I got it, it is beacuse of the FDTD and symmetric BCs are defiend only for the half of the structure, due to that the lower portion of the BCs is taken as same as the upper portion where the FDTD is defined.

I think, it is not possible to see the similar modes as like as the third party (Comsol multiphysics) since Lumerical is taking the structure as waveguide and the propagation is normal to the FDTD plane.But I am interested in propagation modes along the x-direction and wanted study the longitudinal modes in the x-y plane. I am not interested in the transverse plane.

Can you please clarify where is the excitation point defined exactly for my structure as per the FDE eigen mode solver ? Is it defined from the end of straight waveguide ? or Some where in the middle?