Single mode fiber coupling

1. Mar 13, 2015

eahaidar

Hello
What
kind of lens (focal length and numerical apper.) i should choose to couple light ( wave length 1565nm, beam diameter 2mm, M-square>1) to a single mode fiber (core diameter 8 microns, mode field diameter 10 microns and NA=0.14)?
Any thoughts
Thank you

2. Mar 18, 2015

Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Mar 18, 2015

eahaidar

Thank you
Actually I have a friend who helped me out and the solution is as follows

Hei Man!

no worries, I was asleep when you wrote yesterday I guess... Anyways, it should be very simple. The only formula to consider should be:

2w = (4/pi) * (Lambda*F)/D

where:

w = radius of the point spread function (focused spot) under the gaussian approximation
Lambda = wavelength in air (n=1)
F = Lens' focal length
D = Diameter of the beam hitting the lens.

In order to couple into a SMF what matters is the mode field diameter, in this case 10 microns. This is because you want the width of the main lobe of the PSF (namely 2w) to match the mode filed diameter as much as possible in order to maximise the coupling efficiency. Since D, Lambda and 2w=MFD are given, you can easily calculate F:

F (mm) = 2w*pi*D/(Lambda*4)

If the lens is bigger than the incoming beam, you will see that the numerical apertures (focused beam and SMF) will match automatically. In fact, you can get to the equations for the NA from the previous by substitution. Just remember that makes no much sense to speak of NA for a lens if you do not specify the diameter of the beam that hits the lens. Or better, it does make sense but only if the incoming beam has the same diameter of the lens. Narrower beams will in general give rise to smaller NAs.

If you follow that eq, theoretically you'll be coupling 100%. In practice, you might want to buy a lens with a suitable antireflection coating so that you minimise the energy scattered back, and I would also make sure that the fiber is nice and clean and cut properly.
Hopefully it makes sense to me it made sense and got 60% efficiency