In the last years many efforts have been invested in the development of augmented reality devices. Depending on the application different constraints need to be faced. Providing full color see-through augmented reality on eyeglasses with ophthalmic correction, and valid for a wide range of use cases, is one of the most challenging and ambitious applications. We are within a European Project aiming to this goal. One of the key components in this eyewear is the holographic lens mirror (HLM), acting as the beam combiner responsible for the see-through capability. In this work, we present the main goals of this European Project and, more specifically, the holographic approach being developed for the HLM within our research group.
The see-through application of holographic optical elements (HOEs) has gained a lot of attention in the scientific literature in recent years. Regarding this kind of holograms recorded in photopolymers, the shrinkage plays an important role in the final properties of the display, as it may alter the Bragg angle. The present work is focused on the characterization of a HOE as a coupler in a waveguide combiner, recorded in holographic transmission geometry without prisms in the experimental set-up. From this point of view, it has been found that for specific geometries where the diffracted beam cannot be trapped a priori, a significant coupling effect exists: this variation in the diffracted energy and the propagation angle inside the glass can be used to measure the shrinkage of the photopolymer for this HOEs recording.
Estimating the actual parameters of real holographic volume gratings from diffraction efficiency measurements is challenging. The natural formation of the grating provides different phenomena, such as shrinkage, bending of the fringes, or non-homogeneous modulation as a function of the thickness, amongst other issues. This work proposes a deep learning Convolutional Neural Networks (CNNs) and Feedforward Neural Networks (FNNs) hybrid architecture capable of predicting the grating parameters from theoretical and experimental diffraction efficiency patterns. For the training set of this regression problem, Kogelnik’s Coupled Wave Theory simulated data has been employed. Our best model has been trained with an 8000-sized dataset of 80 points of diffraction efficiency patterns simulated from a range of values for the normalized grating wavelengths, index modulations, and optical depths. It achieves test losses under one per cent (mean absolute error) for predicting the normalized grating wavelengths, index modulations and optical depths.
Photopolymers are designed and engineered with versatile applications including optics and photonics. Holography is one of the classical porpoises that use photopolymers as holographic recording materials. The success of these materials can be seen in the market with the photopolymer fabricated by Covestro. Some of these holographic applications require a long-time life of the holograms recorded in photopolymers. Nevertheless, initial tests of Covestro holograms show significant degradation after less than one year of exposure even after sealing and degradation occurs under solar light exposition. In this sense, it is important to perform deeper studies of the different possibilities for hologram conservation. Usually, the first step after recording is the material cure, with UV or visible light, to eliminate the residual dye and monomer. With this process high efficiency holograms can also be obtained. Afterwards, an index matching technique can be used to cover the material with a glass or it is possible the application of aerosol sealant. In this paper we analyze the introduction of holograms between two glasses linked by pressure, using Bayfol HX 200 from Covestro as the recording material. In order to characterize the process, four different spatial frequencies were tested, which were stored either by transmission or reflection schemes. The data of the reconstruction step has been measured before and after the encapsulation. In addition, multiple holograms have been superposed in the same glass, where we have found that shrinkage is more significant.
Polymer nanocomposites are designed and engineered on a nanometer scale with versatile applications including optics and photonics. During the last two decades, different photopolymerizable nano-compounds were introduced and developed to modify polymer properties. In this sense, inorganic and organic nanoparticles have been introduced to increase the refractive index modulation and/or to reduce the shrinkage. Liquid crystal polymer composites have been added to the category of active photopolymer materials with an electrically switchable option. Nowadays, in the design of smart glasses some problems remain on the table, like power consumption, the limitation of the resolution, the wide field of view, etc. The inclusion of holographic optical element has provided some possible solutions. In particular the photopolymers have been reported a good system to bring the photons produced in the image creation to the eye. Our group proposed an alternative scheme using transmission holographic elements. The fabrication architecture was tested with different photopolymers in order to optimize their chemical composition, and we proposed three schemes adapted to each material properties. In this paper we study the influence of the initiator concentration, for Holographic polymer dispersed liquid crystal photopolymer, on the refractive index modulation and on the tunable properties of these holographic optical elements.
We examine the validity of Eq. (5) in [A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng., 2007, Vol. 46(12), pp. 128001-1–128001-7] to describe the diffraction pattern of an optical fiber. We show that Eq. (5) must be changed to account for the phase introduced by the fiber correctly. In particular, we show that, to agree with the implicit criterion for representing traveling waves, given when using the Fresnel–Kirchoff integral [Eq. (4)], the phase introduced by the object must be carried by positive exponentials. The results obtained correcting Eq. (5) are compared with those obtained by the rigorous solution of Maxwell equations in the optical fiber. We demonstrate the importance of adequately taking into account the criterion implicitly assumed in the Fresnel–Kirchoff integral to represent traveling waves.
Photosensitive materials and optical information processing technologies based on holographic and photonic techniques are suffering a huge improvement. Furthermore Spatial Light Modulators (SLMs) based on LCoS microdisplays (PALCoS) open new possibilities to modulate the wavefront of a light beam. The improving of the models of the photopolymers as optical recording material together with the modelling of PALCoS, high resolution reflective devices, make possible the generation and recording of Diffractive Optical Elements (DOE) on the photosensitive materials. This DOEs have many important applications in photonics, communications of optical information processing. Working with a setup based on a LCoS display as a master, we can store complex DOEs. We used in this work PVA/AA based on acrylamide with coverplating and index matching system to avoid the influence of the thickness variation on the transmitted light in the material. With the 3-Dimensional diffusion model we can predict the DOE properties before recording and optimize the recording time and the exposure dose. Experimental data is compared with the simulation results to evaluate the accuracy of our model to reproduce the recording of any kind of complex DOE onto a photopolymer. This allows us to choose the appropriate characteristics for the material depending on the application and evaluate the influence of different parameters involved in the DOE generation. In this work we evaluate the simulation of the recording of optical vortexes, axicons, fork gratings and diffractive lenses comparing with the results using our experimental set-up.
