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Thanks for the detailed description! There are two changes I suggest.
Firstly, I would use the Spatial CW Laser. You can set the output of the transmitter to single mode operation, in fact I believe it is set by default. I think this would be a closer match to the lab experiment. It has all of the details that come with the CW Laser Source with the added benefit of supporting spatial modes.
You should also switch the Linear Multimode Fiber for the Measured-Index Multimode Fiber. The linear multimode fiber does not have an effect on the spatial profile. It is more concerned with applying modal delay, modal dispersion etc., but then again it is much faster for simulating! In the Measured-Index model you can quickly define a simple multimode fiber by core radius, cladding thickness and their refractive indices. As the name suggests, you can also import a refractive index profile for more complicated fiber designs.
Let me know if this helps!