will be possible to improve the characteristics of photopolymer materials by altering the chemical composition, for example by controlling the crosslinker concentration or through the careful use of inhibitor and/or retarders to control the polymer chain growth.