Dear Muhammad Dawood Jawad , Andersen et al.- the authors of the paper you cited- used Comsol Multiphysics 5.1 for their simulation, but results should be equal with Lumerical if the same structure, light beam and the rest of boundary conditions are also the same they used.
They used a 2D slice of the bull-eye structure, that simplifies the calculations and can be used as a good approximation (at least for this 2D slice) about the field distribution. The slice is a transversal cut of the bull-eye through the diameter.
A detailed description of the numerical model used by the authors is provided by them in the article´s supporting information, probably you have already checked it, but if not, here is the link:
Article Hybrid Plasmonic Bullseye Antennas for Efficient Photon Collection
By implementing these parameters into your Lumerical model you should be able to replicate their results.
Hope it helps. Good luck with your simulation and research work.
However the mesh setting needs to be mantained properly for 3D FDTD with trade off between computation resource utilization and accuracy. U can try 2.5D FDTD as the device structure can be quite overwhelmimg to mesh