Phase spatial light modulators and, in particular, parallel-aligned liquid crystal on silicon (PA-LCoS) microdisplays are widely used to display programmable diffractive optical elements (DOEs). These are pixelated elements with inherent different characteristics when compared with DOEs produced with micro-optics fabrication techniques. Specifically, programmable DOEs may be affected by the fill factor, time-flicker, fringing-field and interpixel cross talk effects, and limited and quantized modulation depth of the LCoS device. Among the multilevel DOEs, we focus on the important case of the blazed gratings. We develop the corresponding analytical expressions for the diffracted field where, as novelties of this work, fill factor and flicker are introduced together with phase depth and the number of quantization levels. Different experimental-based normalizations are considered, which may lead to wrong conclusions if the fill factor is not considered in the expressions. We also analyze the differences arising between one- and two-dimensional pixelated devices. When compared with numerical procedures, our approach provides an analytical expression that facilitates the design, prediction, and discussion of experiments. As an application, we prove, for the limiting case of no interpixel cross talk, that multiorder DOEs cannot be more efficient than the equivalent single-order DOE. We also show how the results for DOEs with a unit fill factor can be adapted to DOEs with a fill factor smaller than one with a very efficient procedure.
In this work we study and characterize and holographic waveguide system composed of two volume diffraction gratings, which act as optical couplers and a glass substrate that acts as a waveguide. The features such us high diffraction efficiencies and Bragg angle selectivity exhibited by volume diffraction gratings allow the appropriated adjustment of the incident light to be diffracted in the direction of total reflection condition inside the glass substrate with high efficiency. In this work the holographic waveguide is recorded on different photopolymer materials, which optimization is controlled to obtain high spatial frequencies and stable fringes. The effect of the shrinkage of the holograms after recording in the quality of the image obtained from the optical waveguide is also studied. To perform the experiments two kind of photopolymers were studied: a nanoparticle-(thiol-ene) polymer composite, NPC, and a penta/hexa-acrylate based polymer with dispersed nematic liquid crystal molecules, PDLC. The holographic characteristics such as diffraction efficiency or wavelength selectivity obtained with the waveguides recorded on the different photopolymers were also studied and compared.
We have included a Parallel Aligned Liquid Crystal on Silicon (PA-LCoS) microdisplay in a Holographic Data Storage System (HDSS). This novel display, widely accepted as Spatial Light Modulator (SLM), presents some advantages and disadvantages. One of these disadvantages is the anamorphic and frequency dependent effect. In this work we want to test this effect and see its effects in the complete optical process involved in the HDSS. We will use stripe-based patterns with different orientation (vertical and horizontal). To check the limits, we will increase the data density by decreasing the minimum stripe width. For evaluating the degradation suffered by the data page, we use the Bit Error Rate (BER) as figure of merit. We make a BER calculation from the statistical analysis of the histogram. In addition to the anamorphic effects we evaluate the degradation effects introduced by the non-uniformity in the illumination. To this goal we divide the image in several regions that are processed in the same way that the entire image. The error analysis of the entire optical system is useful for its calibration and fine adjustment. Once we have characterized the experimental setup we introduce the holographic material. Thus, by making the same analysis, we can evaluate the errors introduced by the material. As holographic material we use Polyvinyl Alcohol Acrylamide (PVA/AA), that has been characterized and developed in previous works by our group.
The improving of the technology related to the Spatial Light Modulators (SLM), which can be used to modulate the wavefront of a light beam in many different applications in Optics and Photonics, has widespread their use in many new ways. In particular, the continue miniaturization of the pixel size let them be used as a master for Diffractive Optical Elements(DOE) recording applications. One of these displays isthe parallel-addressed liquid crystal on silicon (PA-LCoS) microdisplay, which offers easily the possibility of phase-only modulation without coupled amplitude modulation, but can be use also as an amplitude master just rotating the angles of two polarizers. Together with the DOEs, the optic recording material is also one of the crucial componentsin the system. Photoresist has been used classically for this purpose. Recently some works provide results of the incorporation of photopolymers, initially used for holographic recording, to fabricate DOEs. Among photopolymers, polyvinil alcohol/acrylamide (PVA/AA) materials have been studied firstly due to the accurate control of their optical properties and the ease of fabrication. Nevertheless, this kind of photopolymer presents a high level of toxicity due mainly to the monomer, acrylamide. In this sense, we made efforts to search alternative “green” photopolymers, one of these is called “Biophotopol”. This material presents good optical properties; although, it has two principal drawbacks: its refractive index modulation is lower than the PVA/AA one and the dye used presents very low absorption at 532 nm. In order to solve these problems for recording spherical diffractive lenses, in the present work we have explored different possibilities. On the first place, we have modified the fabrication technique of the solid layer to achieve thicker samples, on the second place, we have introduced a biocompatible crosslinker monomer. These two actions provide us a higher value of the phase modulation capability. On the third place, we have modified the dye to record DOE’s with the wavelength of 532 nm and obtain a direct comparison with the results obtained with PVA/AA materials.
