About simulation mesh

Is it OK to add two simulation meshes with different mesh sizes near to each other? I need to see higher resolution at some layers of my structure and I add finer mesh on these layers.

It should be fine to use different mesh settings in neighboring regions in FDTD. The solver automatically prevents the mesh from changing its size drastically between two neighboring grids and allows the size to change gradually over a few grid points. This prevents the amount of numerical error that might arise from having two very different grid sizes close to each other.