A New Analytical Profile to Characterize Planar Waveguides

Ion-exchange technique has been by far the most popular technique to produce optical waveguides in glass [1]. In order to design, fabricate, and study their properties, it is necessary to have an accurate knowledge of the refractive index profile resulting from this fabrication process. Until a few years ago, the refractive-index profile has been approximated by several functions that, generally, have not provided a satisfactory model. Some ones, for instance the Gaussian one, are only empirical functions that does not fulfil the physical boundary conditions of the process. Other ones, the Erfc and the truncated-parabolic ones, are only valid for determined values of the parameter α = 1 - r, with r the ratio between the self-diffusion coefficient of the incoming (Di) and outgoing (Do) ions. Recently, it has been presented [2,3] new more accurate models, to characterize silver (Ag+) and potassium (K+) waveguides, valid in a wide range of α. Nevertheless, these models do not describe well almost steplike profiles (α → 1) because the approximations used in their derivation are not adequate.