The paraxial Gaussian beam calculation is the simplest of the analytic tools we will use to characterize the fiber coupler. Its use is recommended to get a "feel" for the performance of the system.

The mode field diameter of the fiber at 1.31 µ is 9.2 ± 0.4 µm according the the Corning datasheet. Therefore, we set up the paraxial Gaussian beam calculation (Analysis > Physical Optics > Paraxial Gaussian Beam) as follows:

The beam waist is always positioned relative to surface 1, which in this case is positioned at the same place as the object surface. Therefore, a Gaussian waist of 4.6 µ is positioned at the source fiber location. It then propagates through the optical system:

It can be seen from this that the 1/e² beam size is 65µ at surface 3 and  70µ at surface 4. The physical semi-diameter of these surfaces is 120µ. This means that energy outside approximately two beam-widths will be truncated. Note also that the beam is not in best focus on the image surface: it has a size of 5.3 µ whereas it should be 4.6 µ on the assumption of symmetry. We will optimize the thickness of surface 1 (which also controls the thickness of surface 5 via a pick-up solve) to improve this. Note that the thickness of surface 5 is on a pick-up solve because the system should give the same coupling when used either way round: we are using identical fibers and identical lenses (within manufacturing tolerances) and so we expect the best system to be symmetric.

ZEMAX has an optimization operand GBPS, Gaussian Beam Paraxial Size, which can be used to optimize the fiber/coupler lens distance. Because we know the system will work best if symmetric, we know that the desired Gaussian Beam Size is 4.6 µ, and so the merit function is a simple one-liner:

Optimizing the fiber/lens distance gives a value of  0.117 mm for the fiber/lens distance, and the following Gaussian beam data:

This as as much as a simple paraxial Gaussian analysis can tell us. The file at this point is saved as after Gaussian optimization.zmx.