Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth

Aubrecht, Ivo; Miler, Miroslav; Koudela, Ivo

doi:10.1080/095003498151140

Cited by 45 publications

(86 citation statements)

References 10 publications

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“…Besides, the differences in the refractive indexes of the binder and monomer are critical in determining the refractive index modulations achieved. 8 However, these effects alone cannot explain the enormous differences observed. Some recent studies 5,7 propose very short exposures using a holographic setup to obtain an estimation of D 0 .…”

mentioning

confidence: 89%

Direct analysis of monomer diffusion times in polyvinyl/acrylamide materials

Gallego¹,

Márquez²,

Méndez³

et al. 2008

Applied Physics Letters

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We propose an alternative, direct method to calculate monomer diffusion times in photopolymer materials. Very long period gratings are recorded in the photopolymer, and the real time variation in diffraction efficiency due to monomer diffusion is then analyzed. In photopolymers, monomer diffusion plays a fundamental role in hologram formation. However, since many interrelated parameters affect hologram formation, the usual techniques do not allow for an independent estimation of monomer diffusion times. The direct method proposed is applied to two polyvinyl based photopolymers with different molecular weights. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2836948͔ Polyvinyl/acrylamide ͑PVA/AA͒ photopolymers have very good properties as holographic recording materials. In order to characterize the hologram formation in this type of material, many parameters must be taken into account: the diffusion of components inside the material, 1,2 the relation between intensity and polymerization, the nonlocality of the polymerization process, the higher harmonics in monomer and polymer concentrations, the importance of dye variations, diffusivity variations, etc. Therefore, if we use a diffusion model, we can obtain only an indirect estimation of monomer diffusion times. This means that depending on the importance given to the different interrelated processes, enormous differences in the estimation of this important parameter, monomer diffusion times, could appear. There are studies that propose values of 10 −14 , 3,4 10 −10 , 5,6 or 10 −7 cm 2 / s for the initial monomer diffusion coefficient ͑D 0 ͒. 7 It is obvious that each group uses different PVA molecular weights, different PVA refractive indexes and different component concentrations. Furthermore, the drying process depends on the temperature and humidity of each individual laboratory. Besides, the differences in the refractive indexes of the binder and monomer are critical in determining the refractive index modulations achieved. 8 However, these effects alone cannot explain the enormous differences observed. Some recent studies 5,7 propose very short exposures using a holographic setup to obtain an estimation of D 0 . Nevertheless, important drawbacks have to be solved to apply this method. Firstly, the influence of the refractive indexes of the components involved in the process must be correctly estimated, 5 and secondly the grating evolution due to monomer diffusion after exposure lasts for only around 0.1 s ͑the time that it takes to stop the diffraction efficiency variation in the dark for spatial frequencies around 1000 lines/ mm͒. 5 Furthermore, this effect can only be observed for very weak diffraction efficiencies. 5 Therefore, we can conclude that monomer diffusion should be estimated using only direct real time determination methods. We thus propose a direct method to determine the monomer diffusion times in photopolymers.Our proposal consists in recording very long period gratings in the photopolymer to observe the monomer diffusion directly: t...

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mentioning

confidence: 89%

Direct analysis of monomer diffusion times in polyvinyl/acrylamide materials

Gallego¹,

Márquez²,

Méndez³

et al. 2008

Applied Physics Letters

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“…However, we also need to account for the influence of the free volume created due to hole formation during the recording process. Therefore assuming that volume is conserved 18,20 we can write While the collapse of holes will result in a reduction in the overall volume, the total volume fraction is by definition conserved. The total refractive index can then be expressed using the Lorentz-Lorenz relation,…”

Section: A Refractive Index Measurementsmentioning

confidence: 99%

“…The model is solved using a finite-difference time-domain method 19 ͑FDTD͒ and the effects of the nonlocal temporal response on refractive index modulation using the Lorentza͒ Lorenz relation are examined. 20 These results are used to calculate diffraction efficiency using rigorous coupled wave analysis 21 ͑RCWA͒ and to carry out fits to experimental data. An inhibition process has been noted at the beginning of the recording process.…”

Section: Introductionmentioning

confidence: 99%

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

Kelly

Gleeson

et al. 2006

Journal of Applied Physics

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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.

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“…Some early models [24][25][26] predict a linear dependence on intensity. Kwon et al postulated that the polymerisation rate depends on the square root of the recording intensity [27] and define the relationship between polymerisation rate and recording intensity as:…”

Section: Theorymentioning

confidence: 99%

Determination of the polymerisation rate of a low-toxicity diacetone acrylamide-based holographic photopolymer using Raman spectroscopy

Cody¹,

Mihaylova²,

O’Neill³

et al. 2015

Optical Materials

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. (2016). Determination of the polymerisation rate of a low-toxicity diacetone acrylamidebased holographic photopolymer using Raman spectroscopy. Optical Materials, vol. 48, Oct. 2015, pp. 12-17. doi.org/10.1016/ j.optmat.2015 Determination of the polymerisation rate of a low-toxicity diacetone acrylamide-based holographic photopolymer using Raman spectroscopy t r a c tThe polymerisation rate of a low-toxicity Diacetone Acrylamide (DA)-based photopolymer has been measured for the first time using Raman spectroscopy. A value for the polymerisation rate of 0.020 s À1 has been obtained for the DA photopolymer by modelling the polymerisation reaction dynamics as a stretched exponential or Kohlrausch decay function. This is significantly lower than the polymerisation rate of 0.100 s À1 measured for the well known Acrylamide (AA)-based photopolymer composition. The effect of the additive glycerol on the polymerisation rate of the DA-based photopolymer has also been investigated. The inclusion of glycerol is observed to increase the rate of polymerisation of the DA photopolymer by up to 60%. It is also observed that the polymerisation rate of the DA photopolymer is less dependent on the recording intensity when glycerol is present.

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Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth

Cited by 45 publications

References 10 publications

Direct analysis of monomer diffusion times in polyvinyl/acrylamide materials

Direct analysis of monomer diffusion times in polyvinyl/acrylamide materials

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

Determination of the polymerisation rate of a low-toxicity diacetone acrylamide-based holographic photopolymer using Raman spectroscopy

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