  In a coherent monoenergetic beam of non-interacting particles, the phase
velocity and the particle transport velocity are functions of position, with
the strongest variation being in the focal region. These velocities are
everywhere parallel to each other, and their product is constant in space. For
a coherent monochromatic electromagnetic beam, the energy transport velocity is
never greater than the speed of light, and can even be zero. The phase
velocities (one each for the non-zero components of the electric and magnetic
fields, in general) can be different from each other and from the energy
transport velocity, both in direction and in magnitude. The phase velocities at
a given point are independent of time, for both particle and electromagnetic
beams. The energy velocity is independent of time for the particle beam, but in
general oscillates (with angular frequency 2w) in magnitude and direction about
its mean value at a given point in the electromagnetic beam. However, there
exist electromagnetic steady beams, within which the energy flux, energy
density and energy velocity are all independent of time.
