See-through display based on commercial photopolymer: Optimization and shrinkage effects

Nowadays augmented reality, 3D Image, mixed reality and see-through applications are very attractive technologies due to their great potential. Holographic optical elements can provide interesting solutions for injection and extraction of the image in the waveguides that are part of the see-through devices. We have developed a coupled waveguide system based on slanted transmission gratings recorded in manufactured photopolymers. In this work we optimize our schedule to a commercial photopolymer for this high demanded application. We demonstrate that high diffraction efficiencies can be obtained if we optimize the recording geometry, recording intensity and recording time for this material. In addition, we study the effects of shrinkage in our holographic system. In general shrinkage is an important drawback for holographic applications, nevertheless we demonstrate how shrinkage can help these systems open new possibilities. Lastly, we show how to significantly improve the quality of the guided image.

Precise-Integration Time-Domain Formulation for Optical Periodic Media

A numerical formulation based on the precise-integration time-domain (PITD) method for simulating periodic media is extended for overcoming the Courant-Friedrich-Levy (CFL) limit on the time-step size in a finite-difference time-domain (FDTD) simulation. In this new method, the periodic boundary conditions are implemented, permitting the simulation of a wide range of periodic optical media, i.e., gratings, or thin-film filters. Furthermore, the complete tensorial derivation for the permittivity also allows simulating anisotropic periodic media. Numerical results demonstrate that PITD is reliable and even considering anisotropic media can be competitive compared to traditional FDTD solutions. Furthermore, the maximum allowable time-step size has been demonstrated to be much larger than that of the CFL limit of the FDTD method, being a valuable tool in cases in which the steady-state requires a large number of time-steps.

Tunable Waveguides Couplers Based on HPDLC for See-Through Applications

Photopolymers have become an important recording material for many applications, mainly related to holography. Their flexibility to change the chemical composition together with the optical properties made them a versatile holographic recording material. The introduction of liquid crystal molecules in a photopolymer based on multifunctional monomer provides us the possibility to generate tunable holograms. The switchable holographic elements are a key point for see-through applications. In this work, we optimize the holographic polymer-dispersed liquid crystals composition to improve the performance of tunable waveguide couplers based on transmission gratings and specifically their response under an applied electric field. A variation around 60% in the transmission efficiency was achieved.

Accurate, Efficient and Rigorous Numerical Analysis of 3D H-PDLC Gratings

This work presents recent results derived from the rigorous modelling of holographic polymer-dispersed liquid crystal (H-PDLC) gratings. More precisely, the diffractive properties of transmission gratings are the focus of this research. This work extends previous analysis performed by the authors but includes new features and approaches. More precisely, full 3D numerical modelling was carried out in all analyses. Each H-PDLC sample was generated randomly by a set of ellipsoid geometry-based LC droplets. The liquid crystal (LC) director inside each droplet was computed by the minimisation of the Frank elastic free energy as a function of the applied electric field. The analysis carried out considered the effects of Frank elastic constants K11, K22 and K33; the anchoring strength W0; and even the saddle-splay constant K24. The external electric field induced an orientation of the LC director, modifying the optical anisotropy of the optical media. This effect was analysed using the 3D split-field finite-difference time-domain (SF-FDTD) method. In order to reduce the computational costs due to a full 3D tensorial analysis, a highly optimised method for high-performance computing solutions (HPC) was developed. The influences of the anchoring and voltage on the diffraction efficiencies were investigated, showing the potential of this approach.

Holographic waveguides in photopolymers

The possibilities that offer the holographic optical elements for photovoltaic and "see through display" applications open new windows for holographic recording materials. In this sense, some specific characteristics are required for each particular application. Waveguides are one of the key elements for these applications. Photopolymers are one of the most competitive candidates for waveguide fabrication. In this work, we evaluate the performance of one example from each of three families of photopolymer material in fabrication of a 633nm waveguide. Firstly, polyvinyl alcohol acrylamide, PVA/AA, the second one, a nanoparticle-thiol-ene, NPC, and on the last place a penta/hexa-acrylate based polymer with dispersed nematic liquid crystal molecules, PDLC. We study the critical role of the material and in particular, spatial resolution for this application.

Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles

In recent works, we demonstrated the accuracy and physical relevance of a highly simplified reverse-engineering analytical model for a parallel-aligned liquid crystal on silicon devices (PA-LCoS). Both experimental measurements and computational simulations applying the rigorous split-field finite difference time domain (SF-FDTD) technique led to this conclusion in the low applied voltages range. In this paper, we develop a complete rigorous validation covering the full range of possible applied voltages, including highly non-linear liquid crystal (LC) tilt angle profiles. We demonstrate the applicability of the model for spectral and angular retardation calculations, of interest in spatial light modulation applications. We also show that our analytical model enables the calculation of the retardance for novel PA-LC devices as a function of the LC compound and cell gap, becoming an appealing alternative to the usual numerical approaches for PA-LC devices design.

Numerical Analysis of H-PDLC Using the Split-Field Finite-Difference Time-Domain Method

In this work, an accurate numerical modeling of the diffraction properties of transmission holographic polymer dispersed liquid crystal (H-PDLC) gratings is presented. The method considers ellipsoid geometry-based liquid crystal (LC) droplets with random properties regarding size and location across the H-PLDC layer and also the non-homogeneous orientation of the LC director within the droplet. The direction of the LC director inside the droplets can be varied to reproduce the effects of the external voltage applied in H-PDLC-based gratings. From the LC director distribution in the droplet, the permittivity tensor is defined, which establishes the optical anisotropy of the media, and it is used for numerically solving the light propagation through the system. In this work, the split-field finite-difference time-domain method (SF-FDTD) is applied. This method is suited for accurately analyzing periodic media, and it considers spatial and time discretisation of Maxwell's equations. The scheme proposed here is used to investigate the influence on the diffraction properties of H-PDLC as a function of the droplets size and the bulk fraction of LC dispersed material.

Holographic Lenses in an Environment-Friendly Photopolymer

In this paper, we theoretically and experimentally evaluated the quality of volume phase transmission lenses stored in an environmentally friendly photopolymer. Holographic lenses (HLs) were obtained using symmetrical and asymmetrical experimental setups with the same positive and negative focal length and pupil diameter. The image quality was evaluated from the calculation of the modulation transfer function (MTF) by capturing the point spread function (PSF) with a charge-coupled device (CCD). A maximum frequency of 14 L/mm, reaching an MTF value of 0.1, was obtained for a negative asymmetrically recorded HL, evaluated at 473 nm wavelength. A theoretical study of aberrations was carried out to qualitatively evaluate the experimental results obtained.

Optimization of Photopolymer Materials for the Fabrication of a Holographic Waveguide

In this work, we present a method of manufacturing an optical see-through display based on a holographic waveguide with transmission holograms that couple the incident light between air and the glass substrate, accomplishing total internal reflection. The holograms (slanted transmission gratings with a spatial frequency of 1700 lines/mm) were recorded on a polyvinyl alcohol acrylamide (PVA/AA) photopolymer. We will also show that the addition of N,N'-methylene-bis-acrylamide (BMA) to the composition of the photopolymer allows the achievement of the index modulations necessary to obtain high diffraction efficiencies in non-slanted diffraction gratings of 1000 and 2200 lines/mm, and also in slanted gratings of 1700 lines/mm (which are the base of the optical system proposed).

Two diffusion photopolymer for sharp diffractive optical elements recording

Photopolymers as recording media are widely used in optical applications. In such materials, changes in the phase of the transmittance function are generated during exposure due to refractive index and thickness modulations. These changes arise primarily as a consequence of photopolymerization and mass transport processes. Characterizing polymers' performance, for example, quantifying the value of monomer diffusion, is therefore very important. Applying index matching, the volume and surface optical effect are separated in an acrylamide/polyvinylalcohol (AA/PVA) material. Using a simplified model that includes the effects of the holes produced during polymerization, both hole and monomer diffusion are analyzed. The analysis presented indicates higher material sensitivity than previously estimated. The results also indicate the possibility of recording sharper diffractive optical elements profiles, like blazed gratings, having diffraction efficiencies higher than 80%.

Analysis of holographic reflection gratings recorded in polyvinyl alcohol/acrylamide photopolymer

Holographic reflection gratings in a polyvinyl alcohol/acrylamide based photopolymer were stored using symmetrical geometry in three different thicknesses of the material. The advantage of symmetrical geometry is that exact expressions for transmittance, reflectance, and electric fields can be obtained analytically. Using these expressions, experimental data were fitted to obtain parameters such as refractive index modulation, spatial period of the grating, optical thickness or shrinkage of the material.

Linear response deviations during recording of diffraction gratings in photopolymers

In a holographic recording is advisable that the diffraction efficiency increases linearly with the exposure in a wide zone of the curve of diffraction efficiency versus energetic exposure and the slope of the curve must be approximately constant before saturation in order to improve the energetic sensitivity and to get reproducibility in different recordings with the same kind of photopolymer, although to find examples of deviations to this behavior it is usual. The more important deviation experimentally observed in photopolymers with high thickness happen when the first maximum in the curve is lower than the second one. This effect is opposed to an overmodulation. We present a main hypothesis related to the dye concentration into the layer and with the molecular weight of the polymer chains generated in the polymerization process in order to explain this effect.

Analysis of PVA/AA based photopolymers at the zero spatial frequency limit using interferometric methods

One of the problems associated with photopolymers as optical recording media is the thickness variation during the recording process. Different values of shrinkages or swelling are reported in the literature for photopolymers. Furthermore, these variations depend on the spatial frequencies of the gratings stored in the materials. Thickness variations can be measured using different methods: studying the deviation from the Bragg's angle for nonslanted gratings, using MicroXAM S/N 8038 interferometer, or by the thermomechanical analysis experiments. In a previous paper, we began the characterization of the properties of a polyvinyl alcohol/acrylamide based photopolymer at the lowest end of recorded spatial frequencies. In this work, we continue analyzing the thickness variations of these materials using a reflection interferometer. With this technique we are able to obtain the variations of the layers refractive index and, therefore, a direct estimation of the polymer refractive index.

Real-time interferometric characterization of a polyvinyl alcohol based photopolymer at the zero spatial frequency limit

We characterize the optical modulation properties of a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer at the lowest end of recorded spatial frequencies. To achieve this goal we have constructed a double beam interferometer in combination with the setup to expose the recording material. This is a novel approach since usually holographic recording materials are only characterized at high spatial frequencies. Some benefits are provided by the approach we propose: a direct calculation of the properties of the material is possible, and on the other hand additional information can be obtained since the results are not influenced by diffusion processes. Furthermore, this characterization is needed to optimize the PVA/AA photopolymers for another range of applications, such as recording of diffractive optical elements, where very low spatial frequencies are recorded. Different PVA/AA compositions and layer thicknesses have been analyzed. We have found that, depending on the layer characteristics, we can achieve high values of the phase-shift modulation depth and enhance the sensitivity of the material.

Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories

We show an accurate procedure to obtain a Fourier transform (FT) with no dc term using a commercial twisted-nematic liquid-crystal display. We focus on the application to holographic storage of binary data pages, where a drastic decrease of the dc term in the FT is highly desirable. Two different codification schemes are considered: binary pi radians phase modulation and hybrid ternary modulation. Any deviation in the values of the amplitude and phase shift generates the appearance of a strong dc term. Experimental results confirm that the calculated configurations provide a FT with no dc term, thus showing the effectiveness of the proposal.

Improved maximum uniformity and capacity of multiple holograms recorded in absorbent photopolymers

In order to use photopolymers in the recording of holographic memories, high physical thickness is required. This generates many problems associated with the attenuation of light in the recording due to Beer's law. One of the more significant disadvantages is the fact that there are differences between the physical thickness of the material and the optical thickness of the holograms recorded. The optical thickness characterizes the angular selectivity of the holograms and determines the separation between two consecutive holograms in angular peristrophic multiplexing. In this work we propose a new method to record many holograms multiplexed with similar diffraction efficiency values taking into account the different effective optical thickness of each hologram.

