
Fernandez, Roberto; Gallego, Sergi; Márquez, Andrés; Francés, Jorge; Martínez Guardiola, Francisco Javier; Beléndez, Augusto
Photopolymers present appealing optical properties for holographic and diffractive applications. They enable modulation of the electrical permittivity and thickness and are selfprocessing, and layers with a wide range of thicknesses and properties can be fabricated on demand. In order to obtain a complete characterization of the material, low spatial frequency analysis has become a fundamental tool because the motion of the components inside of the material can be measured. We propose to use an index matching component to carry out a complete characterization and to differentiate the “apparent” and the real monomer diffusion. We also have quantified the minimum thickness...

Fernandez, Roberto; Gallego, Sergi; Márquez, Andrés; Francés, Jorge; NavarroFuster, Víctor; Pascual, Inmaculada
Photopolymers can be appealing materials for diffractive optical elements fabrication. In this paper, we present the recording of diffractive lenses in PVA/AA (Polyvinyl alcohol acrylamide) based photopolymers using a liquid crystal device as a master. In addition, we study the viability of using a diffusion model to simulate the lens formation in the material and to study the influence of the different parameters that govern the diffractive formation in photopolymers. Once we control the influence of each parameter, we can fit an optimum recording schedule to record each different diffractive optical element with the optimum focalization power.

NavarroFuster, Víctor; Ortuño, Manuel; Gallego, Sergi; Márquez, Andrés; Beléndez, Augusto; Pascual, Inmaculada
In order to obtain a highly environmentally compatible photopolymer to replace the wellknown acrylamide photopolymer we optimized the previously developed Biophotopol composition to obtain volume transmission gratings in 300 μm layers, at a recording wavelength of 488 nm. The results obtained show an improved energetic sensitivity with similar diffraction efficiency to that obtained at the standard recording wavelength of 514 nm.

Fernandez, Roberto; Gallego, Sergi; Márquez, Andrés; Ortuño, Manuel; Marini, Stephan; Pascual, Inmaculada; Beléndez, Augusto
One of the most promising phase optical recording mediums are photopolymers. In these materials, the use of an index matching component permits a better conservation of the stored information and, additionally, the study of the molecules migration and shrinkage/swelling phenomena separately. In general, the transmitted beam has the information of the thickness and refractive index modulation mixed. Therefore, we propose the introduction of a coverplate besides with an index matching liquid in order to improve the characterization and the conservation. The index matching techniques have been classically used for holographic recording materials. In principle, to obtain an accurate index matching...

Martínez Guardiola, Francisco Javier; Fernandez, Roberto; Márquez, Andrés; Gallego, Sergi; Alvarez, Mariela L.; Pascual, Inmaculada; Beléndez, Augusto
We focus on the novelty of three elements in holographic data storage systems (HDSS): the data pager, where we introduce a parallelaligned liquid crystal on silicon (PALCoS) microdisplay; the recording material, where we consider the highly versatile PVA/AA photopolymer; and also in the architecture of the object arm, where a convergent correlator system is introduced. We show that PALCoS devices cannot implement pure hybridternary modulated (HTM) data pages but a rather close approximation. Validation of the HDSS expressions for the convergent correlator and comparison with the widespread 4f system is performed. Experimental results with PVA/AA material showing biterror rates (BER)...

Fernandez, Roberto; Gallego, Sergi; Francés, Jorge; Pascual, Inmaculada; Beléndez, Augusto
Freeradical photopolymer materials can be fabricated using a wide range of monomers, binders, dyes, etc. It was shown that in some photopolymers the surface and the internal diffusion for acrylamide materials are very different and also it was demonstrated the viability of acrylamide materials to achieve 2π phase depth for low spatial diffractive optical elements. Building on the work developed previously, in this paper, a characterization and a comparison is carried out for three different photopolymers: crosslinked acrylamide based photopolymers, a biophotopol and an HPDLC material. We have measured the motion of the components inside the material and through the...

Gallego, Sergi; Fernandez, Roberto; Márquez, Andrés; Ortuño, Manuel; Neipp, Cristian; Gleeson, Michael R.; Sheridan, John T.; Beléndez, Augusto
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...

Gallego, Sergi; Márquez, Andrés; Neipp, Cristian; Fernandez, Roberto; Martínez Guardiola, Francisco Javier; Francés, Jorge; Ortuño, Manuel; Pascual, Inmaculada; Beléndez, Augusto
Photopolymer are appealing materials for diffractive elements recording. Two of their properties when they are illuminated are useful for this goal: the relief surface changes and the refractive index modifications. In this paper we use a 2dimensional model, based on direct parameter measurements, for predicting the refractive index distributions during and after illumination. We have analyzed different recording spatial frequencies for photopolymers based on PVA/Acrylamide. This model was successfully applied to different photopolymer compositions with different values of monomer diffusion and polymerization rates.

Gallego, Sergi; Ortuño, Manuel; Márquez, Andrés; Fernandez, Roberto; Alvarez, Mariela L.; Beléndez, Augusto; Pascual, Inmaculada
For photopolymers the compound concentrations and final thickness of the sample should be known in order to model hologram formation and introduce the reactiondiffusion kinetics of the monomerpolymer system. In principle the cell thickness can be controlled by bead spacers between the two pieces of ITO glass. In this paper we report a study of the influence of thickness on the holographic properties of this type of materials. To fit the physical and optical thickness of the samples we used the rigorous coupled wave analysis assuming an exponential decay in the refractive index modulation.

