In FDE, if the materials have no loss and PML is used, the imaginary part of neff is from the PML;
In varFDTD or FDTD simulation, the PML BCs do not contribute to the loss (except the mode source which has its own PML BCs). However, due to discrete errors, the mode can leak some power during propagation, which contributes the loss if you use transmission monitors.
So if your purpose is to know the mode loss in an infinitely long waveguide, FDE gives you ideal result (of course it has some numerical errors, but should be small). You do not need to use FDTD .
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