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

Abstract

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.