Based on the previous study of the time varying photon absorption effects, the behavior of four different photosensitizers
in an AA/PVA photopolymer material has been further examined by using the developed 1-D Nonlocal Photopolymerization
Driven Diffusion (NPDD) model. In order to characterize the photosensitizers precisely, holographic
illuminations with different spatial frequencies are applied. Material parameters, i.e., the nonlocal response parameter,
σ, the diffusion rate of monomer, Dm, the chain initiation kinetic constant, ki, and the termination rate, kt, are extracted by
numerically fitting experimentally measure the refractive index modulation growth curve using the theoretical models.
In this paper, the four different photosensitizers under investigation are Erythrosin B; Eosin Y; Phloxine B; Rose Bengal.
Phenanthrenequinone (PQ) doped poly(methyl methacrylate) (PMMA) photopolymer material has been studied
extensively due to the growing interest in application involving photopolymers. However, to progress the development
a more physical material model has become necessary. In this article, a kinetic model is developed, which includes: (i)
the time varying photon absorption, including the absorptivity of a second absorber, i.e., the singlet excited state of PQ,
(ii) the recovery/regeneration and the bleaching of the excited state PQ, (iii) the nonlocal effect, and (iv) the diffusion
effects of both the ground and excited state PQ molecules and of the methyl methacrylate (MMA). A set of rate
equations are derived, governing the temporal and spatial variations of each chemical component concentration. 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 mol.%, 2 mol.% and 3 mol.%. The effect of different exposure intensities is
also examined. Material parameters are extracted by numerically fitting experimentally measure normalized
transmission curves and the refractive index modulation growth curve using the theoretical models.
Phenanthreneauinone (PQ) doped poly(methyl methacrylate) (PMMA) photopoplymer material has been actively investigated in the literature. Based on the previously developed NPDD model and the analysis of the mechanisms, the behavior of the material is being further studied. The first harmonic refractive index modulation has been examined for both long time post-exposure and under thermal treatment. Twelve and four spatial concentration harmonics in the Fourier series expansions are applied respectively for comparison. Several effects, i.e., the non-local effect, the diffusion of both the ground state and excited states PQ molecules, which occur during and post-exposure in PQ-PMMA photopolymer materials, have been studied under thermal treatment. For long time post-exposure or when the heating treatment is applied, the formation of the photoproduct, PQ/PMMA, has become very important. The effects of nonlocality, diffusion and the different exposing intensities on the distribution of PQ/PMMA over space and higher harmonic PQ/PMMA concentration have been shown. The experimental results are presented, where no thermal treatment is applied.
In recent work carried out, we introduced the developments made to the Non-local Photo-polymerization Driven Diffusion model, and illustrate some of the useful trends, which the model predicts and then analyse their implications on photopolymer improvement. The model was improved in its physicality through the inclusion of viscosity effects (changes in fractional free volume), multiple components and their photo-kinetic and photo-physical behaviour, and free space vacuoles. In this paper, we further explore this model to provide a more rigorous and informed basis for predicting the behaviours of photopolymer materials in both photo-chemical and photo-physical sides. Such improvements include a) the analysis of the effects of viscosity on the refractive index modulation, b) the effects of the introduction of free space holes, e.g. the volumetric changes, and c) an examination of the effects of local temperatures and various concentration ratios to optimise material performance.
The photopolymer materials in Holographic Data Storage (HDS) have been increasingly studied due to their growing interest in applications. In this article we make use of the time varying parameters to study the behaviors of the photopolymer materials during exposure time. The nonlocal photo-polymerization driven diffusion (NPDD) model and electromagnetic theories of Maxell equations are combined in our model development. Moreover in this model, the theories of the material molecule polarization and the excited photosensitizer conductivity production are also introduced. The numerical simulation results in both cases of transmittance and diffraction efficiency are all analyzed. Several physical parameters and photochemical rate constant values are estimated by fitting the model predictions to the experimental results of AA/PVA material.
Several studies of the time varying photon absorption effects, which occur during the photo-initiation process in
photopolymer materials, have been presented. Three primary mechanisms have been identified: (i) the dye absorption,
(ii) recovery, and (iii) bleaching. Based on an analysis of these mechanisms, the production of primary radicals can be
physically described and modelled. In free radical photo-polymerization systems, the excited dye molecules induce the
production of the primary radicals, R•, which 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
overcome the complexicy of estimating the rate constant of intersystem crossing, kst, in going from the excited singlet
state dye to the excited triplet state dye, by introducing kaS and kaT into the model, which are the rate constant of photon
absorption from ground state to singlet state and triplet state respectively.
The Non-local Photo-Polymerization Driven Diffusion (NPDD) model was introduced to describe the observed drop-off
in the material's response for higher exposing spatial frequencies. Recent work carried out on the modeling of the
mechanisms which occur in photopolymers during- and post-exposure, has led to the development of a tool, which can
be used to predict the behaviour of these materials under a wide range of conditions. In this article, based on the
chemical reactions of chain transfer agents, we explore this extended NPDD model, illustrating some of the useful trends,
which the model predicts and we analyse their implications on the improvement of photopolymer material performance.
