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I would not use FDE to simulate the facet as it has less control. It is better to use FDTD. Please refer to this example: https://optics.ansys.com/hc/en-us/articles/360042304894-Facet-reflection-and-transmission-calculations
It is physical that as long as the mode leaves the waveguide, it spreads since there is no confinement anymore. I do not know if you have any theory to support
" it would have a size narrowing up to a distance (similar to a waist of a Gaussian beam), and then expand again."Â I did a test using FDTD and the fields spreads after leavning the waveguide. I am not sure if there is any mechanism for the narrowing. Here is my result for a ridge waveguide:
Fig. 1: farfield from the monitor immediate the facet
Fig.2: far field from the monitor 3 um away from the facet.
FIg.3 The waveguide mode profile
Fig.4 The field in the plane, where mode source is located at z=00.3um, and the facet it at 0um.
I did not use farfieldexact to project fields at specified distance. Please use  farfieldexact3d - Script command for your application