Grating Formation In Photopolymers Research Articles

Temporal response and first order volume changes during grating formation in photopolymers

We examine the evolution of the refractive index modulation when recording gratings in an acrylamide based photopolymer. A nonlocal diffusion model is used to predict theoretically the grating evolution. The model has been developed to account for both nonlocal spatial and temporal effects in the medium, which can be attributed to polymer chain growth. Previously it was assumed that the temporal effect of chain growth could be neglected. However, temporal effects due to chain growth and monomer diffusion are shown to be significant, particularly over short recording periods where dark field amplification is observed. The diffusion model is solved using a finite-difference technique to predict the evolution of the monomer and polymer concentrations throughout grating recording. Using independently measured refractive index values for each component of the recording medium, the Lorentz-Lorenz relation is used to determine the corresponding refractive index modulation. The corresponding diffraction efficiency is then determined using rigorous coupled wave analysis. The diffraction efficiency curves are presented for gratings recorded using short exposure times, monitored in real time, both during and after recording. The effect of volume shrinkage of polymer on grating evolution is also examined. Both the nonlocal temporal response of the material and monomer diffusion are shown to influence refractive index modulation postexposure.

Holographic grating formation in photopolymers: analysis and experimental results based on a nonlocal diffusion model and rigorous coupled-wave analysis

The one-dimensional nonlocal diffusion model for holographic recording in photopolymers proposed by Sheridan [J. Opt. Soc. Am. A17, 1108 (2002)] is rewritten in dimensionless form by introduction of four dimensionless variables. The dimensionless nonlocal diffusion equation is rigorously solved by use of the finite-difference time-domain method and compared with the four-harmonic-component approximation. In general, the error in the four-harmonic-component approximation increases as RD and σD decrease. The dynamic behavior of holographic grating formations based on DuPont OmniDex613 photopolymers (recorded with UV light of free-space wavelength 363.8 nm) are experimentally studied by use of the real-time diffraction-monitoring technique. By application of rigorous coupled-wave analysis (RCWA), the growth curves of experimentally monitored diffraction efficiencies are converted to the corresponding refractive-index modulations. After the holographic recording reaches steady state, the refractive-index modulation is ∼0.01. Furthermore, the conversion from diffraction efficiencies to refractive-index modulations is also accomplished by use of Kogelnik’s theory (corrected for reflection losses) and compared to the RCWA. As a result, the error in refractive-index modulations estimated by Kogelnik’s theory at steady state is ∼30%. The effects of postbaking conditions on the refractive-index modulation are investigated for the first time to the authors’ knowledge. To accomplish this we baked the holographic grating samples at various temperatures (Tb= 90, 120, 150 °C) for three time periods (tb=1, 1.5, 2 h). In general, it was found that refractive-index modulation can increase from ∼0.01 to ∼0.02 after baking. Finally, we estimated the characteristic parameters including diffusion coefficient and the nonlocal response length by fitting the theoretical model to the experimental data for the recording UV wavelength of 363.8 nm.

Adjusted intensity nonlocal diffusion model of photopolymer grating formation

Diffusion-based models of grating formation in photopolymers have been proposed in which the rate of monomer polymerization (removal) is directly proportional to the illuminating intensity inside the medium. However, based on photochemical considerations, the rate of polymerization is proportional in the steady state to the square root of the interference intensity. Recently it was shown that, by introducing a nonlocal response function into the one-dimensional diffusion equation that governs holographic grating formation in photopolymers, one can deduce both high-frequency and low-frequency cutoffs in the spatial-frequency response of photopolymer materials. Here the first-order nonlocal coupled diffusion equations are derived for the case of a general relationship between the rate of polymerization and the exposing intensity. Assuming a two-harmonic monomer expansion, the resultant analytic solutions are then used to fit experimental growth curves for gratings fabricated with different spatial frequencies. Various material parameters, including monomer diffusion constant D and nonlocal variance σ, are estimated.

Comparison of holographic photopolymer materials by use of analytic nonlocal diffusion models.

The one-dimensional diffusion equation governing holographic grating formation in photopolymers, which includes both nonlocal material response and generalized dependence of the rate of polymerization on the illuminating intensity, has been previously solved under the two-harmonic expansion assumption. The resulting analytic expressions for the monomer and polymer concentrations have been derived and their ranges of validity tested in comparison with the more accurate numerical four-harmonic case. We used these analytic expressions to carry out a study of experimental results presented in the literature over a 30-year period. Automatic fitting of the data with these formulas allows material parameters, including the nonlocal chain-length variance sigma, to be estimated. In this way, (i) a quantitative comparison of different materials can be made, and (ii) a standard form of experimental result presentation is proposed to facilitate such a procedure.

Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses

It has recently been shown by Sheridan and Lawrence (Sheridan J T and Lawrence J R 2000 J. Opt. SA A 17 1108-14) that, introducing a Gaussian non-local material response function into the one-dimensional diffusion equation governing holographic grating formation in photopolymers, both high-frequency and low-frequency cut-offs in the spatial frequency response of the materials can be deduced.

Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model

It has recently been shown [Sheridan and Lawrence, J. Opt. Soc. Am. A 17, 1108 (2000)] that by introducing a nonlocal response function into the one-dimensional diffusion equation governing holographic grating formation in photopolymers, both high frequency and low frequency cutoffs in the spatial frequency response of photopolymer materials can be deduced. Starting with this result, analytic solutions to this equation are derived assuming a two harmonic expansion of the monomer concentration. These expressions are first compared to the more rigorous four harmonic numerical results, indicating the range of physical parameters for which they are accurate. They are then compared to the experimental diffraction intensity growth curves produced during the formation of sinusoidal gratings recorded with different spatial frequencies. Fitting these curves using the analytic expressions, various material parameters, including the monomer diffusion constant, D, and the nonlocal variance, σ, can be estimated. Trends in material behavior as the grating spatial frequency is changed are discussed.

First-harmonic diffusion model for holographic grating formation in photopolymers

We present a model with which to describe and predict the formation of gratings during exposure in holographic photopolymers. This model combines the action of photopolymerization and of free-monomer diffusion during holographic exposures. We consider the free-monomer density to be spatially varying, during exposure, with a single first-harmonic term out of phase with respect to the intensity interference pattern. Examples of behavior predicted by the model include the variation of the saturation diffraction efficiency with recording exposure intensity and with beam intensity modulation, as well as the variation of recorded grating modulation during dark diffusion transient. The model is supported by experiments carried out by exposure of DuPont HRF-150-38 holographic photopolymers.

Dynamics during holographic exposure in photopolymers for single and multiplexed gratings

Abstract Under the assumption that at low recording intensity the grating formation process is much slower than the free monomer diffusion, we present a model that describes the dynamics of the holographic grating formation in photopolymers. The model indicates how the beam intensity modulation influences the saturation value of the grating modulation, while the average recording intensity is related in a nonlinear fashion to the process time constant. An extension of this model describes and predicts the recording of a single grating in the presence of an additional mutually incoherent light beam, and the simultaneous recording of angularly mutliplexed gratings. The model is validated by comparing with experimental results obtained using DuPont HRF-150-38 photopolymer.

Dynamics during holographic exposure in photopolymers for single and multiplexed gratings

Under the assumption that at low recording intensity the grating formation process is much slower than the free monomer diffusion, we present a model that describes the dynamics of the holographic grating formation in photopolymers. The model indicates how the beam intensity modulation influences the saturation value of the grating modulation, while the average recording intensity is related in a nonlinear fashion to the process time constant. An extension of this model describes and predicts the recording of a single grating in the presence of an additional mutually incoherent light beam, and the simultaneous recording of angularly mutliplexed gratings. The model is validated by comparing with experimental results obtained using DuPont HRF-150-38 photopolymer.

Holographic grating formation in photopolymers

We introduce a model describing real-time grating formation in holographic photopolymers, under the assumption that the diffusion of free monomers is much faster than the grating formation. This model, which combines polymerization kinetics with results from coupled-wave theory, indicates that the grating formation time depends sublinearly on the average holographic recording intensity, and the beam intensity ratio controls the grating index modulation at saturation. We validate the model by comparing its predictions with the results of experiments in which DuPont HRF-150X001 photopolymer was used.

Holographic grating formation in photopolymers—Polymethylmethacrylate

AbstractPolymethylmethacrylate has been sensitized to 4880 A light and used as a holographic recording medium. The polymer is sensitized with a material which may itsel be degraded by exposure to ultraviolet light. The new process is, therefore, both self‐developing and fixable without chemical processing. Holographic diffraction gratings written into this material have diffracting efficiencies as high as 70 percent. Various parameters such as angular selectivity, film thickness, variation of diffracting efficiency with writing angle etc., have been studied. The spontaneously produced diffracted intensity is so high that efficient interference between first and zero ordes is observed during the writing process.