Single- and Multi-mode fibre
Your fibre might be multimode because you are operating below the cutoff wavelength. So-called "Panda" PM fibres from OZ optics are specified with the following operating ranges:
- 4 micron: 630-820nm
- 5 micron: 810-980nm
- 6 micron: 980-1300nm
It would seem that 4 micron would be appropriate for 767 and 780nm light. The only caviat is that the cutoff wavelength could be lower for most fibres produced, and that they spec it conservatively. And larger core does give lower insertion loss and lower attenuation: 0.5dB for 5 micron and 0.9dB for 4 micron. But there's no substitute for checking in the lab.
Another reason your fibre might be multimode is that you've stressed it unduly along its length. A sharp bend or tight clamp can mix the polarization modes. Be gentle!