I need to collimate a gaussian laser beam out of a single mode fiber (NA0.15) with a single lens so that the full-width half maximum (FWHM) of collimated beam is 3mm.

This question may sound naive, and I understand that when lens is set at it focal length from the fiber, the diameter of the beam is easy to calculate: diameter = 2*FL/((sqrt(1-NA^2))/NA). So for instance with FL=20mm lens, the diameter will be 4.551mm.

But the term "diameter" is this case seems to me a bit vague and to be honest I can't figure out how much is the FWHM if the "diameter" is said to be 4.551mm. I could try, measure and live with that, but I am sure there should be a simple relation to calculate the diameter at FWHM (or at 1/e2) asssuming that the beam is perfectly gaussian, and knowing the NA of the fiber and the FL of the lens.

Correct me if I'm wrong, but in these calculations, the intensity doesn't play a role, because the signal comes from a single mode fiber.

Can you please suggest a solution for this question?

Thanks!

Karl