Channel waveguides in glass via silver-sodium field-assisted ion exchange

Abstract

Multimode channel waveguides were formed by field-assisted diffusion of Ag+ ion from vacuum-evaporated Ag films, into a sodium aluminosilicate glass reported to yield high diffusion rates for alkali ions. Two-dimensional index profiles of channel waveguides formed by diffusion from a strip aperture were controlled by means of diffusion time, temperature, and electric field. The diffusion equation for diffusion through a strip aperture in the presence of a one-dimensional electric field was solved. Its solution was in agreement with measured concentration profiles: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{C(x,y,t)}{C_{0}} = \frac{1}{2} \{ erf (\frac{a - x}{2\sqrt{Dt}}) + erf (\frac{a + x}{2\sqrt{Dt}})\}</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.\frac{1}{2} \{ erfc (\frac{y - \muE_{y}t}{2\sqrt{Dt}}) + e^{(yE_{y}/D)} erfc (\frac{y + \muE_{y}t}{2\sqrt{Dt}})\}</tex> Diffusion coefficients in this aluminosilicate glass were determined to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D =(2.41 \times 10^{-13}) (\frac{m^{2}}{s}))</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.\exp (\frac{-3.1 \times 10^{4}\frac{J}{mol}}{RT})</tex> Diffusion coefficients were higher (between 150°C and 300°C) than those of a low-iron soda-lime silicate glass "standard" also studied, for which diffusion coefficients were <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D =(3.28 \times 10^{-13} (\frac{m^{2}}{s}))</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.\exp (\frac{-3.6 \times 10^{4}}{RT} (\frac{J}{mol}))</tex> This difference in diffusion coefficients is due to the higher activation energy of diffusion in the soda-lime silicate glass. The Gladstone-Dale relation was used to calculate the maximum possible refractive index change via Ag+-Na+ ion-exchange for each type of glass. The maximum index change in the sodium aluminosilicate glass is found to be about 65 percent of that in the soda-lime silicate glass.