Output Intensity Profile of Multimode Fiber

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I am trying to model light that (1) exits a multimode fiber (2) passes through a cylindrical lens system and (3) enters a multimode fiber (and yes I know that a cylindrical lens system is not ideal for fiber coupling).

The radius of curvature for each of the cylindrical lenses in my system is known and fixed, so I know that on one axis the light converges and on the other the light diverges. For this reason I am thinking that the best position for the collection fiber will not be at the focus of the converging axis. Instead I suspect that the optimal location for the collection fiber will be at some point in front of the focus.

I have been trying to evaluate the intensity profile of the light as it exits the lens system. My thought is to place the fiber where the intensity is maximum. I have the transfer matrix for the lens system. If the output from a multimode fiber is Gaussian, then I know how to use the transfer function to get the E-field on the other side of the lens system. From the E-field I can get the intensity profile. The problem is that I am not sure if the output of a multimode fiber is Gaussian, and I have not been able to find whether it is or is not in any of my books or from several hours a google searching.

So, is the output of a multimode fiber Gaussian? Whether yes or no, please provide a reference if you can.

Here is why I do not think that it is.

the light exiting a fiber should obey NA = n*sin(B) (where NA = numerical aperture, n is the index of the medium outside the fiber, and B is the acceptance angle/ exit angle)

so for example with NA=0.22, n=1, B would be 12.71 degrees
this means that if the fiber core is 50 μm then the spot size 1 mm away from the fiber output should be 250 μm.

If I treat the output as Gaussian by letting the beam waist (w0) be the radius of the core then I can use wz = w0*((1+(z/zR)^2)^.5) and zR = (pi*(w0^2))/λ. Using one micron for λ at 1 mm away I get wz = 28 μm.

Obviously there is a big difference between these two models (assuming I did the math correctly). Please show me the steps if I did it wrong.

If the output from a multimode fiber is not Gaussian, then can someone tell me how to model the intensity profile (1) as the light exits the fiber, and (2) after passing though a lens system?

If someone can think of a better way to find the optimal location for the collection fiber, I would love to hear it.
 

Answers and Replies

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Claude Bile
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If I treat the output as Gaussian by letting the beam waist (w0) be the radius of the core then I can use wz = w0*((1+(z/zR)^2)^.5) and zR = (pi*(w0^2))/λ. Using one micron for λ at 1 mm away I get wz = 28 μm.
This has to be wrong because, in the case where there is not focusing optic (like the output of a fibre), the beam waist cannot possibly reduce. The diameter of the fibre output must be the minimum diameter. Note than wz is a function of z, exactly what value of z are you evaluating wz at to get a value of 28 microns?

In any case, the output of a multimode fibre is most definitely not Gaussian. Look up Optical Waveguide Theory by Snyder and Love for your reference.

Claude.
 
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This has to be wrong because, in the case where there is not focusing optic (like the output of a fibre), the beam waist cannot possibly reduce. The diameter of the fibre output must be the minimum diameter. Note than wz is a function of z, exactly what value of z are you evaluating wz at to get a value of 28 microns?

In any case, the output of a multimode fibre is most definitely not Gaussian. Look up Optical Waveguide Theory by Snyder and Love for your reference.

Claude.
In the definition that I am using the beam waist (w0) is the radius of the fiber core not the diameter, so 28 μm is an acceptable wz for z=1mm.

Any thoughts on how I can model the intensity profile as the light exits the fiber, and after passing though a lens system, or a better way to find the optimal location for the collection fiber?
 

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