An understanding of the photochemical and photo-physical processes, which occur during photo-polymerization, is of
extreme importance when attempting to improve a photopolymer material's performance for a given application.
Recent work carried out on the modeling of photopolymers during- and post-exposure, has led to the development of a
tool, which can be used to predict the behavior of a number of photopolymers subject to a range of physical conditions.
In this paper, we explore the most recent developments made to the Non-local Photo-polymerization Driven Diffusion
model, and illustrate some of the useful trends, which the model predicts and then analyze their implications on
photopolymer improvement.
The use of theoretical models to represent the photochemical effects present during the formation of spatially and
temporally varying index structures in photopolymers, is critical in order to maximise a material's potential. One such
model is the Non-local Photo-Polymerization Driven Diffusion (NPDD) model. Upon application of appropriate
physical constraints for a given photopolymer material, this model can accurately quantify all major photochemical
processes. These include i) non-steady state kinetics, (ii) non-linearity iii) spatially non-local polymer chain growth, iv)
time varying primary radical production, v) diffusion controlled effects, vi) multiple termination mechanisms, vii)
inhibition, (viii) polymer diffusion and ix) post-exposure effects. In this paper, we examine a number of predictions
made by the NPDD model. The model is then applied to an acrylamide/polyvinylalcohol based photopolymer under
various recording conditions. The experimentally obtained results are then fit using the NPDD model and key material
parameters describing the material's performance are estimated. The ability to obtain such parameters facilitates
material optimisation for a given application.
The Non-local Photo-Polymerization Driven Diffusion (NPDD) model indicates how a material's performance might be
improved, and provides a tool for quantitive comparison of different material compositions and to predict their
fundamental limits. In order to reduce the non-locality of polymer chain growth (i.e the non-local response parameter, σ)
and to improve the spatial frequency response of a photopolymer material, we introduce the chain transfer agent (CTA).
In the literature, extensive studies have been carried out on the improvements of the non-local response modifying by the
CTA, sodium formate, in the polyvinyl alcohol-acrylamide (PVA/AA) material. In this article, i) based on the chemical
reactions of CTA, we extended the CTA model in the literature; ii) we compare two different CTA materials, sodium
formate and 1-mercapto-2-propanol without cross-linker in order to obtain the experimental confirmation of the
reduction in the average polymer molecular weight is provided using a diffusion-based holographic technique; iii) we
examine the non-local responses of several spatial frequencies with the two CTAs. Using the extended CTA model it is
demonstrated that the CTA has the effect of decreasing the average length of the polyacrylamide (PA) chains formed,
thus reducing the non-local response parameter, especially, in the high spatial frequency case.
Holographic recording at shorter wavelengths enables to capture holograms with a greater resolution. Photopolymer
material sensitisation to a blue or violet wavelength might require replacement of photosensitive dye or whole
photosensitiser system which leads to different photoinitiation kinetics. There are known photoinitiator systems which
have high values of key photoinitiation parameters, e.g., molar absorption coefficient at a broad range of wavelengths,
quantum yield etc. An example of such photosensitiser is an organometallic titanocene, Irgacure 784. However Irgacure
784 in an epoxy resin photopolymer undergoes a complex photo-kinetics which is neither fully understood nor
quantified. This complex photo-kinetics results in different bleaching evolution when using green and blue exposing
light. The aim of this paper is to identify relevant photo-kinetic reactions taking place during exposure and driving the
bleaching process. For this purpose photopolymer layers of four material compositions containing Irgacure 784 were
prepared and exposed for nine exposure times. Absorbance spectrum was measured before after each exposure. We
report on our experimental results and draw conclusions identifying relevant reactions of the Irgacure 784 photo-kinetics
in epoxy resin photopolymers.
Photopolymer materials exhibit good characteristics when used as holographic recording media. Extensive studies have been carried out on the behavior of the various chemical components in such materials, with photosensitizers in particular receiving much attention. In all previous analysis of photopolymer kinetics, the effects of photosensitiser diffusion have been neglected. For rapid sequential holographic recordings in photopolymers, for example, in an application such as holographic data storage, dye diffusion effects may become more pronounced. Therefore, we examine the dye diffusion effects of erythrosine B in an acrylamide/polyvinyl alcohol material. This is achieved using simple experimental techniques and a proposed theoretical model.
KEYWORDS: Molecules, Absorption, Photopolymers, Holography, Oxygen, Data modeling, Modulation, Molecular energy transfer, Optoelectronics, Refractive index
In the literature, several studies of the time varying photon absorption effects, which occur during the photo-initiation
process in photopolymer materials, have been presented. Three primary mechanisms have been identified: (i) The
photon absorption, (ii) the regeneration or recovery of the photosensitizer, and (iii) the photosensitizer bleaching. Based
on the analysis of these mechanisms, the production of primary radicals can be physically described and modelled. In
free radical photo-polymerization systems, the excited dye molecules induce the production of the primary radical, R•, which is a key factor that in determining how much monomer is polymerized. This in turn is closely related to the
refractive index modulation, Δn, formed during holographic recording. In this article, by modifying the composition of a Polyvinylalcohol/Acrylamide (PVA/AA) based photopolymer material, i.e., excluding any co-initiator, the photo-kinetic
behaviour of the material is greatly simplified, an experimental study is performed, which makes possible development
and verification of a new model capable of accurately predicting the time varying concentration of primary radicals.
