Abstract

We present a systematic study of modeling of the diffusion profile of single-mode channels and tapers. The model involves solution of the 2-D nonlinear diffusion equation and of the 2-D Helmholtz equation by the finite difference method. The calculated diffusion coefficients and the estimated index change were in agreement with the measured values. We utilize these parameters for the 2-D modeling of straight channel waveguides of different widths. The modeling is applicable to any binary ion-exchanged glass waveguide and we have ensured its accuracy for waveguides fabricated by the Ag⁺ – Na⁺ in BK7 glass. The taper fabrication process involves the exchange through straight channel mask openings in the first step and postbaking the channels for a specific period of time under a thermal gradient in the second step. The gradient causes the maximum refractive index change at the surface to decrease and the size of the waveguides to increase along the taper in the longitudinal direction. The taper is sectioned so that each section can be analyzed as a 2-D channel waveguide with its own, distinct waveguide parameters. The calculated index profile and the mode sizes along the taper length agree very well with the measured values for the cases of straight channel and tapered waveguides.

© 1989 Optical Society of America