I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of glass, for instance, should be IMO described by group velocity, at least in ordinary materials like water or glass (I know that sometimes even group velocity could be greater than light velocity in vacuum). Is usage of the phase velocity correct?
Phase velocity is the correct quantity, because Fermat's principle arises due to destructive interference between paths which are not extremal. The "principle of least time" is more accurately a "principle of extremal phase". However, if dispersion can be neglected then phase and group velocity are equal so they are somewhat interchangeable.