19 June 2000 New method to obtain GRIN-lenses through numerical modeling
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Abstract
A new technique to produce a radial gradient in the refractive index in organic-inorganic nanocomposite materials using sol- gel techniques in combination with electrophoretically induced concentration profiles of oxide nanoparticles is presented. Electric charges of the ZrO2 nanoparticle surface force the particles to diffuse in the gel state in the presence of an electric field employed by appropriate electrodes. In a previous study is has been shown that there exists a linear relation between the refractive index and the concentration of the oxide particles. In this paper the emphasis is focused to the development of appropriate electrodes through numerical modeling. The underlying time dependent parabolic partial differential equation is solved numerically using implicit methods. For the electric potential, a parametric model is assumed from which the spatial dependent electric field follows by gradient expansion. The parameters of the model are optimized using an iterative modified Levenberg-Marquardt algorithm to match with the prescribed refractive index. The results of this new approach are discussed.
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Harald Wern, Harald Wern, Clemens Funk, Clemens Funk, "New method to obtain GRIN-lenses through numerical modeling", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); doi: 10.1117/12.388801; https://doi.org/10.1117/12.388801
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