Modes in diffused optical waveguides of arbitrary index profile

A method is presented for numerical calculation of the phase constants of the modes of diffused optical waveguides of arbitrary index profile. For a given bulk and surface index, the phase constants can be plotted against diffusion depth. Graphs giving the number of modes supported by a guide with a particular diffusion depth and index change can also be calculated. Examples are given for complementary error function, Gaussian, and exponential profiles, with indices representative of metal-diffused LiNbO3guides. It is also shown that, by making certain approximations, the modes of a diffused waveguide may be described by just two quantities, a normalized diffusion depth and a normalized mode index. A single universal chart of these two quantities can be made for any diffusion shape, and all diffused guides with this diffusion shape are described by this chart. Charts are given for complementary error function, Gaussian, and exponential shapes. Careful measurement of effective mode indices of Ni-diffused LiNbO3guides fit the universal chart for a complementary error-function shape. A second type of universal chart for each shape relates the number of modes to the diffusion depth and indices of refraction.