Diffraction-limited gradient-index (GRIN) microlenses with high numerical apertures produced by silver ion exchange in glass: diffusion modeling and process optimization
Cylindrical and rod gradient-index lenses with numerical apertures of 0.5 are produced by silver ion exchange in a sodium-aluminosilicate glass. Choosing the appropriate glass composition enables the generation of refractive index changes of 0.145 in the glass without coloration in the visible range. Diffraction-limited optical performance of lenses of up to 1.3 mm in thickness or diameter is achieved by ion exchange modeling which comprises the following steps: (1) The concentration-dependent diffusion coefficient of the glass is experimentally determined by the Boltzmann- Matano method, (2) Process control is provided by the measured dopant concentration/refractive index relation and the glass/salt equilibrium dependence, (3) The ion exchange process is optimized by solving the non-linear diffusion equation for two steps under different boundary conditions, (4) Diffraction-limited lenses up to numerical apertures of 0.5 are generated by applying the optimized process parameters to the ion exchange.