Confused about intensity of a laser beam

Question

For normal natural light coming from the sun, the electromagnetic waves emanate from the sun with a spherical wavefront, then we can calculate the intensity of these waves reaching us on Earth by $ I = \frac {P}{4 \pi r^2}$

We used the surface area $ 4 \pi r^2$ because we know the wavefront is spherical, but in the case of lasers, how do we approach this using the idea of wavefronts?

I know it's easy to imagine that a laser beam with a negligible divergence has a specific diameter and we can calculate the intensity by dividing by $ \pi r^2$ because the beam has a circular cross section, but how are we sure that's right? I searched for the type of the laser wavefront and I found that it is called the Gaussian wavefront, is it responsible for this kind of intensity and is it even relevant to what I'm talking about or am I just overthinking?

Answer 1

We often make the approximation that a laser beam is in the so-called "fundamental Gaussian mode" where the intensity of the laser beam falls off exponentially as we move away from the beam axis in the transverse plane. [1]

The Gaussian beam is the lowest-order solution of the Helmholtz equation in the paraxial approximation. [2]

This is only a simplified picture however: the Gaussian beam does not describe every possible beam, only a subset. Any full solution can be described by the complete Hermite-Gaussian or Laguerre-Gaussian modes. [3]

In general, the intensity is dependent on position in the beam, so it will be a function of position rather than just a number as in your example. Then we integrate it over some area to get the beam power passing through that area.

[1] https://en.wikipedia.org/wiki/Gaussian_beam

[2] https://en.wikipedia.org/wiki/Helmholtz_equation#Paraxial_approximation

[3] https://en.wikipedia.org/wiki/Gaussian_beam#Hermite-Gaussian_modes