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

Abstract

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.

Determination of diffusion activation energy from self-similarity of concentration profiles in glasses

“…When studying diffusion processes in optical materials, profile of normalized refractive index increment dN = DN/DN max is often considered instead of normalized concentration profile C/C max in assumption of proportionality of these profiles (see examples in [9][10][11]). If refractive index (RI) increases due to diffusion, it is convenient to use a waveguide effect for determination of RI profiles in thin layers (less than 100 lm).…”

Aluminum-boro-silicate glasses for ion exchange: Characterization and influence of diffusion non-linearity

“…Here we used erf-function for the direction of abscissa to coincide with the direction of diffusion. 2 Applying this generalised depth coordinate enables one to compare the deviations of various index profiles from the profiles corresponding to the linear diffusion in the same scale, and this technique allows using the same coordinates and scale for all variety of index profiles. Information concerning maximal index variation and diffusion depth, i.e.…”

“…D = D(C). This strongly influences the shape of concentration profiles C(x, t), or, the same, index variation profiles Dn(x, t), for in most cases the relation between Dn and C is linear [1,2]. The D(C) function of a glass for producing given GRIN structures should allow the formation of a particular Dn(x) profile in one-stage ion exchange processing [3], i.e.…”

Refractive microoptics

“…5 Oikawa et al (1984) [53] The characteristics of the ion-exchange process in various material systems is strongly influenced by the application of an electric field across the substrate-melt interface. The Efield E supports an ion current J el additional to the one which stems from the concentration gradient [54,55].…”