I am trying to get output of laser beam from a FOC laser beam with diameter ranging from 100 microns to 1000 microns. The FOC diameter is 200 micron and NA is 0.22. What kind of lens or combination of lenses is possible to do this kind of focussing and how much should be the focal size of the lens. Any additional info is also welcome. Thanks
You can get a first-order estimate of the beam diameter using the formula BD = 2.f.NA where the BD is the desired beam diameter, f is the focal length of the lens and NA is the NA of your fiber. I suggest collimating the beam first using an off-the-shelf collimator (a molded asphere) from LIghtpath http://www.lightpath.com/product/collimator/ or Thorlabs etc. The multi-mode nature of the 200 um .22 NA fiber will not give you perfect collimation or a totally predictable beam diameter but if you use a large diameter collimator you may be able to manage the residual divergence. Once you have a collimated beam - say 15 - 20 mm diameter, you can use a simple 1" lens to get the waist size you want using the formula waist = [(M2).4.f.lambda]/(Pi.BD) where the M2 is the M-squared value - the number of times diffraction limited your beam quality is coming out of the fiber, f is the focal length of the focusing lens, lambda is the wavelength, Pi = 3.14159 etc, BD is the beam diameter at the focusing lens. Note that you cannot increase the brightness - so when you focus down to 100 um you will have an NA of at least .44. If you are trying to make a collimated beam of 100 - 1000 um then you will need a telescope after the collimator but again the multi-mode nature of the FOC fiber will make small diameters hard to get to with reasonable Rayleigh ranges.
Are you saying that you would like the imaged spot to be continuously variable between 100um to 1000um? That is going to be tough. I believe that would require a custom designed zoom lens system that is probably beyond your scope. However, you can easily swap lenses to make several discrete choices in your range.
Here is a lens which is designed for the 2 X demagnification you want (100 um spot) https://www.thorlabs.com/thorproduct.cfm?partnumber=C440TMD-B
Turn it around to get 2 X magnification (400 um spot) (Check the coating. You didn't mention your wavelength.)
For other sizes start by collimating the beam with one of these:
https://www.thorlabs.com/thorproduct.cfm?partnumber=C171TMD-B
Then add a second lens to make the desired magnification.
To make a 200 um spot, buy another C171TMD-B. For bigger spots the image NA becomes small enough that you can use plano-convex spherical lenses. The effective focal length of the C171TMD-B is 6.2 mm, so the magnification you get with a plano-convex lens will be the ratio of its focal length compared to 6.2 mm. For example, https://www.thorlabs.com/thorproduct.cfm?partnumber=LA1074-B-ML has a 20 mm focal length and so will produce a (20/6.2) * 200 = 650 um spot size. (Note: the plano side should be away from the first lens)
As John explained, it is not possible from a 200µm/25° light source to get a collimated beam from 100µm to 1000µm. The beam parameter product of your source (diameter×divergence) is a constant. You can then expect 100µm/50° or 1000µm/5° spots. Now if you want spots ranging continuously from 100µm to 1000µm, I would look first for a 10× zoom lens (5-50mm for instance). I would then collimate the output of my fiber with a FOC with twice the shortest focal length of my objective (here 10mm). The collimated beam passing through the zoom will give you at the image plane spot sizes ranging from 100µm to 1000µm . However, the equivalent aperture of your source is F/2.2. It means that the aperture of your zoom have to be greater than F/1.1 for your 100µm spot if you do not want to lost energy and it will be hard for 10× zoom lens. If you can deal with a 30% loss at 100µm, it should work. Good luck.
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