I have seen several qeustions about this and would like to share some of my thoughts.:)

It is common users ask which method they should use for their system or if the results are different, which one should they trust. To answer this question, let's first talk about the difference between the two methods.

When we calculate coupling efficiency, no matter with which method, what we do is the normalized overlap integral (more details in Help) between the beam amplitude, W(x,y), and fiber receiving mode, Fr(x,y). The overlap integral is like you compare the two complex-valued amplitude distribution. If they are same, the integrated value is 1. If they are not same, the result will be less then 1. For a single-mode fiber, it's a cylinder waveguide and the Fr(x,y) can be approximated by a Gaussian beam mode.

Now we can say, the main difference between POP and Single Mode Coupling is about mainly how we calculate the beam amplitude W(x,y). For POP, this is naturally the beam profile AFTER the image plane. Note the POP result is always shown as after refraction of the specified surface. On the other hand, the Single Mode Coupling basically uses the Huygens PSF when we check the "Use Huygens Integral". Note we assume users use Huygens in this discussion because it's more accurate than FFT PSF in most of cases. Therefore, to ask the difference of coupling efficiency calculated by POP and Single Mode Fiber methods is fundamentally same as to ask the difference of spot profile predicted by POP and Huygens PSF.

It is important we should not be surprised the calculated result is different between the two methods becuase they are based on different algorithms. It is possible the result is very different when the condition is far from assumptions of one method.

Both methods have their assumptions and limitations. Huygens PSF calculates the beam amplitude by tracing rays through the system and only considers the diffraction at final step. In contrast, POP propagate beams fully considering diffraction from the start to the end. Therefore, in most of cases, we would say POP is more trustable. Note that, however, POP needs more cares to make sure the result is correct. A surface by surface system check is always required.

However, POP has some algorithm assumptions, where the details can be found in Help file. When the system doesn't well meet the assumptions, it's suggested to switch to use Huygens. A typical case is when you have a laser source where divergence is faster than F/1. In that case, it's common we need to switch to use Huygens PSF. Practically, side-emitting type of laser diode usually has a large divergence and it's suggested to use Huygens PSF. And for VCSEL, it's possible the divergence angle is not too large and thus POP is adequate. When POP is adequate, it's should always be a better choice.