Analysis of wave modes in slab waveguide with truncated parabolic index

The exact wave equation for a lenslike dielectric medium derived from Maxwell's equations contains the term of gradient of permittivity e. The purpose of this correspondence is to clarify the effect of the \bigtriangledown \epsilon term on the propagation constants of the modes. We find that the propagation constants of the lower order modes suffer significant modification by taking the \bigtriangledown \epsilon term into account, while for the higher order modes the effects are small enough to be disregarded.