A perturbation analysis of modes in diffused optical waveguides with Gaussian index profile

Inclusion of a quartic term with adjustable coefficient in the Taylor expansion approximation to gaussian index profiles of diffused optical waveguides is shown to provide an improved approximation to the true gaussian curve to beyond the e-folding depth. A first-order perturbation to the square-law “harmonic oscillator” solutions is applied to improve the calculations of mode indexes and to illustrate the manner in which the corrected wave functions are extended deeper into the substrate.