Impact of initiation species on index distribution in diffusion photopolymers

Models of the index response of diffusion photopolymers typically assume that polymerization is proportional to optical intensity. However, common radical initiators self-terminate. This reduces the polymerization rate and has been shown in steady state to result in polymerization that is proportional to the square root of intensity. We examine the impact of sublinear polymerization rate on the spatial distribution of index in volume photopolymers. In contrast to previous work based on spatial frequency harmonics, we consider a Gaussian focus and examine the index in the spatial domain. This can thus be thought of as the impulse response of the material which, due to the nonlinear response, is not the Fourier transform of the previous studies. We show that sublinear polymerization rate dramatically impacts the spatial confinement of the index response. A case of particular interest to applications such as shift-multiplexed holography is a Gaussian beam translated orthogonal to its axis. In this geometry, a square-root material response yields an index profile of infinite axial dimension. We verify this prediction experimentally. The axial confinement of cationic (linear) photopolymer is shown to be significantly smaller than a radical (sublinear) photopolymer under the same writing conditions, confirming the prediction.