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.

Analysis of the Imaging Characteristics of Holographic Waveguides Recorded in Photopolymers.

In this work, we study the imaging characteristics of an optical see-through display based on a holographic waveguide. To fabricate this device, two transmission holograms are recorded on a photopolymer material attached to a glass substrate. The role of the holograms is to couple the incident light between air and the glass substrate, accomplishing total internal reflection. The role of noise reflection gratings and shrinkage on the imaging characteristics of the device will be also explored. The holograms (slanted transmission gratings with a spatial frequency of 1690 lines/mm) were recorded on a polyvinyl alcohol acrylamide holographic polymer dispersed liquid crystal (HPDLC) material. We will show that sufficient refractive index modulation is achieved in the material, in order to obtain high diffraction efficiencies. We will demonstrate that the final device acts as an image formation system.

Complex Diffractive Optical Elements Stored in Photopolymers.

We study the recording of complex diffractive elements, such as achromatic lenses, fork gratings or axicons. Using a 3-D diffusion model, previously validated, we are able to predict the behavior of photopolymer during recording. The experimental recording of these complex elements is possible thanks to a new generation spatial light modulator capable of generating periodic and aperiodic profiles. Both experimental and theoretical are analyzed and compared. The results show not only the good response of theoretical model to predict the behavior of the materials, but also the viability of photopolymers to store these kind of elements.

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.

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.

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.

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).

Beta value coupled wave theory for nonslanted reflection gratings.

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik's coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik's coupled wave theory.

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.

Biophotopol: A Sustainable Photopolymer for Holographic Data Storage Applications.

Photopolymers have proved to be useful for different holographic applications such as holographic data storage or holographic optical elements. However, most photopolymers have certain undesirable features, such as the toxicity of some of their components or their low environmental compatibility. For this reason, the Holography and Optical Processing Group at the University of Alicante developed a new dry photopolymer with low toxicity and high thickness called biophotopol, which is very adequate for holographic data storage applications. In this paper we describe our recent studies on biophotopol and the main characteristics of this material.

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.

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.

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.

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.