Nonlocal Photopolymerization-driven Diffusion Research Articles

Improving the uniformity of holographic recording using multilayer photopolymer. Part I. Theoretical analysis.

An experimental and theoretical investigation of the preparation and exposure of multilayer photosensitive materials is presented. It is shown how the recorded change in the refractive index in each layer depends on the dye (photosensitizer) concentrations in each layer. It is also shown how the photosensitive material properties in each layer can be controlled to optimize some recording characteristics for particular applications. To do so, a set of equations, predicting the amplitude of higher harmonics refractive index amplitudes induced in the material layers with depth during exposure, is derived. This results in a technique for varying the dye concentration in each layer of a multilayer, so as to optimize volume diffraction grating performance. In part I of this paper, the 3D nonlocal photopolymerization-driven diffusion (NPDD) model is applied to calculate the resulting combined multilayer absorption and polymerization processes. The NPDD describes the time-varying behaviors taking place during exposure in such photopolymer materials. Simulations are performed for an acrylamide/polyvinyl alcohol-based photopolymer containing erythrosine-B dye. It is predicted that, in general, non-uniform gratings are formed, with the resulting refractive index being distorted both from the ideal sinusoidal cross-sectional spatial distribution and also with depth. This agrees with previous results indicating that increasing the thickness of a single photopolymer layer does not in practice lead to ever-increasing angular selectivity. In part II of this paper, it is confirmed experimentally that a suitably modified multilayer can be used to increase grating angular selectivity, i.e., reduce the width of the off-Bragg replay curve.

Holographic characterization of diffraction grating modulation in photopolymers.

In general, the holographic grating refractive index profiles in photopolymer materials are not identical to the exposing pattern. During exposure, high harmonics of the fundamental refractive index period are generated within the layer volume. A set of equations to calculate the amplitudes of the higher harmonics of refractive index induced in the grating is introduced. Then, an algorithm involving the use of the 3D nonlocal photopolymerization-driven diffusion model is presented and applied to calculate the resulting grating diffraction efficiencies. The experimental observation that the grating diffraction efficiency cannot reach the theoretical maximum value (ηmax=100%) and that, in the case of over-modulation, the minimum value (ηmin=0%) is also never achieved, are explained theoretically. The predictions of the simulations are also fit to experimental data for an acrylamide/polyvinyl alcohol photopolymer material with good agreement being achieved.

PQ/PMMA photopolymer: Modelling post-exposure

Phenanthrenequinone (PQ) doped poly(methyl methacrylate) (PMMA) photopolymer material is currently being actively investigated. A previously developed 1-D Nonlocal Photo-polymerization Driven Diffusion (NPDD) model is applied to further examine the behavior of the material post-exposure. The use of the nonlocal parameter when examining PQ/PMMA is discussed. The resulting predicted evolution of the first harmonic refractive index modulation is simulated both: (i) a long time post-exposure, and (ii) in the case of thermal treatment post-exposure. The convergence of the numerical simulations is examined, when both 12 and 4 spatial concentration harmonics are retained in the Fourier series expansions describing the various component material distributions. Several physical processes are studied, including the nonlocal material response and the effects of the diffusion of both the ground state and excited states PQ molecules (during and post-exposure). The effects of the use of different exposing intensities on the final grating formed are studied. The size of the higher grating harmonic concentration amplitudes in this final distribution is also discussed. Thus in this paper for the first time the effects/treatments taking place post-exposure are systematically studied. Our aim is to characterize the final stable grating. We show that both the nonlocal effect and the diffusion of the PQ excited states tend to weaken the PQ-PMMA grating but lead to higher fidelity of the recorded pattern. It is also shown that higher harmonic gratings are generated when higher exposing intensity is applied.

Three-dimensional extended nonlocal photopolymerization driven diffusion model Part I Absorption

When holographic gratings are recorded in a photopolymer material layer, the spatial distributions of the photoreactions taking place lead to the formation of nonuniform gratings in depth. In an effort to study such effects, in this series of papers a three-dimensional (3D) nonlocal photopolymerization driven diffusion (NPDD) model is developed. In Part I, we focused on describing the photoinitiation mechanisms by introducing a 3D dye absorption model that more accurately and physically describes the processes taking place. Then, the values of physical parameters are extracted by numerically fitting experimentally obtained normalized transmittance growth curves for a range of layer thicknesses in an acrylamide/polyvinyl alcohol (AA/PVA) photopolymer material sensitized by Erythrosine B (EB). In Part II [J. Opt. Soc. Am. B31, 2648 (2014)10.1364/JOSAB.31.002648JOBPDE0740-3224], applying the results in Part I, the full 3D photophysical and photochemical evolutions are modeled. Then the resulting 3D NPDD model is validated experimentally.