There is an increasing demand for new holographic recording materials. One of them are photopolymers, which are becoming a classic media in this field. Their versatility is well known and new possibilities are being created by including new components, such as nanoparticles or dispersed liquid crystal molecules in classical formulations, making them interesting for additional applications in which the thin film preparation and the structural modification have a fundamental importance. Prior to obtaining a wide commercialization of displays based on photopolymers, one of the key aspects is to achieve a complete characterization of them. In this sense, one of the main parameters to estimate and control is the shrinkage of these materials. The volume variations change the angular response of the hologram in two aspects, the angular selectivity and the maximum diffraction efficiency. One criteria for the recording material to be used in a holographic data storage application is the shrinkage, maximum of 0.5%. Along this work, we compare two different methods to measure the holographic recording material shrinkage. The first one is measuring the angle of propagation for both diffracted orders ±1 when slanted gratings are recorded, so that an accurate value of the grating vector can be calculated. The second one is based on interference measurements at zero spatial frequency limit. We calculate the shrinkage for three different photopolymers: a polyvinyl alcohol acrylamide (PVA/AA) based photopolymer, one of the greenest photopolymers whose patent belongs to the Alicante University called Biophotopol and on the last place a holographic-dispersed liquid crystal photopolymer (H-PDLC).
In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.
Photopolymers are optical recording materials appealing for many different applications such as holography, data storage, interconnectors, solar concentrations, or wave-guides fabrication. Recently the capacity of photopolymers to record diffractive optical elements (DOE’s) has been investigated. Different authors have reported proposes to record DOE like fork gratings, photonics structures, lenses, sinusoidal, blazed or fork gratings. In these experiments there are different experimental set-ups and different photopolymers. In this work due to the improvement in the spatial light modulation technology together with the photopolymer science we propose a recording experimental system of DOE using a Liquid Cristal based on Silicon (LCoS) display as a master to store complex DOE like cylindrical lenses. This technology permits us an accurate control of the phase and the amplitude of the recording beam, with a very small pixel size. The main advantage of this display is that permit us to modify the DOE automatically, we use the software of the LCoS to send the voltage to each pixel In this work we use a photopolymer composed by acrylamide (AA) as polymerizable monomer and polyvinyl alcohol (PVA). We use a coverplated and index matched photopolymer to avoid the influence of the thickness variation on the transmitted light. In order to reproduce the material behaviour during polymerization, we have designed our model to simulate cylindrical lenses and used Fresnel propagation to simulate the light propagation through the DOE and analyze the focal plane and the properties of the recorded lenses.
A wide range of chemical compositions are possible to design photopolymers. These materials are also appealing for diffractive and holographic applications due to their capability to modulate the refractive index and/or the thickness when illuminated. Some of the most interesting applications for photopolymers are the optical data storage, security systems, surface relief photo-embossing, diffractive and refractive optical elements, holographic elements, solar concentrators, optical detectors and hybrid optoelectronic 3-D circuitry. Looking for an optimized chemical composition for each application many different photopolymers compositions may be needed enabling a variety of materials properties: materials with low or high rates of monomer diffusion, low or high values of shrinkage, long or short length of polymer chains and low or high light absorption. In parallel many models are presented in order to predict the photopolymers recording and the post exposure evolution. In this work we use one of these experimentally checked models to study the influence of the material characteristics in the final diffractive optical element recorded in the material. We study the changes in the surface relief and in the refractive index in order to understand the importance of each material property in the final diffractive optical element recorded.
Photopolymers are often used as a base of holographic memories displays. Recently the capacity of photopolymers to record diffractive optical elements (DOE’s) has been demonstrated. To fabricate diffractive optical elements we use a hybrid setup that is composed by three different parts: LCD, optical system and the recording material. The DOE pattern is introduced by a liquid crystal display (LCD) working in the amplitude only mode to work as a master to project optically the DOE onto the recording material. The main advantage of this display is that permit us modify the DOE automatically, we use the electronics of the video projector to send the voltage to the pixels of the LCD. The LCD is used in the amplitude-mostly modulation regime by proper orientation of the external polarizers (P); then the pattern is imaged onto the material with an increased spatial frequency (a demagnifying factor of 2) by the optical system. The use of the LCD allows us to change DOE recorded in the photopolymer without moving any mechanical part of the set-up. A diaphragm is placed in the focal plane of the relay lens so as to eliminate the diffraction orders produced by the pixelation of the LCD. It can be expected that the final pattern imaged onto the recording material will be low filtered due to the finite aperture of the imaging system and especially due to the filtering process produced by the diaphragm. In this work we analyze the effect of the visibility achieved with the LCD and the high frequency cut-off due to the diaphragm in the final DOE recorded into the photopolymer. To simulate the recording we have used the fitted values parameters obtained for PVA/AA based photopolymers and the 3 dimensional models presented in previous works.
The implementation of split-field finite difference time domain (SF-FDTD) applied to light-wave propagation through periodic media with arbitrary anisotropy method in graphics processing units (GPUs) is described. The SF-FDTD technique and the periodic boundary condition allow the consideration of a single period of the structure reducing the simulation grid. Nevertheless, the analysis of the anisotropic media implies considering all the electromagnetic field components and the use of complex notation. These aspects reduce the computational efficiency of the numerical method compared with the isotropic and nonperiodic implementation. Specifically, the implementation of the SF-FDTD in the Kepler family of GPUs of NVIDIA is presented. An analysis of the performance of this implementation is done, and several applications have been considered in order to estimate the possibilities provided by both the formalism and the implementation into GPU: binary phase gratings and twisted-nematic liquid crystal cells. Regarding the analysis of binary phase gratings, the validity of the scalar diffraction theory is evaluated by the comparison of the diffraction efficiencies predicted by SF-FDTD. The analysis for the second order of diffraction is extended, which is considered as a reference for the transmittance obtained by the SF-FDTD scheme for periodic media.
