FDE solves eigen values of the Maxwell Equations. There is no known relationship bettwen the loss (or neff) and the mesh size. If the material has no loss, then the loss is from the PML, which is very lossy. Therefore increasing simulation region can reduce the effect of PML. However, the eigen values are solved with beta square where beta is the propagation wave vector. When the loss is small, neff=beta/k0 where k0 is the wavelenumber in vacuum, the imaginary part of neff is very small. FDE uses single precision digit which can be accurate at most the 6th digits. Due to discritization it is easy to have numerical errors in the 5th digits. So as long as it is accurate in the 5th digit, it is ok. Further improvements may be done with careful settings of the simulation size, PML, and mesh size.