A Comprehensive Study of Photorefractive Properties in Poly(ethylene glycol) Dimethacrylate— Ionic Liquid Composites

A detailed investigation of the recording, as well as the readout of transmission gratings in composites of poly(ethylene glycol) dimethacrylate (PEGDMA) and ionic liquids is presented. Gratings with a period of about 5.8 micrometers were recorded using a two-wave mixing technique with a coherent laser beam of a 355-nm wavelength. A series of samples with grating thicknesses d0=10…150 micrometers, each for two different exposure times, was prepared. The recording kinetics, as well as the post-exposure properties of the gratings were monitored by diffracting a low intensity probe beam at a wavelength of 633 nm for Bragg incidence. To obtain a complete characterization, two-beam coupling experiments were conducted to clarify the type and the strength of the recorded gratings. Finally, the diffraction efficiency was measured as a function of the readout angle at different post-exposure times. We found that, depending on the parameters, different grating types (pure phase and/or mixed) are generated, and at elevated thicknesses, strong light-induced scattering develops. The measured angular dependence of the diffraction efficiency can be fitted using a five-wave coupling theory assuming an attenuation of the gratings along the thickness. For grating thicknesses larger than 85 microns, light-induced scattering becomes increasingly important. The latter is an obstacle for recording thicker holograms, as it destroys the recording interference pattern with increasing sample depth. The obtained results are valuable in particular when considering PEGDMA-ionic liquid composites in the synthesis of advanced polymer composites for applications, such as biomaterials, conductive polymers and holographic storage materials.


of the Paper)
To characterize the morphology of the gratings, we used optical microscopy. Due to the large grating spacing of about 6 µm, this is the tool of choice. Below are pictures taken with a polarizing light optical microscope (Zeiss Axiophot) for gratings of various thicknesses. It can be seen that the morphology is determined by the light-induced phase-separation of the polymeric matrix and the ionic liquid component. The gratings formed are of excellent periodicity. With increasing thickness, droplet forming is more visible, in particular for d 0 ≥ 125 µm. Figure 4

of the Paper)
The temporal evolution of the relative diffraction efficiency for different thicknesses of the gratings (t p = 12 s) is non-monotonous, as discussed in the paper, and is shown in the following figure.
Note that the use of η is somewhat inappropriate for d 0 > 100 µm, as discussed in the paper.  Figure 6 of the Paper)

Angular Dependence of the Relative Diffraction Efficiency η
As an addendum to Figure 6 of the manuscript, we show the relative diffraction efficiency η s for all of the samples where this definition is appropriate, i.e., d 0 ≤ 100 µm ( Figure S3).
, η 0 are indicated by red, blue and green markers, respectively.
To give the reader an idea of the second order contribution also for d 0 ≤ 100 µm, we add logarithmic plots ( Figure S4).  Figure S5 shows the diffraction efficiency E s for all investigated thicknesses.  Figure 6).

Diffraction Regime and Klein-Cooke Parameter (Related to Section 4.5 of the Paper, Figures 6 and 9)
It has been pointed out in a series of papers by Gaylord, Magnusson and Moharam [1][2][3] that the use of the popular Klein-Cooke parameter Q is not appropriate in certain cases to discriminate between thick and thin gratings. The problem can be understood by the fact that Q is independent of the refractive-index modulation n 1 , which, of course, decisively limits the use of Q.
In their papers, Gaylord et al. identified three diffraction regimes: the Bragg regime (only two waves with considerable amplitudes propagate in the grating provided that the Bragg condition is fulfilled) [1], the Raman-Nath regime (a large number of waves propagates at the same time) [2] and the intermediate regime. For the latter, the rigorous coupled wave analysis (RCWA) has to be applied to correctly describe the diffraction properties. To discriminate between these cases, the following inequalities have to be considered [3]: Bragg regime (S1) where: and θ is the angle of incidence in the medium. In the case that one of the inequalities is obeyed, but the other is violated, the use of the RCWA is mandatory (intermediate regime). Now, let us have a look at Table 2 of the manuscript: we find that 1 < Q < 10 for all of our samples, and thus, they meet the criteria for the intermediate regime. By inspecting Figure 6, it is obvious that for d 0 = 20 µm, the diffraction is similar to what is expected for a "thin" grating, whereas this not the case for, e.g., the grating with thickness d 0 > 125 µm (similar to a "thick" grating). Figure S6 shows the diffraction regimes according to [3]. The figure is interpreted as follows: the black lines divide the parameter space (log 10 (ν), log 10 (Q )) into four regions:
• RCWA regime: this occurs if just one of the inequalities is fulfilled. It is the inconvenient case, in which the grating is neither "thick" nor "thin".  Figure S6. Discrimination between different diffraction regimes: black lines divide the parameter space (log 10 (ν), log 10 (Q )) into four regions: Raman-Nath regime, Bragg regime and RCWA regime (two-fold). The labeled symbols visualize that except for d 0 = 20 µm, the gratings are neither thin nor thick. The hatched region indicates where the Klein-Cooke criterion for thick gratings is met (Q > 10).