The implementation of the Split-Field Finite Difference Time-Domain (SP-FDTD) method in Graphics Pro-
cessing Units is described in this work. This formalism is applied to light wave propagation through periodic media with arbitrary anisotropy. The anisotropic media is modeled by means of a permittivity tensor with non-diagonal elements and absorbing boundary conditions are also considered. The split-field technique and the periodic boundary condition allow to consider a single period of the structure reducing the simulation grid. Nevertheless, the analysis of anisotropic media implies considering all the electromagnetic field components and the use of complex notation. These aspects reduce the computational efficiency of the numerical method compared to the isotropic and non-periodic implementation. With the upcoming of the new generation of General-Purpose Computing on Graphics Units many scientific applications have been accelerated and others are being developed into this new parallel digital computing architecture. Specifically, the implementation of the SP-FDTD in the Fermi family of GPUs of NVIDIA is presented. An analysis of the performance of this implementation is done and several applications have been considered in order to estimate the possibilities provided by both the formalism and the implementation into GPU. The formalism has been used for analyzing different structures and phenomena: binary phase gratings and twisted-nematic liquid crystal cells. The numerical predictions obtained by means of the FDTD method here implemented are compared with theoretical curves achieving good results, thus validating the accuracy and the potential of the implementation.
In this work a set of simplified theories for predicting diffraction efficiencies of diffraction phase and triangular gratings
are considered. The simplified theories applied are the scalar diffraction and the effective medium theories. These
theories are used in a wide range of the value Λ/λ and for different angles of incidence. However, when 1 ≤ Λ/λ ≤ 10, the
behaviour of the diffraction light is difficult to understand intuitively and the simplified theories are not accurate. The
accuracy of these formalisms is compared with both rigorous coupled wave theory and the finite-difference time domain
method. Regarding the RCWT, the influence of the number of harmonics considered in the Fourier basis in the accuracy
of the model is analyzed for different surface-relief gratings. In all cases the FDTD method is used for validating the
results of the rest of theories. The FDTD method permits to visualize the interaction between the electromagnetic fields
within the whole structure providing reliable information in real time. The drawbacks related with the spatial and time
resolution of the finite-difference methods has been avoided by means of massive parallel implementation based on
graphics processing units. Furthermore, analysis of the performance of the parallel method is shown obtaining a severe
improvement respect to the classical version of the FDTD method.
The PEA photopolymer is composed of dipentaerythritol penta/hexa-acrylate as monomer and binder, N-vinyl
pirrolidone as crosslinker, ethyl eosin as dye and N-methyl diethanolamine as radical generator. This photopolymer is
suitable to work with dispersed liquid crystal molecules in dynamic holographic and diffractive applications. In order to
characterize these materials we have analyzed the behaviour of different compositions at zero spatial frequency limit.
This method is based on an interferometer that has been successfully applied in the phase-shift versus applied voltage
characterization of liquid-crystal displays, in addition to that it has been applied to characterize PVA/AA and
PVA/NaAO photopolymers. In PEA case there is no shrinkage since the photopolymer is coverplated. Samples have a
glass substrate as the cover plate. In our analysis we have studied the importance of the monomer, crosslinker and crystal
liquid molecules concentrations, in the phase shift produced in the layer during photopolymerization process.
We use 4,4' azo-bis-(4-cyanopentanoic acid) as chain transfer agent in a photopolymer with
triethanolamine/yellowish eosin as initiator system. It is possible to work in a particular conditions to
get a chain transfer effect minimizing the decomposition of 4,4' azo-bis-(4-cyanopentanoic acid) by
the sensitized dye. The improved photopolymer has a low scattering due to the low molecular weight
of the generated polymer chains. This is related to the chain transfer effect in the size of the polymer
chains. It is important to establish the optimum concentration of chain transfer agent to avoid
decreasing the maximum diffraction efficiency due to a low molecular weight of the polymer chains.
In this paper four different photopolymers are compared on the basis of their suitability for
holographic data storage. The optical recording parameters of these photopolymers were directly
determined using the zero spatial frequency limit. The behavior of cover plated and uncover plated
material layers was analyzed. Once the main parameters were determined, we proposed a novel model
to simulate the recording of relief diffractive elements onto the photopolymers without cover plating.
Relief surface changes provide interesting possibilities for storing diffractive optical elements on
photopolymers and are an important source of information for characterizing and understanding the
material behaviour. In this paper we also present a 3-dimensional model, based on direct parameter
measurements, for predicting the relief structures generated on the material. This model was
successfully applied to different photopolymers with different values of monomer diffusion.
In this work we present an analysis of non-slanted reflection gratings by using a corrected Coupled Wave Theory which
takes into account boundary conditions. It is well known that Kogelnik's Coupled Wave Theory predicts with great
accuracy the response of the efficiency of the zero and first order for volume phase gratings, for both reflection and
transmission gratings. Nonetheless, since this theory disregard the second derivatives in the coupled wave equations
derived from Maxwell equations, it doesn't account for boundary conditions. Moreover only two orders are supposed, so
when either the thickness is low or when high refractive index high are recorded in the element Kogelnik's Theory
deviates from the expected results. In Addition, for non-slanted reflection gratings, the natural reflected wave
superimpose the reflection order predicted by Coupled Wave theories, so the reflectance cannot be obtained by the
classical expression of Kogelnik's Theory for reflection gratings. In this work we correct Kogelnik's Coupled Wave
Theory to take into account these issues, the results are compared to those obtained by a Matrix Method, showing good
agreement between both theories.
