Phase-shifted gratings in azo-doped polymers and their analysis by coupled-wave theory

Grating inscription in azo-dye doped polymers is an interesting phenomenon because of its high diffraction performance and applicability to real-time 3D displays. Although some of these materials were investigated under no external electric field with symmetric optical alignments in preceding studies, they often showed a phase shift of periodic modulation of refractive index from the interference fringe formed by irradiation beams, resulting in asymmetric energy exchange between two coupled beams. The mechanism of the behavior has been usually attributed to the molecular motions triggered by trans-cis isomerization, but their details are still unknown. Therefore, studies on temporal evolution of the process and their translation into physical meaning are necessary. In order to investigate the evolution of grating inscription and phase shift, several methods have been developed. In this study, we analyzed the coupled wave equations proposed by Kogelnik, and derived general solution applicable to the system with both phase and amplitude gratings with arbitrary phase relationship. We showed that the analysis based on the equation can give a direct evidence of the phase shift between the phase and amplitude gratings if it exists. This method was applied to the fringe pattern inscribed in thick films of PMMA doped with an azo-carbazole dye, showing that observed signals indicated the phase deviation between two types of gratings.

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