  We prove the possibility of achieving unidirectional edge modes in
time-modulated supercell structures. Such finite structures consist of two
trimers repeated periodically. Because of their symmetry, they admit degenerate
edge eigenspaces. When the trimers are time-modulated with two opposite
orientations, the degenerate eigenspace splits into two one-dimensional
eigenspaces described by an analytical formula, each corresponds to a mode
which is localized at one edge of the structure. Our results on the
localization and stability of these edge modes with respect to fluctuations in
the time-modulation amplitude are illustrated by several numerical simulations.

Analysis of PDEs;Applied Physics;Optics