In this work a vectorized and parallel version of the Finite-Difference Time-Domain method (FDTD) is applied to
Volume Holographic Gratings (VHG) and Thin-Film Filters (TFF). In particular, in this work gratings with a grating
period vector forming an arbitrary angle with the perpendicular to the plane of incidence are analyzed. Angular and
wavelength selectivity are obtained by means of the normalized diffraction efficiency. These parameters are positively
compared with experimental values and also with analytical closed expressions, thus validating our method.
Furthermore, analysis of the performance of the parallel method is shown obtaining a severe improvement with respect
to the classical version of the FDTD method. This improvement of the algorithm provides a feasible and accurate scheme
for simulating a wide range of optical devices.
We develop the Interpolatory Fixed-Point Algorithm (IFPA) to compute efficiently the TE and TM reflectance
and transmittance coefficients for arbitrary 1D structures at oblique incidence. For this purpose, we demonstrate
that the semi-analytical solutions of the Helmholtz equation provided by the fixed-point method have
a polynomial dependence on variables that are related to the essential electromagnetic parameters -incidence
angle and wavelength-, which allows a drastic simplification of the required calculations taking the advantage of
interpolation for a few parameter values. The first step to develop the IFPA consists of stating the Helmholtz
equation and boundary conditions for TE and TM plane incident waves on a 1D finite slab with an arbitrary
permittivity profile surrounded by two homogeneous media. The Helmholtz equation and boundary conditions
are then transformed into a second-order initial value problem which is written in terms of transfer matrices.
By applying the fixed-point method, the coefficients of such transfer matrices are obtained as polynomials on
several variables that can be characterized by a reduced set of interpolating parameters. We apply the IFPA to
specific examples of 1D diffraction gratings, optical rugate filters and quasi-periodic structures, for which precise
solutions for the TE and TM modes are efficiently obtained by computing less than 20 interpolating parameters.
In this work we present an analysis of non-slanted holographic reflection gratings by using a matrix method. A transfer
matrix which relates the values of the electric field and its derivatives is obtained for a permittivity which varies
cosenoidally for one period. The coefficients of this matrix can be calculated in terms of Mathieu's functions and their
derivatives. Then the matrix of the entire medium is obtained as the Nth power of the matrix for one period. Since the
reflectance and transmittance coefficients are related to the coefficients of the medium matrix, it is possible to calculate
the efficiencies of orders -1 (reflected) and 0 (transmitted) by using this method. The results obtained by using the
Trensference Matrix Method are compared to those obtained using Kogelnik's expressions for the transmission and
diffraction efficiency. As will be seen there is good agreement between the results obtained by the Transference Matrix
Method and those of the Coupled Wave Theory.
In holographic recording photopolymers the diffraction efficiency develops according to Kogelnik
expression during hologram recording stage. In the ideal situation, the curve of diffraction efficiency
versus energetic exposure has a linear zone, although it is usual to find examples of deviations to this
behavior. In this investigation we study different cases in which there are deviations to ideal behavior,
proposing different hypothesis in order to explain the situations that can be experimentally obtained.
The more important deviation experimentally observed is when the first maximum is lower than the
second one in the diffraction efficiency versus exposure curve during recording. A main hypothesis is
presented, which is related to the dye concentration into the layer and the molecular weight of the
polymer chains generated in the polymerization process.
Photopolymers are light sensitive materials with adequate characteristics for application as holographic recording media in new devices as optical elements and holographic memories. A specific set of parameters are required from the photopolymers: good energetic sensitivity to save energy during the recording process, an adequate spectral sensitivity, a higher resolution to let the necessary fidelity in the stored information reproduction, a better environmental compatibility including low toxicity, easy making management and good recycling properties. We present the main research lines in this area and the last results obtained with the new photopolymeric materials that we are developing.
Recently, we have proposed the application of interferometric techniques, both in transmission and in reflection, to
characterize in real-time the modulation performance of the photopolymers. In this work we use this approach to
characterize the optical modulation properties of a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer. A double
beam interferometer is constructed, both in transmission and in reflection, in combination with the setup to expose the
recording material. Some benefits are provided by this approach: direct calculation of the properties of the material is
possible, index and surface modulation can be decoupled, and additional information can be obtained since the results are
not influenced by diffusion processes. With this scheme we mainly characterize the properties at very low spatial
frequencies, which can be useful to analyze the applicability of holographic recording materials in another range of
applications, such as recording of diffractive optical elements (DOEs). Comparison with the conventional holographic
characterization shows significant differences.