Ortuño, Manuel; Márquez, Andrés; Gallego, Sergi; Fernandez, Roberto; NavarroFuster, Víctor; Beléndez, Augusto; Pascual, Inmaculada
Holographic polymer dispersed liquid crystals (HPDLC) are made by holographic recording in a photopolymerization induced phase separation process in which the liquid crystal molecules diffuse to dark zones in the diffraction grating. The devices with HPDLC materials develop a dynamic behavior that may be modified by means of an electric field. We study a photopolymer formulation with high diffraction efficiency but with the problem of high electric conductivity. We use a bleaching postexposure treatment to obtain devices with a better electrooptical performance.

Gallego, Sergi; Fernandez, Roberto; Márquez, Andrés; Martínez Guardiola, Francisco Javier; Neipp, Cristian; Ortuño, Manuel; Beléndez, Augusto; Pascual, Inmaculada
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 photoembossing, diffractive and refractive optical elements, holographic elements, solar concentrators, optical detectors and hybrid optoelectronic 3D 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,...

Gallego, Sergi; Fernandez, Roberto; Márquez, Andrés; Neipp, Cristian; Beléndez, Augusto; Pascual, Inmaculada
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...

Gallego, Sergi; Márquez, Andrés; Fernandez, Roberto; Piera, Álvaro; Martínez Guardiola, Francisco Javier; Ortuño, Manuel; Francés, Jorge; Beléndez, Augusto; Pascual, Inmaculada
Recently the possibility to record phase diffractive optical elements (DOEs) onto photopolymers has been explored. Two of their properties when they are illuminated are useful to this goal: the relief surface changes and the refractive index modifications. The recording intensity distribution with a sinusoidal profile is the easiest profile to record in a holographic recording material, i.e. it can be obtained by the simple interference of two plane wave beams or alternatively using a spatial light modulator. This second method is more flexible and opens the possibility to record a wide range of diffractive elements such as binary, blazed gratings,...

Gallego, Sergi; Márquez, Andrés; Martínez Guardiola, Francisco Javier; Riquelme Morell, Marina; Fernandez, Roberto; Pascual, Inmaculada; Beléndez, Augusto
Photopolymer are appealing materials for diffractive elements recording. Two of their properties when they are illuminated are useful for this goal: the relief surface changes and the refractive index modifications. To this goal the linearity in the material response is crucial to design the optimum irradiance for each element. In this paper we measured directly some parameters to know how linear is the material response, in terms of the refractive index modulation versus exposure, then we can predict the refractive index distributions during recording. We have analyzed at different recording intensities the evolution of monomer diffusion during recording for photopolymers...

Gimeno, Encarnación; Alvarez, Mariela L.; Yebra Calleja, María Soledad; RosaHerranz, Julio; Beléndez, Augusto
A secondorder modified rational harmonic balance method is used for approximately solve the nonlinear differential equation that governs the oscillations of a system typified as a mass attached to a stretched elastic wire for which the restoring force for this oscillator has an irrational term with a parameter lambda that characterizes the system. A frequencyamplitude relation is constructed and this frequency is valid for the complete range of oscillation amplitudes A and parameter lambda, and excellent agreement of the approximate frequencies with the exact one is demonstrated and discussed. The discrepancy between the approximate frequency and the exact one never...

Beléndez, Augusto; Gimeno, Encarnación; Alvarez, Mariela L.; Gallego, Sergi; Ortuño, Manuel; Méndez Alcaraz, David Israel
An analytical approximate procedure for a class of conservative single degreeoffreedom nonlinear oscillators with odd nonlinearity is proposed. This technique is based on the generalized harmonic balance method in which analytical approximate solutions have rational forms. Unlike the classical harmonic balance techniques, in this new procedure the approximate solution and the restoring force are expanded in Fourier series prior to substituting them in the nonlinear differential equation. This approach gives us not only a truly periodic solution but also the frequency of the motion as a function of the amplitude of oscillation. Four nonlinear oscillators are presented to illustrate the...

Gimeno, Encarnación; Beléndez, Augusto
This paper presents a new approach for solving accurate approximate analytical solutions for nonlinear phenomena governed by pendulumlike differential equations. The new approach couples Taylor series expansion with rational harmonic balancing. An approximate rational solution depending on a small parameter is considered. After substituting the approximate solution into the governing differential equation, this equation is expanded in Taylor series of the parameter prior to harmonic balancing. The approach gives a cubic equation, which must be solved in order to obtain the value of the small parameter. A method for transforming this cubic equation into a linear equation is presented and...

Beléndez, Augusto; Gimeno, Encarnación; Alvarez, Mariela L.; Méndez Alcaraz, David Israel
The homotopy perturbation method is used to obtain the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^1/3. We find this method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 0.60% for small and large values of oscillation amplitude, while this relative error is as low as 0.050% for the second iteration. Comparison...

Beléndez, Augusto; Gimeno, Encarnación; Beléndez Vázquez, Tarsicio; Hernández Prados, Antonio
A secondorder modified rational harmonic balance method is used to approximately solve the nonlinear differential equation that governs the oscillations of a conservative autonomous system with one degree of freedom. The Duffing oscillator is analyzed to illustrate the usefulness and effectiveness of the proposed technique. We find that this method works very well for this oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the secondorder approximation we have shown that the relative error in the analytical approximate frequency is as low as 0.0055% when A tends to infinity. We also...

Beléndez, Augusto; Gimeno, Encarnación; Alvarez, Mariela L.; Yebra Calleja, María Soledad; Méndez Alcaraz, David Israel
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have rational form. This approach gives us not only a truly periodic solution but also the frequency of the motion as a function of the amplitude of oscillation. Three truly nonlinear oscillators including cubic Duffing oscillator, fractionalpower restoring force and antisymmetric quadratic nonlinear oscillators are presented to illustrate the usefulness and effectiveness of the proposed technique. We find that this method works very well for the cubic oscillator, and excellent agreement of the approximate...