Abstract

The silver concentration profile has been measured for a series of electric field and thermally driven silver, indiffused optical waveguides. Silver-ion concentration was measured as a function of depth using a scanning electron microprobe while scanning in the depth direction across a cleaved, polished silver waveguide sample. Because the excitation beam in the microprobe was 2.0 µm in diameter and had a nonuniform intensity distribution, the concentration of silicon was also measured as a function of depth. Detection of both silver and silicon was accomplished, using wavelength dispersive analysis of the L_α x-rays for silver (0.4162 nm) and K_α x-rays for silicon (0.7131 nm). Smoothing of the experimentally measured silver and silicon concentration curves was accomplished by Fourier synthesis of the experimental curves, keeping only the first forty Fourier components and filtering out the remaining higher Fourier frequencies. A discrete Fourier transform technique, incorporating Keiser-Bessel function windowing, was used to remove the S-shaped leading edge of the silver concentration profile created by excitation beam artifacts. The deviation from a perfect step function of the silicon profile was used in the deconvolution procedure. The final silver concentration profile was non-Gaussian and the deconvolut-ed silver profile fell off rapidly in the region of the Gaussian tail. For a moderately doped silver waveguide, the final profile followed a (1 – x^α)² dependence, where x is the depth measured from the waveguide surface and a ranges from 3.0 to 4.0. The final concentration profile represents a more compact refractive index profile. This finding is supported by theoretical analysis as suggested by comparing inverse WKB analyses of experimental modal indices with the eigenvalues determined from a zero-element analysis of the same silver waveguides if these guides had a perfect Gaussian index profile.

© 1989 Optical Society of America