Establishing the rate of monomer diffusion in a polyvinylalcohol and acrylamide based photopolymer
holographic material is of importance in terms of modelling the processes taking place during and postrecording
and in working towards improving the materials response. Many methods have been used to
estimate this value, resulting in a very wide range of suggested rates from 10-7-10-14 cm2/s. We
examine the diffusion of polymer chains formed using short low intensity exposures, recorded in a
modified material composition and then use these results to provide an estimate of monomer diffusion
under low viscosity conditions i.e. minimal uncrosslinked polymerisation. Our modification of the
material involves removing the crosslinking agent, the purpose of which is to increase polymer chain
size and complexity and so make the recorded grating more stable. Removing it, the chains should be
shorter and more linear - i.e. closer to the size of the monomer and so the rate of diffusion of the
polymerised chains should approach the rate of diffusion of the monomer as the exposure and duration
energy are smaller.
Photopolymer materials are practical materials for use as holographic recording media due to the fact that they are
inexpensive, self-processing materials with the ability to record low loss, highly diffraction efficient volume holographic
gratings. Extensive studies have been carried out on the behaviour of the various chemical components in such materials,
with photosensitizers in particular receiving much attention, as they are an important component in initialising the
photopolymerisation reaction. However in all such analyses dye diffusion is neglected. To further develop such
materials, a deeper understanding of behaviours the photosensitizer present during the formation of holographic gratings
in these materials has become ever more crucial. We report on experimental results and theoretical analysis of the
diffusion rate of Erythrosine B, in a Polyvinylalcohol/Acrylamide layer.
Despite the physical significance of the slanted holographic gratings, most materials research presented in literature
involves the use of the unslanted recording geometry. A physically accurate electromagnetic model of the slanted
holographic non-uniform gratings recorded in photopolymers is necessary in order to extract key material parameters. In
this paper we present derivation of a model based on a set of two coupled differential equations, which include the
effects of: (i) An exponential decay of refractive index modulation in the direction of the beam propagation due to the
variation of absorption with depth; (ii) Gaussian profile of refractive index modulation due to recording by finite
Gaussian beams profile, and (iii) A quadratic variation in the spatial period of the grating (i.e. chirp). The model is
applied to fit experimental data, i.e. angular scans, of unslanted gratings recorded in Polyvinylalcohol/Acrylamide
material for different slant angles in order to extract key volume grating parameters.
In photopolymers knowing the rate of diffusion of the monomer is of great interest in terms of modelling the evolution of
recordings and predicting material behaviour. A wide range of values have been proposed using various indirect optical
measurement techniques. A method involving the recording of very large period gratings, i.e. which diffract in the
Raman-Nath regime, has been proposed, the results of which have been interpreted to suggest a diffusion rate of the
order of 10-8cm2/s. Using a similar acrylamide and polyvinylalcohol based material, the experiment involves monitoring
the evolution of the zeroth order diffraction efficiency, the decay of which it is assumed is solely due to diffusion of the
monomer. Repeating these experiments for different periods and for coverplated and uncoverplated layers, we offer a
more complete analysis of the processes taking place indicating that not only is a volume holographic grating formed but
also a surface relief profile. Evolution of both the holographic and the surface relief gratings will have an impact on the
estimated rate of monomer diffusion. Results illustrating the variation are demonstrated and from these we show that the
rate of diffusion of monomer to be closer to the order of ~10-10 cm2/s.
The one-dimensional Non-local Photo-Polymerization Driven Diffusion (NPDD) model, which governs the temporal
evolution of holographic grating formation in photopolymers, has been further developed to include all major
photochemical processes. These effects include: i) non-steady state kinetics, ii) spatially non-local polymer chain
growth, iii) time varying photon absorption, iv) diffusion controlled effects, v) multiple termination mechanisms, vi)
inhibition, and vii) post-exposure or dark-reaction effects. The resulting analytic expressions for the monomer and
polymer concentrations are then derived and their validity tested against experimental data using a 4-harmonic,
numerical fitting regime. The temporal variation in the refractive index modulation is accounted for using the Lorentz-
Lorenz relation, and the effects of dark reactions for short holographic exposures are examined for a range of
photopolymer materials.
In order to further improve photopolymer materials for applications such as data storage, a deeper understanding of
the photochemical mechanisms which are present during the formation of holographic gratings has become ever
more crucial. This is especially true of the photoinitiation processes, since holographic data storage requires
multiple sequential short exposures. Previously, models describing for the temporal variation of the photosensitizer
concentration as a function of exposure have been presented and applied to two different types of photosensitizer,
which includes the effects of photosensitizer recovery and bleaching under certain conditions. In this paper, based
on a detailed study of the photochemical reactions, the previous model is improved to more closely represent these
physical effects in a more general fashion, enabling a more accurate description of the time varying absorption and
thus of the generation of primary radicals.
