Parity-Time Symmetry for Microelectromechanical Systems

Silicon micromechanical resonators have been the subject of extensive research and commercial development for use in sensors and frequency-selective devices. Moving forward, there is a need to explore new physical principles that can not only further enhance their performance but also potentially lead to devices that were previously considered unattainable. This tutorial will introduce the parity-time (PT) symmetric silicon resonator. The concept of PT-symmetry stems from quantum mechanics. However, due to the mathematical equivalence between the Schrödinger equation and classical wave equation, PT-symmetric systems have attracted considerable attention across photonics, electronics, acoustics, and mechanics areas. As non-Hermitian systems, they display unique characteristics that can be leveraged to develop devices in an unconventional way. To illustrate an emerging idea for designing the devices in microelectromechanical systems (MEMS), this tutorial introduces how to construct a PT-symmetric system using two coupled silicon micromechanical resonators, one of which possesses a gain while the other exhibits a loss. The coupled silicon resonators exemplify the attributes of PT-symmetric systems with balanced gain and loss, including an exact PT-symmetric regime, an exceptional point (EP), and a broken PT-symmetric regime, all contingent on both the coupling strength between the resonators and the gain/loss contrast. This tutorial highlights PT-symmetric silicon resonators with loss and nonlinear gain configurations, detailing resonant sensors with significantly enhanced sensitivity when the PT-symmetric resonators are biased near the EP, and frequency-selective devices with non-reciprocal transmission when biased at the broken regime. The prospects and challenges associated with PT-symmetric silicon resonators are also discussed. The PT-symmetric silicon resonators offer exciting opportunities for a broad range of basic research and engineering applications relevant to sensors and non-reciprocal transmission.