where is the speed of light "in the medium", and could either refer to the electric or magnetic field vector, as any specific solution for either determines the other. The Gaussian beam solution is valid only in the paraxial approximation, that is, where wave propagation is limited to directions within a small angle of an axis. Without loss of generality let us take that direction to be the direction in which case the solution can generally be written in terms of which has no time dependence and varies relatively smoothly in space, with the main variation spatially corresponding to the wavenumber in the direction: