Revealing photonic symmetry-protected modes by the finite-difference-time-domain method

This Letter is devoted to pointing out a specific feature of the finite-difference-time-domain (FDTD) method through the study of nano-structures supporting geometrical symmetry-protected modes that cannot be excited at certain conditions of illumination. The spatial discretization performed in the FDTD algorithm naturally leads to breaking this symmetry and allows the excitation of these modes. The quality factors of the corresponding resonances are then directly linked to the degree of 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 great care and, more importantly, that very huge quality-factor resonances can be achieved at the cost of nanometer-scale mastered fabrication processes.