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

Abstract

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.

Recent advances in photorefractive and photoactive polymers for holographic applications

“…A new model considering the influence of a Poynting vector on a photoisomerization process was proposed to explain the asymmetric two‐beam coupling gain in a sol–gel matrix doped with Disperse Red 1 in the absence of an external electric field . Based on the coupled wave theory for thick hologram gratings proposed by Kogelnik, Kawabe et al reported a possible mechanism for asymmetric energy transfer without charge redistribution in the matrix . They proposed that beam intensity variations, such as asymmetric energy transfer in a PR medium, could be reproduced if the phase difference between the refractive index (phase) modulation ϕ P and the absorption (amplitude) modulation ϕ A was 90° …”

Molecular design of photorefractive polymers

“…A new model considering the influence of a Poynting vector on a photoisomerization process was proposed to explain the asymmetric two-beam-coupling gain in the sol-gel matrix doped with DR1 in the absence of an external electric field. 113 On the basis of the coupled wave theory for thick hologram gratings proposed by Kogelnik, 36 Kawabe et al 118,119 reported a possible mechanism for this asymmetric energy transfer without charge redistribution in the matrix. They proposed that beam intensity variations, such as asymmetric energy transfer in a PR medium, could be reproduced if a phase difference between the refractive index (phase) modulation φ p and the absorption (amplitude) modulation φ A was 90 degrees.…”

“…They proposed that beam intensity variations, such as asymmetric energy transfer in a PR medium, could be reproduced if a phase difference between the refractive index (phase) modulation φ p and the absorption (amplitude) modulation φ A was 90 degrees. 119 OPTICAL APPLICATIONS Updatable holographic displays Updatable holographic displays are one of the most attractive applications of PR polymer composites. Holograms, which display full-parallax 3D images, were discovered by Gabor 120 in 1948.…”

Optically Inscribed Grating in Azo-Carbazole Dye: Concentration Dependence

“…Intensities of transmitted light beams were sinusoidally modulated due to the interference of diffracted and transmitted parts from two injected beams. Employing Kogelnik's theory for thick gratings characterized by sinusoidal function, relationship among the beam intensity and refractive index change can be formulated as the following expressions under the assumption that diffraction efficiency is much less than unity [6,9,10]. In the derivation, we assumed the equivalent intensity for both incident beams, and intensity was normalized by the incident intensity.…”