3-dimensional characterization of thick grating formation in PVA/AA based photopolymer

Large thickness is required in holographic recording materials to be used as holographic memories. Photopolymers have proved to be a good alternative to construct holographic memories. Nevertheless, modeling the behavior of thick layers poses some problems due to high absorption of the dye, as discussed in previous papers. In this study, the gratings stored in photopolymers based on PVA/AA are analyzed considering the attenuation of light in depth. This is done by fitting the theoretical results, predicted by a model that considers this effect, to the experimental results obtained using diffraction gratings recorded in PVA/AA based photopolymer. In order to determine the diffraction efficiency at the first Bragg angle, an algorithm based on the rigorous coupled wave theory is used. Also, the characteristics of the gratings obtained using different recording intensities are analyzed, and the effective optical thickness is seen to increase as the intensity is increased.

Characterization of polyvinyl alcohol/acrylamide holographic memories with a first-harmonic diffusion model

Several theoretical models have been proposed to predict the behavior of photopolymers as holographic recording materials. Basically these models have been applied to study thin layers (around 100 microm thick). The increasing importance of holographic memories recorded in photopolymers (thickness of > 500 microm) makes it necessary to extend the ideas proposed by these models to study thick photopolymer layers. We calculate the temporal evolution of the diffraction efficiencies for thick layers using a first-harmonic diffusion model, and the results obtained are compared with the corresponding values for thin layers. Furthermore, the values of the average diffusivity of the polymer chains after the grating is formed are also obtained. In general, we find that the monomer and polymer diffusivity increases when higher values of thickness are used.

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

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

3 Dimensional analysis of holographic photopolymers based memories

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

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

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

Clarifications to the paper "Holographic characteristics of a 1-mm-thick photopolymer to be used in holographic memories"

We have corrected typing errors related to the characterization of the dynamic range of the acrylamide photopolymer described in an earlier study [Appl. Opt. 42, 7008 (2003)]. The M number is expressed as M/# instead of M# as appears in the text. The value calculated from the experimental results that are included in the article is M/# = 3.8 instead of 38 as appears in the text.

Holographic characteristics of a 1-mm-thick photopolymer to be used in holographic memories

Poly(vinyl alcohol-acrylamide) photopolymers are materials of interest in the field of digital information storage (holographic memories). We analyzed the behavior of a 1-mm-thick photopolymer. Using a standard holographic setup, we recorded unslanted diffraction gratings. The material has high angular selectivity (0.4 degrees), good sensitivity (88 mJ/cm2), and small losses caused by absorption and scattering of light. It also has a high maximum diffraction efficiency (70%). A significant induction period was seen in the material. The authors hypothesize that, during most of this induction period, polymerization does in fact take place but is not reflected in the appearance of the diffracted light until a certain threshold value of exposure is reached.

Diffusion-based model to predict the conservation of gratings recorded in poly(vinyl alcohol)-acrylamide photopolymer

Photopolymers are interesting materials for use in recording information in holography. We study the holographic behavior and stability of volume holograms recorded in poly(vinyl alcohol)--acrylamide photopolymers with and without a cross linker. Using a first-harmonic diffusion model, we analyze the residual monomer that remains when volume diffraction gratings are recorded in photopolymer materials. The importance of this residual monomer to the stability of the gratings is evaluated.

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.

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

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

Angular responses of the first and second diffracted orders in transmission diffraction grating recorded on photopolymer material

Some of the theoretical models in the literature describing the mechanism of hologram formation in photopolymer materials predict the existence of higher harmonics in the Fourier expansion of the recorded refractive index. Nevertheless, quantitative information is only obtained for the first harmonic of the refractive index using Kogelnik's Coupled Wave Theory. In this work we apply the Rigorous Coupled Wave Theory to demonstrate that when recording phase diffraction gratings in PVA/acrylamide photopolymer materials, a second order grating is also recorded in the hologram even when the material is exposed to a sinusoidal interference pattern. The influence of this second order grating on the efficiency of the first order for replay at the first on-Bragg angular replay condition is studied and the size of the 2nd harmonic examined.

