# Wave optics, intensity distribution

Do Gaussian beams have a gaussian intensity distribution? If so, why?

Does the intensity distribution depend on the profile of the light beam?

Do Gaussian beams have a gaussian intensity distribution?

Yes, in the transverse direction. The full functional form is given in Wikipedia.

If so, why?

By definition. If they didn't have a gaussian intensity distribution, we wouldn't call them gaussian.

The more interesting fact is that there exist solutions to the wave equation (in the paraxial approximation) with a gaussian profile in the first place. This is not guaranteed a priori, though asking "why?" isn't a particularly answerable question. It's partly due to the fact that the wave equation in the paraxial approximation is a relatively simple differential equation, which limits its solutions to a relatively limited class of functions. But from a certain point it just boils down to "because that is one solution to the equation".

Does the intensity distribution depend on the profile of the light beam?

The intensity distribution is the profile of the light beam. This question makes no sense.

• Intensity is the square (or magnitude) of the E field and the beam profile was derived with this equation in mind as well as other relationships. – PhysicsDave Oct 5 '18 at 13:05
• I think you can refer to either the intensity distribution or the complex E-field distribution as the "profile"? It's not well defined – ptomato Oct 6 '18 at 20:27