Gouy phase shift

At position z the Gouy phase of a fundamental Gaussian beam is given by[1]

The Gouy phase results in an increase in the apparent wavelength near the waist (z ≈ 0).

Thus the phase velocity in that region formally exceeds the speed of light.

That paradoxical behavior must be understood as a near-field phenomenon where the departure from the phase velocity of light (as would apply exactly to a plane wave) is very small except in the case of a beam with large numerical aperture, in which case the wavefronts' curvature (see previous section) changes substantially over the distance of a single wavelength.

It is, however, of theoretical importance and takes on a greater range for higher-order Gaussian modes.