Fig. 1: Schematic of PT-symmetric micromechanical resonators for nonreciprocal transmission.
a Schematic of mass (m)—spring constant (k)—damping (c) representation for PT-symmetric resonators. One resonator has a loss and the other has a gain. kc is the coupling strength. The spring constant \(k\) of the loss resonator is adjusted to \(k(1+\delta )\) where \(\delta =\varDelta k/k\) is the perturbation. The forward transmission is considered to be from the loss to the gain resonator. b Schematic of a pair of electrically coupled beam resonators in this study. Res2 and Res1 correspond to gain and loss resonator, respectively. The electrostatic coupling voltage produces an equivalent electrostatic spring kc. The feedback loop consists of trans-impedance amplifier (TIA), voltage amplifier (VA), bandpass filter (BPF), automatic gain control (AGC), and phase shifter (PS). The motional current generated by the gain resonator flows into the feedback loop, and then returns as the form of electrostatic force. A DC (direct current) voltage is applied on the loss resonator as the perturbation δ. c Microscope image of our fabricated silicon micromechanical resonators. The gold part is the electrode for feedback, coupling, perturbation and AC path, respectively. The plates in the black dotted frame are electrically coupled. d Real and imaginary parts of the normalized resonant frequency as a function of perturbation.
