The standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The resulting nonlocal diffusion equation is then solved numerically, in low-harmonic approximation, to describe grating formation. The effects of the diffusion rate, the rate of polymerization, and a new parameter, the nonlocal response length, are examined by using the predictions of the model. By applying the two-wave coupled-wave model, assuming a linear relationship between polymerized concentration and index modulation, the resulting variation of the grating diffraction efficiency is examined.
© 2000 Optical Society of America
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