Photopolymers are promising as holographic recording media as they are inexpensive, versatile materials, which can be
made sensitive to a broad range of wavelengths. A deeper understanding of the processes, which occur during
holographic grating formation in photopolymers, is necessary in order to develop a fully comprehensive model, which
represents their behaviour. One of these processes is photo-initiation, whereby a photon is absorbed by a photosensitiser
producing free radicals, which can initiate free radical polymerisation. These free radicals can also participate in
polymer chain termination (primary termination) and it is therefore necessary to understand their generation in order to
predict the temporally varying kinetic effects present during holographic grating formation. In this paper, a study of the
photoinitiation mechanisms of Irgacure 784 dye, in an epoxy resin matrix, is carried out. This is achieved by analysing
the temporal evolution of a series of simultaneously captured experimental transmittance curves, captured at different
wavelengths, but at the same location, to enable the change in photon absorption during exposure to be estimated. We
report on the experimental results and present a theoretical model to predict the physically observed behaviour.
The one-dimensional diffusion equation, which governs the temporal evolution of holographic grating formation in
photopolymers, which includes the non-local material response, the generalized dependence of the rate of
polymerization on the absorbed illuminating intensity and the inclusion of our material's response to initiation and
inhibition effects has been previously studied and presented. The resulting analytic expressions for the monomer and
polymer concentrations have been derived and their validity tested against experimental data using a four-harmonic,
numerical fitting regime. In this paper we examine the spatial frequency response of our photopolymer material and
using our improved NPDD model we fit experimentally obtained data and extract estimates for material parameters.
We attempt to improve our material's spatial frequency response with the addition of chain transfer agents to reduce the
polymer chain length formed and the non-local chain-length variance. Achieving this should increase the locality of the
polymer chains and hence cause an improvement in the spatial frequency response of the material. It is a material's
response to high spatial frequencies, which determines a material's resolution and data storage density.
Photopolymer materials are practical materials for use as holographic recording media. In order to further develop such
materials, a deeper understanding of the photochemical mechanisms present during the formation of holographic
gratings in these materials has become ever more crucial. This is especially true of the photoinitiation process, which
has already received much attention in the literature. Typically the absorption mechanism varies with exposure time.
This has previously been investigated in association with several effects taking place during recording. Since
holographic data storage requires multiple short exposures, it is necessary to verify the temporal change in
photosensitizer concentration. Post exposure effects have also been discussed in the literature; however, they do not
include post exposure effects such as the photosensitizer recovery. In this paper we report experimental results and
theoretical analysis to examine the effects of the recovery and bleaching mechanisms which arise during exposure.
Photopolymer materials are practical materials for use as holographic recording media, as they are inexpensive
and self-processing. By understanding the mechanisms present during recording in these materials their
limitations for certain processes can be improved and a more efficient, environmentally stable material can be
produced. In this paper we briefly review the application of photopolymer materials in the area of holographic
data storage. In particular we discuss the recent development of the Non-local Polymerisation Driven Diffusion
Model, (NPDD) including absorption and inhibition, and analysis of the photochemical effects present during
the evolution of holographic grating formation. The inclusion of these effects allows a more accurate
understanding of the photo-polymerisation process.
Photopolymer materials are practical materials for use as holographic recording media, as they are inexpensive and selfprocessing. By understanding the mechanisms present during recording in these materials their limitations for certain processes can be improved and a more efficient, environmentally stable material can be produced. Understanding the photochemical and photo-physical processes present during the formation of holographic gratings in photopolymer materials is crucial in enabling further development of holographic applications such as data storage, metrology, free space optical components etc. In order to achieve this, it is necessary to develop material electromagnetic theory, which models these applications. In this paper we begin by experimentally estimating parameters associated with absorption due to dye in the photopolymer. This information is needed when using Non-local Photo-Polymerization-Driven
Diffusion model (NPDD) to characterise such materials. Absorption also leads to the formation of non-uniform tapered grating structures. While the NPDD has been used to characterise materials recording slanted gratings problems have arisen in determining diffusion constants accurately. In order to deal with electromagnetic diffraction by the resulting non-uniform slanted grating structures we develop first order analytic expressions governing the replay of such gratings.
A generalized non-local polymerization driven diffusion (NPDD) model is presented, which
includes the effects of absorption and inhibition. Experimentally obtained growth curves are fit using a
four-harmonic numerical fitting algorithm and key material parameters are extracted.
Holographic data storage systems, utilising various photopolymer materials as the recording medium, are currently being developed. The photopolymer recording material used in this study is an Acrylamide/PVA based material. In this paper, having determined values for some basic properties of the material such as diffusion of Polyacrylamide and diffusion of water, we now look at chemically modifying the material and experimentally determine the impact. An important material characteristic, which determines the performance of any photopolymer medium, is the spatial frequency response of that material. Previously, applying our Non-local Photo-Polymerisation Driven Diffusion Model, (NPDD), we have discussed the effects on material behaviour of the length of the polymer chains and the rates of diffusion within the material. These parameters have been shown to be important in determining the response of the material. If the average length of the Polyacrylamide chains is shortened, an increase in the diffusion coefficient might be observed. Shorter Polyacrylamide chains should then result in an increase in the materials spatial frequency response, and ultimately in an increase in holographic data storage capacity. One possible method of doing this is to modify the chemical composition of the material to control chain length. The rates of diffusion of the material, both before and after modification of the chemical composition, are compared to determine the impact. Shortening the chain lengths should result in the possibility of creating smaller structures in the photopolymer material.
KEYWORDS: Diffraction, Diffraction gratings, Holography, Data storage, Polymers, Data modeling, Diffusion, Polymerization, Photopolymers, Refractive index
The development of an optimized scheduling technique based on an accurate model is necessary for the continued
development of holographic data storage technology. In this paper we examine an algorithm based on the non-local
polymerization driven diffusion model (NPDD), which determines an appropriate recording schedule for use in data
storage. The NPDD model accounts for nonlocal spatial and temporal material effects present in material involving free
radical chain polymerization. The model is solved using a finite difference technique and an optimized schedule
determined. Results are compared to experimental work. The inverse-square scaling law of holographic diffraction is
also examined and is shown to hold for low diffraction efficiency gratings but breaks down for a low number of high
efficiency gratings.
Development of a theoretical model of the processes present during the formation of a holographic grating in photopolymer material is crucial in enabling further development of holographic applications. To achieve this, it is necessary to understand the photochemical and photo-physical processes involved and to isolate their effects enabling them to be modelled accurately. Photopolymer materials are practical materials for use as holographic recording media, as they are inexpensive and self-processing. Understanding the recording mechanisms will allow their limitations for certain processes to be improved and a more efficient, environmentally stable material to be produced. In this paper we further develop our Non-local Polymer Driven Diffusion (NPDD) model to include the effects of absorption and inhibition effects. Thus we attempt to increase the accuracy of our existing model.
Incorporating the effects of volume changes into the Nonlocal Polymerization Driven Diffusion Model we examine these effects on grating evolution. The concept of free volume or hole formation is explored and the subsequent decay and diffusion of holes examined. The inclusion of a nonlocal temporal response function is also shown to be critical to the modeling of grating formation for short recording times. The model is solved using a finite difference technique and results converted initially to refractive index modulation and then to diffraction efficiency using rigorous electromagnetic theory. Fits are carried out to experimental data and model parameters determined.
The Nonlocal Polymerization Driven Diffusion model, NPDD, is can be used to describe holographic grating formation in Acrylamide-based photopolymer. The free radical chain polymerization process results in polymer being generated nonlocal both in space and time to the point of chain initiation. Temporal nonlocality can be used to describepost exposure dark effects. Nonlinear response and the effects of dye bleaching have been examined. Both primary and bimolecular chain termination mechanisms have been included and examined. Recently 3-D, and inhibition effects have also been included. In this paper we review of our recent work. It is shown that temporal effects become most notable for short exposres and the inclusion of the nonlocal temporal response function is shown to be necessary to accurately describe the process. In particular, brief post exposure self-amplification of the refractive index modulation is noted. This is attributed to continued chain growth for a brief period after exposure. Following this a slight decay in the grating amplitude also occurs. This we believe is due to the continued diffusion of monomer after exposure. Since the sinusoidal recording pattern generates a monomer concentration gradient during the recording process monomer diffusion occurs both during and after exposure. The evolution of the refractive index modulation is determined by the respective refractive index values of the recording material components. From independent measurements it is noted that the refractive index value of the monomer is slightly less than that of the background material. Therefore as monomer diffuses back into the dark regions, a reduction in overall refractive index modulation occurs. Volume changes occurring within the material also affect the nature of grating evolution. To model these effects we employ a free volume concept. Due to the fact that the covalent single carbon bond in the polymer is up to 50% shorter than the van der Waals bond in the liquid monomer state, free volume is created when monomer is converted to polymer. For each bond conversion we assume a hole is generated which then collapses at some characteristic rate constant. The Lorentz-Lorenz relation is used to determine the overall evolution refractive index modulation and the corresponding diffraction efficiency of the resulting grating is calculated using Rigorous Coupled Wave Analysis (RCWA). The Lorentz-Lorenz relation is used to determine the overall evolution refractive index modulation and the corresponding diffraction efficiency of the resulting grating is calculated using Rigorous Coupled Wave Analysis (RCWA). Inhibition is typically observed at the start of grating growth during which the formation of polymer chains is suppressed. In this paper experiments are reported, carried out with the specific aim of understanding of these processes. The results support our description of the inhibition process in an PVA/Acrylamide based photopolymer and can be used to predict behaviour under certain conditions.