Comparison of a new photosensitizer with erythrosine B in an AA/PVA-based photopolymer material

Dyes often act as the photoinitiator PI/photosensitizer PS in photopolymer materials and are therefore of significant interest. The properties of the PI/PS used strongly influences grating formation when the material layer is exposed holographically. In this paper, the ability of a recently synthesized dye, D_1, to sensitize an acrylamide/polyvinyl alcohol (AA/PVA) based photopolymer is examined, and the material performance is characterized using an extended nonlocal photopolymerization-driven diffusion model. Electron spin resonance spin-trapping (ESR-ST) experiments are also carried out to characterize the generation of the initiator/primary radical, R(•), during exposure. The results obtained are then compared with those for the corresponding situation when using a xanthene dye, i.e., erythrosine B, under the same experiment conditions. The results indicate that the nonlocal effect is greater when this new photosensitizer is used in the material. Analysis indicates that this is the case because of the dye's (D_1) weak absorptivity and the resulting slow rate of primary radical production.

Study of PQ/PMMA photopolymer Part 2: experimental results

In Part 1 of this paper an extended 1D nonlocal photo-polymerization driven diffusion (NPDD) model was developed, giving the temporal and spatial variations of each chemical component concentration within a phenanthrenequinone-doped poly(methyl methacrylate) (PQ/PMMA) material layer. Simulations to study the predicted normalized transmission, the nonlocal effect, and the diffusion of ground and excited states of PQ are presented. In this paper, the validity of the proposed model is examined by applying it to fit experimental data for PQ/PMMA layers containing three different initial PQ concentrations; i.e., 1, 2, and 3 mol. %. The effect of different exposure intensities is also examined. Material parameter values are estimated by numerically fitting experimental normalized transmission curves and refractive index modulation growth curves using the proposed theoretical model.

Non-local spatial frequency response of photopolymer materials containing chain transferagents: I. Theoretical modelling

The non-local photopolymerization driven diffusion (NPDD) model predicts that areduction in the non-local response length within a photopolymer material willimprove its high spatial frequency response. The introduction of a chain transferagent reduces the average molecular weight of polymer chains formed during freeradical polymerization. Therefore a chain transfer agent (CTA) provides a practicalmethod to reduce the non-local response length. An extended NPDD model ispresented, which includes the chain transfer reaction and most major photochemicalprocesses. The addition of a chain transfer agent into an acrylamide/polyvinyl alcoholphotopolymer material is simulated and the predictions of the model are examined. Thepredictions of the model are experimentally examined in part II of this paper.

High Intensity Response of Photopolymer Materials for Holographic Grating Formation

In order to further develop the understanding of photopolymer materials, a more complete physical model has become necessary. In particular, a more accurate description of the photochemical mechanisms occurring during the photopolymerization processes is needed. Generally, in photopolymers, the photosensitizer absorbs light of an appropriate wavelength, becoming excited and causing the production of primary radicals, R•. In free radical polymerization systems, the generation of R• is a key factor in determining how much monomer is polymerized. This in turn is closely related to the refractive index modulation formed during holographic recording. In this article, we incorporate a detailed photoinitiation model into the nonlocal photopolymerization driven diffusion (NPDD) model. This model describes the following: (1) Photon absorption behavior and primary radical generation during initiation; (2) nonlocal macro-radical chain growth through propagation; (3) oxygen diffusion and replenishment for inhibition; (4) multiple termination mechanisms. This extended model is experimentally validated for high intensity holographic exposures to a polyvinylalcohol/acrylamide based photopolymer material.

Nonlocal photopolymerization kinetics including multiple termination mechanisms and dark reactions Part I Modeling

The photochemical processes present during free-radical-based holographic grating formation are examined. A kinetic model is presented, which includes, in a more nearly complete and physically realistic way, most of the major photochemical and nonlocal photopolymerization-driven diffusion effects. These effects include: (i) non-steady-state kinetics (ii) spatially and temporally nonlocal polymer chain growth (iii) time varying photon absorption (iv) diffusion controlled viscosity effects (v) multiple termination mechanisms, and (vi) inhibition. The convergence of the predictions of the resulting model is then examined. Comparisons with experimental results are carried out in Part II of this series of papers [J. Opt. Soc. Am. B26, 1746 (2009)].

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 medium's 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 algorithm's 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.

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.