Bloch surface eigenstates within the radiation continuum

From detailed numerical calculations,we demonstrate that in simple photonic crystal structures,a discrete number of Bloch surface-localized eigenstates can exist inside the continuum of free-space modes.Coupling to the free space causes the surface modes to leak,but the forward and back-reflected leakage may interfere destructively to create a perfectly bound surface state with zero leakage.We perform analytical temporal coupled-mode theory analysis to show the generality of such phenomenon and its robustness from variations of system parameters.Periodicity,time-reversal invariance,two-fold rotational symmetry and a perfectly reflecting boundary are necessary for these unique states.