Fig. 5: Customized circulator, compact isolator and robustness demonstration.

a–e The exquisitely customized design of four-port circulators based on symmetry rules, which steer inputting waves propagate along the clockwise direction port by port. The gradient-color rings represent the configurations of different circulators. f The compact isolators to reflect and confine waves from the external and internal excitation sources. The normalized out-of-plane displacement field \(\bar{w}\) and amplitude distribution \(|\bar{w}|\) along the black dashed line are displayed numerically. g, h The normalized amplitude \(|\bar{w}|\) versus location and frequency. The sources are placed at the left side and inside of the isolators, respectively. i Routing tailoring by several isolators in a six-ring labyrinth. The anti-interference demonstration of unidirectional robustness to different kinds of defects including (j) absence, (k) disorder and (l) cavity.