"If I use symmetry BCs, I will not see the even and odd modes in a sequential manner as I need two modes together with two different sources placed some distance apart, any comments on this ? "
I do not see the importance of the sequential manner. The important thing is to find them. For example, you can first find the even mode, and then odd mode, and then no-symmetry mode. Not sure what "two different sources placed some distance apart," means. Do you mean the dipole source? You are using FDE for mode analysis. There is no source for FDE.
"How to use symmetrical and anti-symmmetrical in total 4 sets ? please suggest."
You are simulating 2D cross section, let's say in xy plane. both xmin and ymin can be set "symmetrical" and "anti-Symmetrical". Therefore there are 4 combinations. Hopefully the desired mode has such symmetry property. If not, you will need to use full simulation region, which is slow. Symmetry BCs can significantly save simulation time and memory. Please try.
Please refer this article for more information:https://optics.ansys.com/hc/en-us/articles/360034382694-Symmetric-and-anti-symmetric-BCs-in-FDTD-and-MODE
For larger bending redius, please try "FEEM", as it is a finite element method which can use coarser mesh in the central region where there is almost no fields.
Discrete algorithm needs time and memory to conclude the result. If it is a simple disk, you may find some analytical solutions from published papers.
How to use symmetrical and anti-symmmetrical in total 4 sets ? please suggest.