Andrés Márquez

Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics

In this paper we provide evidence of the temporal fluctuations of the phase modulation property of a liquid crystal on silicon (LCoS) display, and we analyze its effect when the device is used for displaying a diffractive optical element. We use a commercial twisted nematic LCoS display configured to produce a phase-only modulation, and we provide time resolved measurements of the diffraction efficiency that show rapid fluctuations of the phase modulation, in the millisecond order. We analyze how these fluctuations have to be considered in two typical methods for the characterization of the phase modulation: two beam interference and diffraction from a binary grating. We finally provide experimental results on the use of this device for displaying a computer generated hologram. A reduction of the modulation diffraction efficiency results from the phase modulation fluctuation.

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.

Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization

In this paper we characterize the polarimetric properties of a liquid crystal on silicon display (LCoS), including depolarization and diattenuation which are usually not considered when applying the LCoS in diffractive or adaptive optics. On one hand, we have found that the LCoS generates a certain degree (that can be larger than a 10%) of depolarized light, which depends on the addressed gray level and on the incident state of polarization (SOP), and can not be ignored in the above mentioned applications. The main origin of the depolarized light is related with temporal fluctuations of the SOP of the light reflected by the LCoS. The Mueller matrix of the LCoS is measured as a function of the gray level, which enables for a numerical optimization of the intensity modulation configurations. In particular we look for maximum intensity contrast modulation or for constant intensity modulation. By means of a heuristic approach we show that, using elliptically polarized light, amplitude-mostly or phase-mostly modulation can be obtained at a wavelength of 633 nm.

3 Dimensional analysis of holographic photopolymers based memories

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

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display.

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.

In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation

Molecular diffusion effects have been widely studied inside photopolymers for holographic applications. Recently some works have focused on low spatial frequencies to evaluate in real time the monomer diffusion effects. Assuming a Fermi-Dirac function-based profile, we have fitted the diffracted intensities, reflected and transmitted (up to the 8th order), to obtain the phase and surface profile of the recorded gratings. We have studied the influence of diffusion in polyvinyl-alcohol/acrylamide for the range of spatial frequencies between 2 lines/mm and 6 lines/mm. We have demonstrated the influence of the spatial frequency on the magnitude and sign of the material volume variations. We also studied in dark the evolution of the grating shape. We show that it is possible to achieve diffractive gratings with diffraction efficiency in the first order near 35% if the in dark evolution is taken into account. Furthermore we present a method to calculate the monomer diffusivity in photopolymers. The differential equation is deduced and solved, and experimental average value is obtained (D=1.1 x 10(-8) cm(2)s(-1)).

Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator

We show that both a lens and a nonuniform amplitude transmission filter can be encoded simultaneously onto a twisted nematic liquid-crystal spatial light modulator (SLM) working in the phase-only mode. The inherent equivalent apodization that is due to the pixelated structure of the SLM is compensated for. In addition, different types of nonuniform transmission pupil such as transverse apodizing, transverse hyperresolving, and axial hyperresolving (multifocusing) filters are implemented. The excellent agreement between numerical and experimental results shows the capability of this method to encode amplitude apodizers on a phase-only SLM.

First-harmonic diffusion-based model applied to a polyvinyl-alcohol– acrylamide-based photopolymer

The photopolymerization diffusion models give accurate comprehension of the mechanism of hologram formation inside photopolymer materials. Although several models have been proposed, these models share the common assumption that there is an interplay between the processes of monomer polymerization and monomer diffusion. Nevertheless, most of the studies to check the validity of the theoretical models have been done by using photopolymers of the DuPont™ type, or photopolymer materials with values of the monomer diffusion time similar to those of the DuPont material. We check the applicability of a modified diffusion-based model to a polyvinyl alcohol–acrylamide photopolymer. This material has the property of longer diffusion times for the monomer to travel from the unexposed to the exposed zones than in the case of other polymeric materials. Some interesting effects are observed and theoretically treated by using the modified first-harmonic diffusion-based model we propose.

Characterization of a PVA/acrylamide photopolymer. Influence of a cross-linking monomer in the final characteristics of the hologram

Abstract The use of high thickness photopolymers for holographic recording is particularly promising for storage of data information. Therefore it is interesting to characterize such materials in order to improve the quality of the holograms recorded on them. In this work we make use of a first harmonic diffusion model to characterize a polyvinyl alcohol/acrylamide photopolymer. In particular we analyze the effect of adding a cross-linking monomer to this material in the temporal evolution of the transmission efficiency.

Programmable apodizer to compensate chromatic aberration effects using a liquid crystal spatial light modulator

Programmable apodizers written on a liquid crystal spatial light modulator (LCSLM) offer the possibility of modifying the point spread function (PSF) of an optical system in monochromatic light with a high degree of flexibility. Extension to polychromatic light has to take into account the liquid crystal response dependence on the wavelength. Proper control of the chromatic properties of the LCSLM in combination with the design of the correct apodizer is necessary for this new range of applications. In this paper we report a successful application of a programmable amplitude apodizer illuminated with polychromatic light. We use an axial apodizing filter to compensate the longitudinal secondary axial color (LSAC) effects of a refractive optical system on the polychromatic PSF. The configuration of the LCSLM has been optimized to obtain a good amplitude transmission in polychromatic light. Agreement between experimental and simulated results shows the feasibility of our proposal.