I am looking for a gradient index profile in the FDTD solver, as there exists in the FDE solver : https://kb.lumerical.com/en/pic_passive_waveguides_exponential_index_profile_slab.html.
Does such an option exist in FDTD?
Yes, you can simply copy-paste the objects from FDE into FDTD, and then use an index monitor to study the index profile of the objects. You can also add a port object, with similar geometry as FDE, to obtain identical results as you obtained for FDE simulations.
For your convenience I prepared similar geometry in FDTD (as exp-wg.lms in FDE):
exp-wg.fsp (358.3 KB)
Please let me know if you had further questions or any difficulties with FDTD simulations.