On the upper bound to a group index in slab dielectric waveguides

Relations are investigated between phase index N = c/vp and group index M = c/vg of a guided mode in slab dielectric waveguides, where vp and vg are the phase and group velocities of the mode, and c is the velocity of light in free space. Examination of the properties of the M vs N curve shows that there exists the upper bound to M, which is expressed in terms of the refractive indices of the film and the substrate.