Analysis of planar optical waveguides using scattering data

Gradient-index planar optical waveguides with exponential and sech2x refractive-index profiles are analyzed. By using a scattering framework, reflection and transmission coefficients for the infinite exponential profile are derived, and these scattering data are analyzed to obtain mode propagation constants and describe the effects of varying the height of the refractive-index profile. The theory is then developed to account for truncations of refractive-index profiles, the effects of a finite core width on the propagation constants for sech2x potentials are illustrated, the behavior of the bound modes in response to variations in the width of the waveguide core is described, and the appearance of leaky modes for the truncated structure is discussed.