Paraxial Gaussian beam (TEM_00)

What you are seeing: the spatial intensity profile of a fundamental Gaussian laser beam as it propagates along the optical axis $z$. The beam is narrowest at its waist $w_0$ (center of the plot), then expands hyperbolically. Each transverse slice has a Gaussian intensity profile $I(r, z) \propto \exp(-2 r^2 / w(z)^2)$.

Three quantities define the beam: $$w(z) = w_0\,\sqrt{1 + (z / z_R)^2},\quad R(z) = z\,[1 + (z_R / z)^2],\quad \eta(z) = \arctan(z / z_R),$$ with Rayleigh range $z_R = \pi w_0^2 / \lambda$. The far-field divergence half-angle is $\theta = \lambda / (\pi w_0)$, the diffraction-limited bound.

The thin curves above the heatmap trace $\pm w(z)$ (1/e^2 spot radius). The yellow vertical bars mark the Rayleigh range; between them the beam stays close to its waist.