The Nonlocal Polymer Driven Diffusion (NPDD) model successfully predicts high spatial frequency cut-off and higher
harmonic generation, experimentally evident in holographic gratings recorded in free radical chain photopolymer
materials. In this paper the NPDD model is extended to include a nonlocal material temporal response. Previously it
was assumed that following a brief transient period, the spatial effect of chain growth was instantaneous. However,
where the use of short exposures is necessary, as in optical data storage, temporal effects become more significant.
Assuming that the effect of past chain initiations will have less effect on monomer concentration at a later point in time
than current initiations, a normalized exponential function is proposed to describe the process. The extended diffusion model is then solved using a Finite-Difference Time-Domain technique to predict the evolution of the monomer and
polymer concentrations during and after grating recording. The Lorentz-Lorenz relation is used to determine the
corresponding refractive index modulation and The Rigorous Coupled Wave Method applied to determine and/or
process diffraction efficiencies. A fitting technique is then used which first solves the diffusion model as described and
determines a set of parameters which give best fits to the experimental data. Results show that the inclusion of the
nonlocal temporal response is necessary to accurately describe grating evolution for short exposures i.e. continued
polymer chain growth for some period after recording resulting in an increase in the refractive index modulation.
Monomer diffusion is also shown to influence refractive index modulation post-exposure. Monomer diffusion rates
determined to be of the order of D ~ 10-11 cm2/s and the time constant of the nonlocal material temporal response
function being of the order of τn ~ 10-2s.
Holographic data storage systems, utilising photopolymer material as the recording medium, have recently been
presented. Because of their relatively low cost and ease of use, due to their self-processing nature, photopolymers
provide many potential advantages as the holographic recording material and data storage medium of choice.
Photopolymers show promise, for example, for Write-Once Read-Many (WORM) storage systems. The photopolymer
recording medium used in this study is an Acrylamide/Polyvinylalcohol (A/PVA) based dry layer. An important
material characteristic, which determines the performance of any photopolymer medium, is the spatial frequency
response of that material. Previously, applying our Non-local Photo-Polymerisation Driven Diffusion Model, (NPDD),
we have discussed the effects on material behaviour of the length of the polymer chains and the rates of diffusion within
the material. These parameters have been shown to be critically important in determining the response of the material.
If the average length of the Polyacrylamide (photopolymerised Acrylamide monomer, PA), chains is shortened, an
increase in the diffusion coefficient of these molecules might be observed. According to the NPDD shorter PA chains
should then result in an increase in the materials spatial frequency response, and ultimately in an increase in holographic
data storage capacity. In this paper we report on several experiments carried out (a) to determine the diffusion constant
of the PA and (b) to also determine the diffusion constants of both water and Propanol in our material layers.
In recent years there has been an increasing interest in holography and its applications. One such application is data
storage. Optimising the holographic recording materials is therefore of critical importance in the capacity and clarity
of the information stored. Photopolymer materials are practical materials for use as holographic recording media, as
they are inexpensive and self-processing. Understanding the photochemical mechanisms present during recording in
these materials is crucial in enabling further developments. Obtaining critical material parameters allows
improvements of the performance of these materials, such as its spatial frequency response or its environmental
stability. This also allows a better understanding of the photochemical processes that occur during the formation of
the holographic grating. Our current work, which is presented in this paper deals with two of the processes that
occur during holographic grating formation. The first of these is the photochemistry involved in the absorption of
the light by the photosensitive dye. We monitor the power of the transmitted beams, which are used for recording
the gratings. The second process we concentrate on is the inhibition effect present during grating growth. It has
been noted in the literature that there is a slight delay at the start of grating growth. The reason for this delay is due
to an inhibition process, which is present to some extent in all photopolymer recordings. The work presented here
explains why it occurs. A theoretical model is developed to predict the behaviour of the temporal evolution of the
grating. This model has been improved to account for the absorption effects of the material due to the photosensitive
dye and the inhibition period, which results in a reduction in the rate of polymerisation.
The nonlocal polymerization driven diffusion model is used to describe holographic grating formation in acrylamidebased
photopolymer. The free radical chain polymerization process results in polymer being generated nonlocal both in
space and time to the point of chain initiation. A Gaussian spatial material response function and an exponential
temporal material response function are used to account for these effects.
In this paper we firstly examine the nature of the temporal evolution of grating formation for short recording
periods. It is shown that in this case, temporal effects become most notable and the inclusion of the nonlocal temporal
response function is shown to be necessary to accurately describe the process. In particular, brief post exposure selfamplification
of the refractive index modulation is noted. This is attributed to continued chain growth for a brief period
after exposure. Following this a slight decay in the grating amplitude also occurs. This we believe is due to the
continued diffusion of monomer after exposure. Since the sinusoidal recording pattern generates a monomer
concentration gradient during the recording process monomer diffusion occurs both during and after exposure. The
evolution of the refractive index modulation is determined by the respective refractive index values of the recording
material components. From independent measurements it is noted that the refractive index value of the monomer is
slightly less than that of the background material. Therefore as monomer diffuses back into the dark regions, a
reduction in overall refractive index modulation occurs.