The acrylamide photolymers are considered interesting materials for holographic media. They have high diffraction efficiency (ratio of the intensities of the diffracted and the incident beams), an intermediate energetic sensitivity among other materials and post-processing steps are not necessary, therefore the media is not altered. The layers of these materials, about 1 mm thick, are a suitable media for recording many diffraction gratings in the same volume of photopolymer using peristrophic multiplexing technique, with great practical importance in the field of holographic memories type WORM (write once read many). In this work we study the recording of diffraction gratings by peristrophic multiplexing with axis of rotation perpendicular to the recording media. The photopolymer is composed of acrylamide as the polymerizable monomer, triethanolamine as radical generator, yellowish eosin as sensitizer and a binder of polyvinyl alcohol. We analyze the holographic behaviour of the material during recording and reconstruction of diffraction gratings using a continuous Nd:YAG laser (532 nm) at an intensity of 5 mW/cm2 as recording laser. The response of the material is monitored after recording with an He-Ne laser. We study the recording process of unslanted diffraction gratings of 1125 lines/mm. The diffraction efficiency of each hologram is seen to decrease as the number of holograms recorded increases, due to consumption of the available dynamic range, in a constant exposure scheduling. It can be seen that the photopolymer works well with high energy levels, without excessive dispersion of light by noise gratings. In order to homogenize the diffraction efficiency of each hologram we use the method proposed by Pu. This method is designed to share all or part of the avaliable dynamic range of the recording material among the holograms to be multiplexed. Using exposure schedules derived from this method we have used 3 scheduling recordings from the
algorithm used. Additionaly, we use an exponential scheduling recording in order to correct the exposure times from the first iteration of the algorithm.
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.
In this work we analyse the complex amplitude response of volume holograms. This analysis suggests a new scheme for encoding complex amplitude wavefront information onto an optical hologram which may prove useful for combining computer-generated holograms (CGH) onto volume holograms. Specifically, we analyse the amplitude and phase
modulation associated with a volume phase unslanted transmission grating. Using the expressions given by the Kogelnik's coupled wave theory (KCWT) we find that there is a coupling between the amplitude and the phase modulations. This coupling can be controlled to some extent by means of the reconstruction angle: we have found that the significant magnitude is the normalized Bragg detune angle. A large variation range of the grating strength is desirable, which is enhanced by the use of shorter wavelengths, and materials exhibiting overmodulation capability and/or with a high thickness.
Research dealing with models to predict and understand the behaviour of photopolymers have generated many interesting studies considering a 2-dimensional geometry. These models suppose that the photopolymer layer is homogeneous in depth. Using this approximation good results can be obtained if the thickness of photopolymers is less than 200 μm. However, it is well known that Lambert-Beer's law predicts an exponential decay of the light inside the material. In recent years intensive efforts have been made to develop new holographic memories based on photopolymers. For this application the thickness of the layer is increased, usually to more than 500 μm, and Lambert-Beer's law plays a significant role in the recording step. The attenuation of the index profile inside these materials has been measured, showing that it is an important phenomenon. This attenuation limits the maximum effective optical thickness of the grating and shows that the 2-D models can not be applied in these cases. For this reason in this work a 3-dimensional model is presented to analyze the real behaviour of the photopolymers and study the variations in the
index profile in depth. In this work we examine the predictions of the model in the case of a general dependence of the polymerisation rate with respect to the intensity pattern, and the effects of varying the exposure intensity are also compared in 3-D cases. Finally, the limitation of the data storage capacity of the materials due to the Lambert-Beer law is evaluated.
The characterization of the behavior of photopolymers is an important fact in order to control the holographic memories
based on photopolymers. In recent years many 2-dimensional models have been proposed for the analysis of
photopolymers. These models suppose that the photopolymer layer is homogeneous in depth and good agreement
between theoretical simulations and experimental results has been obtained for layers thinner than 200 μm. The
attenuation of the light inside the material by Beer's law is an important factor when higher thickness are considered. In
this work we use a Finite-Difference method to solve the 3 dimensional problem. Now diffusion in depth direction and
the attenuation of the light inside the material by Beer's law are also considered, the influence of the diffusivity of
material in the attenuation of the refractive index profile in depth is analyzed.
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.
We present a fruitful student's lab experiment allowing for an effective learning of some of the basics in physical optics. We proceed with the characterization of the surface structure of a compact disk (CD) and a digital versatile disk (DVD). This experiment is an effective means to have a direct hands-on experience on diffraction, Young's fringes interference phenomena, and diffraction chromatic dispersion. The fact that both CD and DVD are widespread consumer electronics devices enhances the interest of the student on the experiment.
We present two laboratory experiments on optical image processing which show complementary modeling approaches. One experiment is based on an optical correlator, where a physical Fourier plane can be identified, and the other is based on the angular response exhibited by a volume grating (Bragg processing) where no Fourier plane is available. In the correlator the frequency content can be visualized as intensity variations in the Fourier plane, whereas in Bragg processing the angular plane waves decomposition of the object is the intuitive approach. Then we have two different approaches to synthesize the transfer function of the system. The combination of the two experiments in a student's lab helps for a deeper understanding of optical image processing, its linear systems mathematical background, and some aspects of volume holography.
In recent years the development of new holographic memories based in photopolymers have a great goal. A new commercial holographic memories has been optimized by Aprilis and Inphase. The advantages of this type of materials to store information are well know: their high capacity and their fast random access. In the behaviour of this type of material two important factors determinate the quality of the material, the capacity and the energetic sensitivity. The base of the high capacity of the holographic memories is the high Bragg’s angular selectivity. The narrow curve of the angular scan are obtained when the effective optical thickness of material is high and permits record many holograms turning the plate only 3°. Others important factors are the dye and monomer concentration, high values of the concentrations origins high values of the index modulation (higher stored capacity, better energetic sensitivity and large dynamic range) but in when the dye and monomer concentrations are high all the light is absorbed in the first 200 μm of the material and the effective optical thickness of the grating recorded decrease (decrease the stored capacity) and the values of the noise are high in this case. In this work this attenuation of the index modulation in depth is having into account using rigorous couple wave theory to obtain the limit of the effective optical thickness for each composition of photopolymer. The optimal composition to obtain high stored capacity, high index modulation, good energetic sensitivity, high dynamic range and low noise are found.
