Theory of 2-D ion exchange in glass: optimization of microlens arrays

The equations of two-component electric field assisted ionic diffusion and exchange are formulated analyticallyand solved numerically for the problem of 2-D (cylindrical) microlenses in glass, both for individual, isolated microlenses and arrays of microlenses. The theoretical formulation represents a proposed extension of the 1-D (planar) formulation of Abou el leil and Cooper. Ray tracing through computed index of refraction distributions is used to estimate optical performance. The inclusion of interactions of neighboring microlenses is shown to be important for optimizing optical performance of a high fill factor array.