Volume changes occurring within the material also affect the nature of grating evolution. To model these
effects we employ a free volume concept. Due to the fact that the covalent single carbon bond in the polymer is up to
50% shorter than the van der Waals bond in the liquid monomer state, free volume is created when monomer is
converted to polymer. For each bond conversion we assume a hole is generated which then collapses at some
characteristic rate constant.
Incorporating each of these effects into our model, the model is then solved using a Finite-Difference Time-
Domain method (FDTD). The Lorentz-Lorenz relation is used to determine the overall evolution refractive index
modulation and the corresponding diffraction efficiency of the resulting grating is calculated using Rigorous Coupled
Wave Analysis (RCWA). Fits are then carried out to experimental data for 1 second exposures. Good quality fits are
achieved and material parameters extracted. Monomer diffusion rates are determined to be of the order of D ~ 10-10
cm2/s and the time constant of the nonlocal material temporal response function being of the order of τn ~ 10-2s.
Material shrinkage occurring over these recording periods is also determined.
Photopolymer materials are practical materials for use as holographic recording media, as they are inexpensive and self-processing. Understanding the mechanisms present during the fabrication of gratings in these materials is crucial in enabling further development. 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 examine the kinetic behaviour involved within the photopolymer material during recording to enable a clear picture of the photochemical processes present. Sets of experiments were carried out with the specific aim of developing an improved understanding of these processes. Here we discuss these experimental results and provide a theoretical model, which attempts to describe the inhibition process in our Acrylamide based photopolymer and predicts this behaviour under certain conditions.
In recent years developments in holographic materials have lead to an increasing interest in many areas such as data storage and metrology. Materials such as Acrylamide-based photopolymers are good holographic recording materials, as they are inexpensive and self-processing. The diffusion rate of monomer and the molecular weight of polymerised monomer determine many material characteristics. The length (size) of the polymer chains has a direct effect on the diffusion rate of the polymer and shortening the chain length leads to an increase in the diffusion rate. Shorter chains also decrease the non-local material response parameter and, in consequence, lead to an increase in the spatial frequency response of the material. Thus it is expected that by controlling the polymer chain length (molecular weight) one might control the material spatial frequency response. In this paper we look at the effect of varying the quantity of crosslinking agents on the material and its impact on the rate of diffusion. We then look at determining the rate of diffusion of water within the material to provide a lower limit to the maximum rate of monomer diffusion.
In this paper we analyze 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 both due to chain growth and monomer diffusion are shown to be significant, particularly of short recording periods. The diffusion model is solved using a Finite-Difference Time-Domain 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. Gratings recorded for short exposure times with the diffraction efficiency growth monitored in real time both during and after recording are presented. The effect of volume shrinkage of polymer on grating evolution is also examined. The temporal response of the material and monomer diffusion is shown to influence refractive index modulation post-exposure. The inclusion of the nonlocal temporal response and the use of the Lorentz-Lorenz relation are shown to be necessary to accurately describe this polymerization process.
Micro-optical devices are very important in current high-tech consumer items. The development of future products depends on both the evolution of fabrication techniques and on the development of new low cost mass production methods. Polymers offer ease of fabrication and low cost and are therefore excellent materials for the development of micro-optical devices. Polymer optical devices include passive optical elements, such as microlens arrays and waveguides, as well as active devices such as polymer based lasers. One of the most important areas of micro-optics is that of microlens design, manufacture and testing. The wide diversity of fabrication methods used for the production of these elements indicates their importance. One of these fabrication techniques is photo-embossing. The use of the photo-embossing technique and a photopolymer holographic recording material will be examined in this paper. A discussion of current attempts to model the fabrication process and a review of the experimental method will be given.
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.
Many of the next generation of high-tech consumer products will take advantage of the manufacturing advances in micro-optics that we are currently taking place. One of the most important areas of micro-optic research is that of microlens design and fabrication. The importance of this area is perhaps highlighted by the range of competing fabrication technologies. Each having important advantages/disadvantages for a given application. It is therefore important to pursue other possible fabrication methods. In this paper we examine two of these novel fabrication techniques: (1) Photo-embossing in holographic recording materials, and (2) Microfluidic lens fabrication. The first of these techniques offers the possibility of combining the advantages of diffractive optical elements with those of conventional refractive optical elements. The second technique in combination with inkjet deposition technology can be used to produce a wide range of optical elements (lenses) and offers the possibility of controlling the lens profile in real time during formation using electric fields.
Photopolymer materials are good materials for the recording of holographic optical elements (H.O.E's), 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.
