Supplementary material from "Topological mode switching in modulated structures with dynamic encircling of an exceptional point"

Exceptional points are special degeneracies occurring in non-Hermitian systems at which both eigenfrequencies and eigenmodes coalesce simultaneously. Fascinating phenomena, including topological, non-reciprocal and chiral energy transfer between normal modes, have been envisioned in optical and photonic systems with the exceptional point dynamically encircled in the parameter space. However, it has remained an open question of whether and how the topological mode switching relying on exceptional points could be achieved in mechanical systems. The present paper studies a two-mode mechanical system with an exceptional point and implements the dynamic encircling of such a point using dynamic modulation mechanisms with the time-driven elasticity and viscosity. Topological mode switching with the robustness against the input state and loop trajectories has been demonstrated numerically. It is found that the dynamical encircling of an exceptional point with the starting point near the symmetric phase leads to chiral mode transfer controlled mainly by the encircling direction, while non-chiral dynamics is observed for the starting point near the broken phase. Analyses also show that minor energy input is required in the process of encircling the exceptional point, demonstrating the intrinsically motivated behaviour in topological mode switching.