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.
In this work we analyse the very specific properties offered by volume holography when applied to image processing with no Fourier plane. Bragg diffraction, exhibited by holographic optical elements (HOEs), modifies the impulse response of an imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane (Bragg processing). We show both experimental and simulated results with holographic phase gratings and with holographic lenses generated on a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer. We determine which are the significant parameters to model the performance of the HOEs for Bragg filtering: orientation and bandwidth of the passband of the filter. We relate these spatial filtering parameters with their corresponding counterparts in volume holography. We also show how the local variation of these parameters is responsible for space-variance properties of the HOE when applied in Bragg processing. We have also analysed the impulse response characteristics of the Bragg filter together with the effects of the limited aperture of the imaging system.
The hard research about the models to predict and understand the behaviour of photopolymers have as a results many interesting works for 2-dimensional cases. These studies permits obtain the mains parameters that governs the process in photopolymers with maximum thickness about 200 μm. Historically this materials, dry layers of photopolymers, have been used in many attractive devices and now a new application of this type of material is being developed: the application of photopolymers as holographic memories. The main characteristics of these layers of photopolymers are their high thickness (higher than 600 μm). In order to optimize this layers the original photopolymer composition has been changed, then a new parameters estimation has be done. In this work this study is made using PVA/Acrylamide photopolymer with layers around 800 μm of thick. The values of monomer and polymer diffusion are obtained and the values of polymerization rate constant and residual monomer are calculated too using and first harmonic diffusion constant. The validity of this model to study the layers with high thickness is evaluated, because this type of materials only a few percent of the initial light arrive to the depth zones of photopolymer.
Different electromagnetic theories have been applied in order to understand the interaction of the electromagnetic radiation with diffraction gratings. Kogelnik's Coupled Wave Theory, for instance, has been applied with success to describe the diffraction properties of sinusoidal volume gratings. Nonetheless the predictions of Kogelnik's theory deviate from the actual behaviour whenever the hologram is thin or the refractive index is high. In these cases, it is necessary to use a more general Coupled Wave Theory (CW) or the Rigorous Coupled Wave Theory (RCW). Both of these theories allow for more than two orders propagating inside the hologram. On the other hand, there are some methods that have been used long in different physical situations, but with relatively low application in the field of holography. This is the case of the finite difference in the temporal domain (FDTD) method to solve Maxwell equations. In this work we present an implementation of this method applied to volume holographic diffraction gratings.
In this study we focus on the properties of acrylamide photopolymer layers about 1 mm thick with hydrofilic binder of polyvinyl alcohol and yellowish eosin as dye. We consider peristrophic multiplexing. Note the differences in the reconstruction step between the next two peristrophic multiplexing schemes: rotation axis parallel and rotation axis perpendicular to the hologram media. In the first case (parallel) a very thick media allows for a high storage density and a highly selective individual hologram reconstruction thanks to the Bragg angular selectivity. In the second case (perpendicular), an additional optical system is necessary to separate the various simultaneous holograms reconstructed. We show experimental evidence for the two schemes. We analyze the behaviour of the material when multiplexing diffraction gratings using peristrophic multiplexing. In the reconstruction step we observe differences, between the various multiplexed holograms, in their angular response shape. We consider that this is due to polymer diffusion in exposed areas or to the dye concentration variation with registered holograms number, because xantene dyes are bleached at the initiation step of radical polymerization reaction. The photopolymer composition is an important factor to be taken into account when single or multiple holograms are registered. The differences in both cases are considered in this work.
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. 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.
In this work we explore the application of volume effects given by holographic optical elements (HOEs) to image processing operations. Bragg diffraction, exhibited by HOEs, modifies the impulse response of an imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. Both the holographic recording material we use and the specific HOE we design are important parameters. In the present communication we report our last results using a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer. This compound combines good optical properties, ease of fabrication, and self-development capability. We are able to produce layers as thick as 1 millimeter (mm) with a diffraction efficiency higher than 80%. Using layers with a thickness of 0.1 mm and 1 mm we have recorded both holographic diffraction gratings and holographic lenses. When using the holographic gratings we can obtain image edge enhancement as demonstrated in previous works. As a novelty, in this work we show that when using the holographic lenses we obtain a space-variant image edge enhancement. We analyse the properties of this space-variant operation in terms of the reconstruction geometry and the local grating structure exhibited by the lens across its aperture.
Photopolymers are systems of organic molecules that rely on photoinitiated polymerization to record volume phase holograms. Characteristics such as good light sensitivity, large dynamic range, good optical properties and relatively low cost make photopolymers one of the most promising materials for write-one, read-many (WORM) holographic data storage applications. Thus, it is interesting to understand the mechanisms that control the way information is stored in photopolymer materials. Different authors have demonstrated that two processes play the main role in hologram formation: monomer polymerization and monomer diffusion. A number of models based on these two processes have been proposed and their prediction capability has been validated. In this work we extend the capabilities of the existent models by introducing another important characteristic: the attenuation of light through the depth of the material which happens in the recording process. In order to check the validity of the theoretical model that we propose, volume phase transmission gratings are recorded in a PVA/Acrylamide photopolymer with different spatial frequencies. Using the Rigorous Coupled Wave
Theory (RCWT) we show that we can obtain information about the higher harmonics in the recorded refractive index modulation. Comparison between simulated and experimental results validates the interpretation provided by the proposed model.
