Hi All,
This is my first post and I greatly appreciate your time.

Here is the problem statement:

I have a waveguide where the light is diverging in the x and y directions with different beam divergences. I would like to capture this light using a optical fiber with a lens (Lensed fiber), which is basically a normal optical fiber with a lens created at the tip. I would like to know how to calculate the radius of curvature of the lens.

To make the problem more simple. We can assume uniform divergence i.e., divergence same in the x and y directions. Knowing the beam divergence of the laser we can compute the Numerical aperture of the laser (NA), and may be pick the lens with larger NA, however how to arrive at the radius of curvature still remains a question. Your feedback is appreciated, and feel free to ask me questions if you need any clarification or details.
Thanks,
Ram