Its good to have some numbers to compare simulations with theoretical values. Maybe this paper has more detailed information and we can try to replicate their results.
The FDTD runs in time domain. This means that if you want to have a single frequency source, you need an infinitely long time domain signal. Even if you set your signal at signal frequency, software automatically chooses a pulse which includes other frequencies. Thus this might cause dispersion that are non-desirable but choosing a material with constant index will avoid the problem.
It will be a good idea if you start with some of our getting started examples and watching webinars.
You can use a Gaussian beam with lower NA (say 0.2). Adjusting beam diameter and lens diameter from beam options-> use thin lens (say to 500 um) might be a good idea so that the injected Gaussian profile in your simulations closely matches with the one from theory. Also, do you have any idea how you want to measure the shift?
This is an interesting problem to study. Maybe we can try to replicate the results of some published papers.