Refractive properties of planar gradient microlenses

The paper presents theoretical possibilities for producing planar gradient microlenses in soda-lime glass using the Ag⁺↔Na⁺ ion exchange method. The modelling of ion exchange processes (pre-diffusion, heating) was used to calculate two-dimensional refractive profiles. A mathematical model of ion exchange was used, considering the dependence of the diffusion coefficients of exchanged ions on their normalised concentrations. Simulations of changes in refraction in glass are based on experimental results. An algorithm based on Snell’s law is used to calculate ray trajectories, determining the refractive properties of microlenses. The proposed algorithm allows determining ray trajectories with arbitrarily small steps in the gradient region of the glass. The refractive properties of the modelled gradient microlenses were analysed for meridional beams. The numerical modelling shows the influence of controlled grinding of the glass surface on the focusing properties of the microlenses. This allows for very good correction of the spherical aberration in manufactured microlenses.