John V. Kelly

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.

Physical and effective optical thickness of holographic diffraction gratings recorded in photopolymers

In recent years the interest in thick holographic recording materials for storage applications has increased. In particular, photopolymers are interesting materials for obtaining inexpensive thick dry layers with low noise and high diffraction efficiencies. Nonetheless, as will be demonstrated in this work, the attenuation in depth of light during the recording limits dramatically the effective optical thickness of the material. This effect must be taken into account whenever thick diffraction gratings are recorded in photopolymer materials. In this work the differences between optical and physical thickness are analyzed, applying a method based on the Rigorous Coupled Wave Theory and taking into account the attenuation in depth of the refractive index profile. By doing this the maximum optical thickness that can be achieved can be calculated. When the effective thickness is known, then the real storage capacity of the material can be obtained.

Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions

The kinetics of photosensitive polymer holographic recording materials are examined assuming a material that exhibits nonideal kinetic behavior. Previously, a linear relationship between monomer concentration and polymerization was assumed when deriving the nonlocal polymer-driven diffusion (NPDD) model. This is consistent with ideal kinetic conditions in which chain termination is governed by a bimolecular process. However, these models have been reported to disagree with experimental results. In a limiting case of nonideal kinetics it is assumed that primary termination is dominant. In this case the NPDD model must be modified to incorporate a quadratic relationship between the monomer concentration and the polymerization rate. By use of a multiharmonic expansion method of solution the predictions of ideal (bimolecular or linear) and nonideal (primary or quadratic) kinetic models are compared. By using these models we carried out numerical fits to experimental growth curves of gratings recorded in an acrylamide-based cross-linked photopolymer system. Superior fits are achieved by use of the primary termination model. Physical parameters such as the diffusion constant are extracted and compared with results previously reported in the literature.

3 Dimensional analysis of holographic photopolymers based memories

One of the most interesting applications of photopolymers is as holographic recording materials for holographic memories. One of the basic requirements for this application is that the recording material thickness must be 500 microm or thicker. In recent years many 2-dimensional models have been proposed for the analysis of photopolymers. Good agreement between theoretical simulations and experimental results has been obtained for layers thinner than 200 microm. The attenuation of the light inside the material by Beers law results in an attenuation of the index profile inside the material and in some cases the effective optical thickness of the material is lower than the physical thickness. This is an important and fundamental limitation in achieving high capacity holographic memories using photopolymers and cannot be analyzed using 2-D diffusion models. In this paper a model is proposed to describe the behavior of the photopolymers in 3-D. This model is applied to simulate the formation of profiles in depth for different photopolymer viscosities and different intensity attenuations inside the material.

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.

Non-local polymerization driven diffusion based model: general dependence of the polymerization rate to the exposure intensity.

The nonlocal diffusion model proposed by Sheridan and coworkers has provided a useful interpretation of the nature of grating formation inside photopolymer materials. This model accounts for some important experimental facts, such as the cut-off of diffraction efficiency for high spatial frequencies. In this article we examine the predictions of the model in the case of a general dependence of the polymerisation rate with respect to the intensity pattern. The effects of this dependence on the different harmonic components of the polymerisation concentration will be investigated. The influence of the visibility on the different harmonic components will also be studied. These effects are compared to the effects of varying RD and sigmaD.

Nonlocal polymerization-driven diffusion-model-based examination of the scaling law for holographic data storage

For the first time to our knowledge, a detailed theoretical basis is provided for the well-known inverse-square scaling law of holographic diffraction, which states that replay diffraction efficiency eta = gamma/M2, where M is the number of gratings stored and gamma is a constant system parameter. This law is shown to hold for photopolymer recording media governed by the predictions of the nonlocal polymerization-driven diffusion model. On the basis of the analysis, we (i) propose a media inverse scaling law, (ii) relate gamma to photopolymer material parameters and the hologram geometry and replay conditions, and (iii) comment on the form and validity of the diffraction efficiency inverse-square scaling law for higher-diffraction-efficiency gratings.

Recording beam modulation during grating formation

Holography has been of increasing interest in recent years, with developments in many areas such as data storage and metrology. Photopolymer materials provide potentially good materials for holographic recording, as they are inexpensive and self-processing. Many experiments have been reported in the literature that describe the diffraction efficiency and angular selectivity of such materials. The majority of these reports discuss the performance of the holographic optical element after the recording stage. It has been observed, however, that sometimes, during exposure, the transmitted recording beam intensities vary with time. A simple phenomenological model is proposed to explain the beam modulation, which incorporates the growth of the phase grating, time-varying absorption effects, the mechanical motion of the plate, the growth of a lossy absorption grating during the recording process, and the effects of nonideal beam ratios.