A new method ot botain GRIN-lenses through numerical modeling

摘要

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 ZrO_2 nanoparticle surface force the particles to diffuse in the gel state in the presence of an electric field employed by appropriate elelctrodes. In a previous study it has been shown that ther esists 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 elecgrodes through numerical modeling. The underlying time dependent parabolic partial differential equation is solved numberically 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 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 disussed.