Realization and optimization of planar refracting microlenses by Ag-Na ion-exchange techniques

We report the fabrication of planar microlenses with numerical apertures (N.A.'s) of 0.2 by field-assisted Ag-Na ion exchange in glass. To measure the N.A. of microlenses, different definitions can be used. We discuss the issue of measuring the N.A. and suggest an additional definition based on diffraction-limited performance. According to a simple model, the N.A. of a spherical lens is limited by the maximum index difference. Owing to this model, the N.A. for Ag-Na ion exchange is limited to a value of ~0.1. From measurements of microlenses, fabricated by field-assisted ion exchange, we obtained N.A.'s as high as 0.2, providing for diffraction-limited performance within the whole aperture.