Phase, group velocity and energy

[CrusaderSean]

I'm studying EM waves right now and I don't understand phase and group velocity very well. I know the definitions of phase and group velocity from here and what they look like from http://www.csupomona.edu/~ajm/materials/animations/packets.html .
What I don't understand is why phase velocity does not carry information/energy where as group velocity does. phase velocity can exceed speed of light c because of this. To me, it doesn't make much sense what it means for phase velocity to exceed c. I look at it as k (wave number) approaching 0 so wavelength goes to infinity... But shouldn't poynting's theorem still apply for such a wave? namely a wave with phase velocity > c still carries energy. I think I'm confusing several issues here.

 

[Doc Al]

You might find this discussion helpful: http://www.mathpages.com/home/kmath210/kmath210.htm

 

[Claude Bile]

Essentially, the energy of a wave is dependant on the amplitude, which is why the envelope of the wave is associated with the energy of the wave rather than the rapid oscillatory component.

The group velocity thus features in equations for power flow and energy and so forth because the group velocity describes the propagation of the envelope.

Claude.