Planar, buried, ion-exchanged glass waveguides: Diffusion characteristics

A detailed theoretical and experimental study of Ag+-Na+ exchange in soda-lime silicate glasses in a molten bath containing a mixture of NaNO3and Ag+ is presented. With no applied field, concentration profilesC(x, t)(and therefore, the index profiles for low concentrations) are given by complementary error function. The estimated value for the self-diffusion coefficientDof Ag+ is 0.133 μm²/min for low concentrations and it monotonically increases with the surface concentration C0until it saturates at about 0.3 μm²/min forC_{0} geq 10^{-3}MF. However, square root dependence of diffusion depth with time seems to be independent of the C0. Presence of an external fieldEcauses the effective depth of diffusion to increase. In fact, for largeEfields, the profile can accurately be described byC/C_{0} = frac{1}{2} erfc(x' - r)wherer = mu Et/sqrt{2Dt}where μ is the ionic mobility of Ag⁺in glass. We define a new diffusion depthWas the distance from the surface to the1/econcentration point, and for large fields,Wvaries linearly withEandt. Experimental results yielded a value of 15.55 μm²/Vmin forμ. As before, square root dependence ofWwithtand the linear variation ofWversus C0forC_{0} leq 10^{-3}MF, withWsaturating forC_{0} > 10^{-3}MF, were observed in the case of field assisted diffusion. A two-step process, where a surface waveguide formed in the first step with eitherEequal to zero or some finite value, is modified by performing a second diffusion in pure sodium nitrate to produce a buried, symmetrical fiber-like profile. This process is also studied in detail.