Guilin Sun
For the 1st question, if your simulation is linear optics, eg, the material property does not change with optical intensity, it absolutely does not need to use special source spectrum. This is because the frequency-domain results are normalized with source spectrum: Understanding frequency domain CW normalization
In case you need absolute power after simulation, you can simply multiply the real source intensity/power to the normalized results. Examples are for solar and detector simulations.
FDTD directly solve Maxwell Equations. Therefore it is coherent. You may need to some post processing for the results required with "partial coherence" if you know the physics. For example, although FDTD uses coherent source, you can get incoherent results by average the intensity/power quantities with 2 or 3 polarized coherent results:
https://optics.ansys.com/hc/en-us/articles/1500006149562-Polarization-incoherenceÂ
https://optics.ansys.com/hc/en-us/articles/360034902293-Understanding-coherence-in-FDTD-simulationsÂ
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