  This letter is devoted to point out a specific character of the
Finite-Difference-Time-Domain method through the study of nano-structures
supporting geometrical symmetry-protected modes that can not be excited at
certain conditions of illumination. The spatial discretization performed in the
FDTD algorithm naturally leads to break this symmetry and allows the excitation
of these modes. The quality factor of the corresponding resonances are then
directly linked to the degree of the symmetry breaking i.e. the spatial grid
dimension even though the convergence criteria of the FDTD are fulfilled. This
finding shows that the FDTD must be handled with a great care and, more
importantly, that very huge quality-factor resonances could be achieved at the
cost of nanometer-scale mastered fabrication processes.
