Fast numerical solution of nonlinear di usion equationfor the simulation of ion - exchanged micro - opticscomponents in glass

Modulation of the refractive index of glass using ion exchange is a common fabrication method for various micro-optics components, such as waveguide devices, microlenses, and diiractive elements. The design of elements with complicated optical functions has increased the demand for fast numerical simulation of the nonlinear ion-exchange process of two monovalent ions. In this paper, a linear implicit nite-diierence Crank-Nicholson-type method is implemented for thermal two-and three-dimensional ion-exchange processes. The resulting system of linear equations is solved by using various iterative methods. Grid spacing, length of the time step, and the number of iterations are chosen so that desired accuracy is obtained within minimum computing time. The implemented methods are compared with the Peaceman-Rachford Alternating Direction Implicit (PR{ADI) and the explicit Du Fort{Frankel method in mod-eling a computer-synthesized diiractive optical element and a waveguide channel system.