In this work we make a comparative study between different theories to predict the efficiencies of the different orders that propagate inside a volume phase grating. For the case of a pure sinusoidal grating, transmission and reflection, the theories of Rigorous Coupled Wave Theory (RCW), Coupled Wave Theory (CW) and Kogelnik's Theory are compared. This comparison allows establishing the range of physical values where the more approximate theories, CW and Kogelnik´s Theory are applicable. On the other hand for the case of a general dielectric grating, transmission and reflection, the RCW, CW, and a thin matrix decomposition method (TMDM) are also compared. The theoretical study is also validated by comparing the theoretical results with experimental data obtained in volume phase diffraction gratings recorded on photographic emulsions. To record the volume phase diffraction gratings BB-640 emulsions were exposed to an interference pattern of light from a He-Ne laser (633 nm).
In order to achieve higher diffraction efficiencies of the volume
gratings stored in acrylamide based photopolymer, we introduce in the photopolymer a crosslinker (N,N'methylene-bis-acrylamide). The presence of this component increase the rate polymerization and the modulation of refraction index. The recording was performed using a holographic copying process. The original was a grating of 1000 lines/mm processed using silver halide sensitized gelatine, with diffraction efficiency around 50 % for a reconstruction wavelength of 532 nm. The main beam was split in two secondary beams by the
original grating, with an intensity ratio 1:1. The results obtained using the new composition of material are compared with the composition without crosslinker. In the other hand the no linearity of the material's response is also studied comparing the energetic sensitivity, diffraction efficiencies and index modulation of gratings recorded with pulsed and continuous laser. This study is realized fitting the angular scan of each grating using Kogelnik's theory. The gratings are recorded with wavelength of 532 nm when pulsed exposure is used and with wavelength of 514 nm when continues exposure is used. Using pulsed laser at 532 nm the photopolymer without crosslinker presents the diffraction efficiencies lightly smaller than 60%. In the other hand when the crosslinker has been
introduced in photopolymer composition, the diffraction efficiencies achieves are higher than 85 %.
Photopolymers are considered one of the most interesting materials for holographic storage applications. The search for optimum chemical formulations to improve the quality of the final polymer materials has yielded a great deal of experimental work. different theoretical models have also been developed by different authors to clarify the mechanism of hologram formation inside photopolymer materials. These advances in both experimental and theoretical fields permit obtaining suitable compositions of photopolymer materials for data storage purposes. In this work we present the results of an optimization of a PVA/acrylamide recording material with a high thickness (over 1 mm) to obtain holographic memories. Diffraction gratings of 1125 lines/mm were recorded in this material by using the peristrophic multiplexing technique and using the light from an Argon laser at a wavelength of 514 nm.
The kinetics of photosensitive polymer holographic recording materials is examined. We discuss why a linear relationship between monomer concentration and polymerization rate does not satisfactorily explain current experimental results and propose a possible solution. Then, using the Rigorous Coupled Wave Model(RCWM) we examine the higher order grating components so as to more clearly understand the non-linear relationship between exposing intensity and polymerization.
Two particular techniques producing high quality thick phase holograms in silver halide emulsions are the fixation free rehalogenating bleaching and the silver halide sensitized gelatin. In this work we compare these two particular techniques applied to three different red sensitive emulsions: Agfa 8E75 HD, BB-640 and PFG-01. The differences between the emulsions influence in the particular experimental conditions which yield to holograms performing high diffraction efficiencies. In this work these differences are analyzed and also its influence on the final hologram.
In this work we expose the results obtained with a wide variety of phase holographic recording materials that we have characterized in the range of low spatial frequencies (≤ 32 lines/millimeter). We have considered bleached photographic emulsion, silver halide sensitized gelatin and dichromated gelatin. This low spatial frequency characterization is necessary in order to generate optimum computer-generated holograms on these materials by means of a low cost technique. In this work, we have generated correlation filters for optical pattern recognition. The experimental results confirm that the correlation filters generated on all the phase materials exhibit a good performance.
Fixation-free rehalogenating bleaching is an interesting process for the production of phase holograms. The shrinkage of the emulsion is reduced in comparison with other bleaching methods (reversal bleaching or rehalogenating bleaching with fixation). In this paper we present experimental results for fixation-free rehalogenating bleached holograms derived from the novel BB- 640, a red-sensitive ultra-fine grain emulsion from Holographic Recording Technologies. The influence of the Potassium bromide concentration in the bleach solution on the final quality of the holograms is also studied. The concentrations of the different components of the bleach solution are adjusted to obtain the highest values of the diffraction efficiency. We studied transmission and reflection fixation-free bleached holograms. We will show that really high diffraction efficiencies can be obtained, as high as 87% for transmission bleached holograms recorded on BB-640 plates, and 72% for reflection bleached holograms.
In this paper we present the results of our research on the recording of SHSG holographic transmission gratings using the new BB-640 photographic emulsion, a red sensitive ultra-fine- grained emulsion from Holographic Recording Technologies. The exposed plates were processed following a process similar to that optimized by Fimia et al. for Agfa 8E75 HD plates but with the temperature of the bleaching bath modified to 70 degrees Celsius. This increase in temperature improves the diffraction efficiency but does not produce an increase in absorption and scattering, as opposed to what happens in the case of the Agfa 8E75 HD emulsion. The influence of the developer on various holographic parameters is analyzed and discussed.
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