A laser beam can be described by a Gaussian Beam. I studied it from here:
Its derivation is a bit brutal, but it includes the main results: between them there are the section of the beam (perpendicular to the propagation direction), the beam profile and the wavefront, which (if I understood) is what you are looking for, since the wave vector is always perpendicular to the wavefront.
A gaussian beam looks like this:
( I took this image from google images, it shows the profile of a gaussian beam propagating along $z$, that exhibits cylindrincal symmetry around that axis. The vertical axis is the radius of the beam, in particular the radius within which $\sim 90$% (usually) of the total power is contained)
You can see that the beam widens as $z$ grows. After a certain distance, called Rayleigh length, it starts to enlarge like a cone (the profile of the beam is described by an hyperbole). The position of the point $z_0$ where the width of the beam ($w_0$) is minimum is called waist: $w_0$ determines how fast the width of the beam will grow with $z$ (smaller $w_0$ means faster growth). The section of the beam is a gaussian, so most of the power is concentrated in the centre, while it decreases fast as the radius increases.
Finally, you can see that the wavefront is plane in $z_0$, but becomes spherical as the beam propagates along $z$: a funtion $R(z)$ describes the curvature of the wavefront.