Temporal evolution of the angular response of a holographic diffraction grating in PVA/acrylamide photopolymer

In this paper we evaluate the temporal evolution, after exposure, of a diffraction grating stored in a PVA/acrylamide photopolymer. We also study the overmodulation of the refractive index inside the hologram, which gives rise to a particular behaviour of the angular response of diffraction efficiency. This evolution takes place in our photopolymer due to the incorporation of dimethylacrylamide (DMAA), which is a liquid at room temperature and so favours diffusion of the species in solution from the zones of greater concentration to those of lower concentration.

Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms

The Coupled Wave Theory of Kogelnik has given a wellestablished basis for the comprehension of how light propagates inside a hologram. This theory gives an accurate approximation for the diffraction efficiency of volume phase holograms and volume absorption holograms as well. Mixed holograms (phase and absorption) have been also treated from the point of view of this theory. For instance, Guibelalde theoretically described the diffraction efficiency of out of phase mixed volume gratings. In this work we will show that when using fixation-free rehalogenating bleaches, out of phase mixed volume gratings can be recorded on the hologram at high exposures. This is due to the oxidation products of the developer and the bleaching agent. The effects described theoretically for out of phase mixed volume hologram gratings are experimentally observed.

Determination of the refractive index and thickness of holographic silver halide materials by use of polarized reflectances

A method to determine the refractive index and thickness of silver halide emulsions used in holography is presented. The emulsions are in the form of a layer of film deposited on a thick glass plate. The experimental reflectances of p-polarized light are measured as a function of the incident angles, and the values of refractive index, thickness, and extinction coefficient of the emulsion are obtained by using the theoretical equation for reflectance. As examples, five commercial holographic silver halide emulsions are analyzed. The procedure to obtain the measurements and the numerical analysis of the experimental data are simple, and agreement of the calculated reflectances, by use of the thickness and refractive index obtained, with the measured reflectances is satisfactory.

Mechanism of hologram formation in fixation-free rehalogenating bleaching processes

The mechanism of hologram formation in fixation-free rehalogenating bleaching processes have been treated by different authors. The experiments carried out on Agfa 8E75 HD plates led to the conclusion that material transfer from the exposed to the unexposed zones is the main mechanism under theprocess. We present a simple model that explains the mechanism of hologram formation inside the emulsion. Also quantitative data obtained using both Agfa 8E75 HD and Slavich PFG-01 fine-grained red-sensitive emulsions are given and good agreement between theory and experiments are found.

Effects of overmodulation in fixation-free rehalogenating bleached holograms

The mechanism for hologram formation by fixation-free rehalogenating bleaching has been treated by several authors. Experiments carried out with Kodak and Agfa photographic plates have led to the conclusion that the transfer of material from the exposed to the unexposed zones is the main mechanism that drives the process. We show that when BB-640 emulsion is used in the recording of holograms by means of fixation-free rehalogenating bleaching, the mechanism for the transfer of material from exposed to unexposed zones is efficient enough to create high refractive-index modulations. We also comment on the overmodulation effects, which result in a decrease in diffraction efficiency.

Silver halide sensitized gelatin derived from BB-640 holographic emulsion

Silver halide sensitized gelatin (SHSG) is one of the most interesting techniques for the production of holographic optical elements, achieving relatively high sensitivity of photographic material with a low scattering of dichromated gelatin. Here we present experimental results for SHSG derived from the novel BB-640, a red-sensitive ultra-fine-grain emulsion from Holographic Recording Technologies (Steinau, Germany). The material is characterized before recording and after processing, and information about the thickness, absorption, and refractive-index modulation of the final holograms is obtained. The influence of the developer is analyzed, and diffraction efficiencies as great as 96.2% (after allowing for reflections) with a transmission of 1% and absorption and scatter losses of 2.8% are obtained with AAC developer. Our investigations reveal that high-quality SHSG transmission holograms may be obtained with the new BB-640 plates.