Main Question or Discussion Point
Is there any unconventional method to find out the relation between group velocity and phase velocity? know there is a method employing Fourier tarnsforms and another easier method as well
That is a very good point. The equation v_g=dk/dw comes from keeping only the first term of a Taylor expansion. Many of the papers claiming funny group velocities for light miss the point you mention.one thing to notice is that, for a group velocity to be meaningful, the wave packet has to be merely composed of wavenumber in a narrow range.