I was reading an article and came across the following paragraph:
"A thin lens of focal length f is used to collimate the light emerging from an optical fibre. The fibre has small core diameter and numerical aperture NA. It achieves a diffraction limited divergence angle θ for the collimated beam."
I am wondering how can there be a "diffraction limited divergence angle θ"? If the lens is placed at exactly focal length f away from the end of the optical fibre, shouldn't all the light be properly collimated with θ=0?
Best Answer
Divergence $\theta=0$ is not possible -- from a quantum mechanical perspective, it would violate the Heisenberg uncertainty principle for position and momentum of a photon. "Collimated" is not really a technical term; it is a qualitative description of a beam with a relatively small divergence angle.
The fact that the divergence is diffraction-limited means that the lens does not cause aberrations, so that the product of the beam width and beam divergence is as small as possible. This can be true regardless of how big the beam divergence is, and instead has to do with the beam quality. A diffraction-limited beam (e.g., a Gaussian) is one for which this product is equal to the smallest value allowed by the uncertainty principle.