# The phase velocity of laser light

• redtree

#### redtree

What are the limitations on the phase velocity of laser light? Is it true to say that the phase velocity of laser light is limited to <c?

That's true in vacuum, where is exactly c. Phase velocity in a medium has no meaning, I think; I've seen some cases where phase velocity is greater than c.

The phase velocity is defined as v = w/k(w), where w is the frequency and k(w) is the wavenumber, similar to 1/wavelength. I've allowed the medium to be dispersive, so k = k(w). The 'group velocity' is dw/dk.

One way to picture this is that a pulsed carrier wave will have two relevant velocities- the phase velocity is the velocity of the carrier wave, while the pulse envelope moves as per the group velocity.

If a pulse moves through resonant media, strange things happen to the group velocity but not to the phase velocity- the phase velocity is simply v = c/(1+X'(w)/2), where X'(w) is the frequency-dependent real part of the susceptibility. The group velocity V =v(w)/(1-(w/v)(dv/dw)) and can become negative or exceed c0 near strong transitions.