The inclusion of a nonlocal spatial response function in the Nonlocal Polymer Driven Diffusion model (NPDD) has been shown to predict high spatial frequency cut-off in photopolymers and more recently it has been shown that use of the nonlocal model is necessary to accurately predict higher order grating components. Here the nature of the temporal response of photopolymer is discussed and a nonlocal temporal response function proposed. The extended model is then solved using a finite element technique and the results discussed. Based on this model we examine the nature of grating evolution when illumination is stopped during the grating recording process. Refractive indices of the components of the photopolymer material used are determined and predictions of the temporal evolution of the refractive index modulation described. Material parameters are then extracted based on fits to experimental data for non-linear and both ideal and non-ideal kinetic models.
The well known scaling law of holographic diffraction states that the replay diffraction efficiency η = Γ/M2, where M is the number of gratings (pages) stored, and G is a constant system parameter. This is an important metric used to quantify HDS material performance, and a great deal of experimental work to validate this rule for a wide variety of materials, (photorefractives, polymers etc.) have been presented over the years in the literature. No paper detailing the theoretical basis of this law, (i.e. including specific material characteristics, the recording geometry and/or the electromagnetic replay conditions), for photopolymers has previously been presented. In a recent paper [1] we have described in a clear way the optimization of the recording schedule in a photopolymer material governed by the Nonlocal Polymerization Driven Diffusion model (NPDD). One of the main assumptions made in [1] is that a long material relaxation time can be permitted between exposures. Another was that no phase shifts of the exposing pattern took place between exposures. In this paper we discuss these assumption and develop an intermediate first-order model. In a second paper [2], based on the results presented in [1] we have shown that our optimized predictions are in agreement with the scaling law of holographic diffraction. Thus the law is shown to hold for photopolymer recording media governed by the predictions of the NPDD. Based on our analysis: (i) A media inverse scaling law is proposed; (ii) G is for the first time related to photopolymer material parameters and the hologram geometry and replay conditions; and (iii) The form and validity of the diffraction efficiency inverse square scaling law for higher diffraction efficiency gratings is commented upon. In this paper we also review this result.
Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is non-local as it is assumed that monomers are polymerised to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The numerical method of solution typically involves retaining either two or four harmonics of the Fourier series of monomer concentration in the calculation. In this paper a general set of equations is derived which allows inclusion of higher number of harmonics for any response function. The numerical convergence for varying number of harmonics retained is investigated with special care being taken to note the effect of the; non-local material variance σ, the power law degree k, and the rates of diffusion, D, and polymerisation F0. General non-linear material responses are also included.
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.
Holography has become of increasing interest in recent years with developments in many areas such as data storage and interferometry. Photopolymer materials such as acrylamide-based photopolymers are ideal materials for the recording of holographic optical elements, as they are inexpensive and self-processing. There are many experiments reported in the literature that describe the diffraction efficiency and angular selectivity of various materials. The majority of these discuss the performance of the holographic optical element after the recording stage. It has been noted however, sometimes, the recording beams are seen to modulate in intensity during fabrication of the grating. In this paper we discuss our current work and improvements on our previous model. This paper incorporates the growth of an absorption grating during the recording process and deals with a non-ideal beam ratio illustrating the effects this has on the modulation. Our new model attempts to better explain the modulation of the recording beams during grating formation resulting in a more accurate approximation to this behaviour.
Many new high-tech consumer products that are now under development require micro-optical elements. The development of these micro-optical devices has been carried out by many different researchers working in a variety of areas. This has lead to a large number of different fabrication techniques. We examine a novel fabrication technique that may allow the development of large arrays of elements quickly and cheaply. It is known that the exposure of dye sensitised Acrylamide layers to light can lead to material refractive index and volume changes. It is therefore proposed that a patterned exposure can be used to form a mixture of volume and surface relief patterning, enabling the production of optical elements. The examination of this fabrication technique, in particular the study of the processes that result in this volume change, may also lead to improvements in the photopolymer material so as to control shrinkage of these materials. The development of low shrinkage holographic recording materials is an active area in holography as most current photopolymer materials exhibit some volume change during the recording process. This has implications for the fidelity of the replayed image. This is of crucial importance in areas such as data storage systems. The further study of this process also has implications for the wider holographic research community. It is important to understand the surface relief profile of the holographic element prior to extracting grating parameters as surface relief effects may influence the experimental data. In this paper we describe initial experimental attempts to produce micro-optical elements for use in the visible spectrum using patterned exposure of an Acrylamide based photopolymer material.
Holography has become of increasing commercial interest in recent years with significant technological developments in many areas such as data storage. Photopolymer materials such as acrylamide-based photopolymers are practical materials for the recording of holographic optical elements, as they are inexpensive and self-processing. A great deal of experimental data is available in the literature describing the diffraction efficiencies, growth curves and the angular selectivity of gratings recorded in various materials. Such testing is often carried out so as to allow a better understanding of the holographic recording processes to be developed and therefore allow material improvement. However, the majority of these discussions are based on the performance of the holographic optical element after the recording stage, once exposure is completed or using a probe beam during recording. It has been noted however, that sometimes, during recording, the recording beams are seen to vary in intensity during the fabrication of the grating. In this paper we discuss some of our recent experimental and theoretical results that attempt to explain the modulation of the transmitted exposing beams during grating formation and offer an explanation for this behaviour.
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